5.2.3 Excitation coding
26.4453GPPCodec for Enhanced Voice Services (EVS)Detailed algorithmic descriptionRelease 15TS
The excitation signal coding depends on the coding mode. In general it can be stated that in the absence of DTX/CNG operation, the excitation signal is coded per subframes of 64 samples. This means that it is encoded four times per frame in case of 12.8 kHz internal sampling rate and five times per frame in case of 16 kHz internal sampling rate. The exception is the GSC coding where longer subframes can be used to encode some components of the excitation signal, especially at lower bitrates.
The excitation coding will be described in the following subclauses, separately for each coding mode. The description of excitation coding starts with the GC and VC modes. For the UC, TC, and GSC modes, it will be described in subsequent subclauses with references to this subclause.
5.2.3.1 Excitation coding in the GC, VC and high rate IC/UC modes
The GC,VC and high rate IC/UC modes are very similar and are described together. The VC mode is used in stable voiced segments where the pitch is evolving smoothly within an allowed range as described in subclause 5.1.13.2. Thus, the major difference between the VC and GC modes is that more bits are assigned to the algebraic codebook and less to the adaptive codebook in case of the VC mode as the pitch is not allowed to evolve rapidly in the VC mode. The high-rate IC and UC modes are similar and are used for signalling inactive frames where only a background noise is detected, and unvoiced frames, respectively. The two modes differ from GC mode mainly by their specific gain coding codebook. The GC mode is then used in frames not assigned to a specific coding mode during the signal classification procedure and is aimed at coding generic speech and audio frames. The principle of excitation coding is shown in a schematic diagram in figure 25. The individual blocks and operations are described in detail in the following subclauses.
Figure 25: Schematic diagram of the excitation coding in GC and VC mode
5.2.3.1.1 Computation of the LP residual signal
To keep the processing flow similar for all coding modes, the LP residual signal is computed for the whole frame in the first processed subframe of each frame, as this is needed in the TC mode. For each subframe, the LP residual is given by
(497)
where 
is the pre-emphasized input signal, defined in subclause 5.1.4 and 
are the quantized LP filter coefficients, described in subclause 5.2.2.1.
In DTX operation the computed LP residual signal 
is attenuated by multiplying an attenuation factor 
for all input bandwidths except NB. The attenuation factor is calculated as
(497a)
where 
as determined in subclause 5.6.2.1.1 is upper limited by 
, 
if the bandwidth is not WB or the latest bitrate used for actively encoded frames 
is larger than 16.4 kbps. Otherwise 
is determined from a hangover attenuation table as defined in Table 35b. 
is only updated in the first SID frame after an active signal period if two criteria are both fulfilled. The first criterion is satisfied if AMR-WB IO mode is used or the bandwidth=WB. The second criterion is met if the number of consecutive active frames in the latest active signal segment was at least 
number of frames or if the current SID is the very first encoded SID frame. The attenuation factor 
is finally lower limited to
.
Table 35b: Attenuation floor
|
|
|
|
|
0.5370318 |
|
|
0.6165950 |
|
|
0.6839116 |
|
|
0.7079458 |
|
|
0.7079458 |
5.2.3.1.2 Target signal computation
The target signal for adaptive codebook search is usually computed by subtracting a zero-input response of the weighted synthesis filter 
from the weighted pre-emphasized input signal. This is performed on a subframe basis. An equivalent procedure for computing the target signal, which is used in this codec, is filtering of the residual signal, 
, through the combination of the synthesis filter 
and the weighting filter
. After determining the excitation signal for a given subframe, the initial states of these filters are updated by filtering the difference between the LP residual signal and the excitation signal. The memory update of these filters is explained in subclause 5.2.3.1.8. The residual signal, 
, which is needed for finding the target vector, is also used in the adaptive codebook search to extend the past excitation buffer. This simplifies the adaptive codebook search procedure for delays less than the subframe size of 64 as will be explained in the next subclause. The target signal in a given subframe is denoted as 
.
5.2.3.1.3 Impulse response computation
The impulse response, 
, of the weighted synthesis filter
()
is computed for each subframe. Note that 
is not the impulse response of the filter
, but of the filter 
. In the equation above,
, is the quantized LP filter, the coefficients of which are 
(see subclause 5.2.2.1). This impulse response is needed for the search of adaptive and algebraic codebooks. The impulse response
is computed by filtering the vector of coefficients of the filter
, extended by zeros, through the two filters: 
and
.
5.2.3.1.4 Adaptive codebook
5.2.3.1.4.1 Adaptive codebook search
The adaptive codebook search consists of performing a closed-loop pitch search, and then computing the adaptive codevector, 
, by interpolating the past excitation at the selected fractional pitch lag. The adaptive codebook parameters (or pitch parameters) are the closed-loop pitch, 
, and the pitch gain, 
(adaptive codebook gain), calculated for each subframe. In the search stage, the excitation signal is extended by the LP residual signal to simplify the closed-loop search. The adaptive codebook search is performed on a subframe basis. The bit allocation is different for the different modes.
In the first and third subframes of a GC, UC or IC frame, the fractional pitch lag is searched with a resolution in the range [34, 91½], and with integer sample resolution in the range [92, 231]depending on the bit-rate and coding mode. Closed-loop pitch analysis is performed around the open-loop pitch estimates. Always bounded by the minimum and maximum pitch period limits, the range [
–8, 
+7] is searched in the first subframe, while the range [
–8, 
+7] is searched in the third subframe. The pitch period quantization limits are summarized in table 36.
Table 36: Pitch period quantization limits
|
Rates (kbps) |
Sampling rate of the limits (kHz) |
IC/UC |
VC |
GC |
|
7.2 |
12.8 |
n.a. |
[17; 231] |
[34; 231] |
|
8.0 |
12.8 |
n.a. |
[17; 231] |
[20; 231] |
|
9.6 |
12.8 |
n.a. |
[29; 231] |
[29; 231] |
|
13.2 |
12.8 |
n.a. |
[17; 231] |
[20; 231] |
|
16.4 |
16 |
n.a. |
[36; 289] |
[36; 289] |
|
24.4 |
16 |
n.a. |
[36; 289] |
[36; 289] |
|
32 |
16 |
[21; 289] |
n.a. |
[21; 289] |
|
64 |
16 |
[21; 289] |
n.a. |
[21; 289] |
For the second and fourth subframes, a pitch resolution depending on the bit-rate and coding mode is used and the closed-loop pitch analysis is performed around the closed-loop pitch estimates, selected in the preceding (first or third) subframe. If the closed-loop pitch fraction in the preceding subframe is 0, the pitch is searched in the range [
–8, 
+7½], where
is the integer part of the fractional pitch lag of the preceding subframe (p is either 0, to denote the first subframe, or 3 to denote the third subframe). If the fraction of the pitch in the previous subframe is 
, the pitch is searched in the range [
–7, 
+8½]. The pitch delay is encoded as follows. In the first and third subframe, absolute values of the closed-loop pitch lags are encoded. In the third and fourth subframe, only relative values with respect to the absolute ones are encoded.
In the VC mode, the closed-loop pitch lag is encoded absolutely in the first subframe and relatively in the following 3 subframes. If the fraction of the closed-loop pitch of the preceding subframe is 0, the pitch is searched in the interval [
–4, 
+3½]. If the fraction of the closed-loop pitch lag in the preceding subframe is 
, the pitch is searched in the range [
–3, 
+4½].
The closed-loop pitch search is performed by minimizing a mean-squared weighted error between the target signal and the past filtered excitation (past excitation, convolved with
). This is achieved by maximizing the following correlation
(499)
where 
is the target signal and
is the past filtered excitation at delay k. Note that negative indices refer to the past signal. Note also that the search range is limited around the open loop pitch lags, as explained earlier. The convolution of the past excitation signal with
is computed only for the first delay in the searched range. For other delays, it is updated using the recursive relation
(500)
where 
, 
, is the excitation buffer. Note that in the search stage, the samples
, 
, are unknown and they are needed for pitch delays less than 64. To simplify the search, the LP residual signal, 
, is copied to
for 
, in order to make the relation in equation () valid for all delays. If the optimum integer pitch lag is in the range [34, 91], the fractions around that integer value are tested. The fractional pitch search is performed by interpolating the normalized correlation of equation () and searching for its maximum. The interpolation is performed using an FIR filter for interpolating the term in equation () using a Hamming windowed sinc function truncated at
. The filter has its cut off frequency (–3 dB) at 5050 Hz and –6 dB at 5760 Hz in the down-sampled domain, which means that the interpolation filter exhibits low-pass frequency response. Note that the fraction is not searched if the selected best integer pitch coincides with the lower end of the searched interval.
Once the fraction is determined, the initial adaptive codevector, 
, is computed by interpolating the past excitation signal 
at the given phase (fraction). In the following text, the fractional pitch lags (not the fractions) in all subframes will be denoted as
, where the index 
denotes the subframe.
In order to enhance the coding performance, a low-pass filter can be applied to the adaptive codevector. This is important since the periodicity doesn’t necessarily extend over the whole spectrum. The low pass filter is of the form 
. Thus, the adaptive codevector is given by
(501)
where 
for 
for rates at and above 32kbps and 
otherwise.
An adaptive selection is possible by sending 1 bit per sub-frame. There are then two possibilities to generate the excitation, the adaptive codebook 
, 
in the first path, or its low pass-filtered version as described above in the second path. The path which results in minimum energy of the target signal 
is selected for the filtered adaptive codebook vector.
Alternatively, the first or the second path can be used without any adaptive selection. Table summarizes the strategy for the different combinations.
Table 37: Adaptive codebook filtering configuration
|
Rates (kbps) |
IC/UC |
VC |
GC |
|
7.2 |
n.a. |
Non-filtered |
LP filtered |
|
8.0 |
n.a. |
Non-filtered |
LP filtered |
|
9.6 |
n.a. |
Non-filtered |
LP filtered |
|
13.2 |
n.a. |
Adaptive selection |
Adaptive selection |
|
16.4 |
LP-filtered |
Adaptive selection |
LP filtered |
|
24.4 |
LP-filtered |
Adaptive selection |
LP filtered |
|
32 |
n.a. |
n.a. |
Adaptive selection |
|
64 |
n.a. |
n.a. |
Adaptive selection |
5.2.3.1.4.2 Computation of adaptive codevector gain
The adaptive codevector gain (pitch gain) is then found by
(502)
where 
is the filtered adaptive codevector (zero-state response of 
to
).
To avoid instability in case of channel errors, 
is limited by 0.95, if the pitch gains of the previous subframes have been close to 1 and the LP filters of the previous subframes have been close to being unstable (highly resonant).
The instability elimination method tests two conditions: resonance condition using the LP spectral parameters (minimum distance between adjacent LSFs), and gain condition by testing for high valued pitch gains in the previous frames. The method works as follows. First, a minimum distance between adjacent LSFs is computed as…
At 9.6, 16.4 and 24.4 kbps, the gain is further constrained. It is done for helping the recovery after the loss of a previous frame.
()
5.2.3.1.5 Algebraic codebook
5.2.3.1.5.1 Adaptive pre-filter
An important feature of this codebook is that it is a dynamic codebook, whereby the algebraic codevectors are filtered through an adaptive pre-filter
. The transfer function of the adaptive pre-filter varies in time in relation to parameters representative of spectral characteristics of the signal. The pre-filter is used to shape the frequency characteristics of the excitation signal to damp frequencies perceptually annoying to the human ear. Here, a pre-filter relevant to WB signals is used which consists of two parts: a periodicity enhancement part 
and a tilt part 
. That is,
(504)
The periodicity enhancement part of the filter colours the spectrum by damping inter-harmonic frequencies, which are annoying to the human ear in case of voiced signals. T is the integer part of the closed-loop pitch lag in a given subframe (representing the fine spectral structure of the speech signal) rounded to the ceiling, i.e.,
, where i denotes the subframe.
The factor
of the tilt part of the pre-filter is related to the voicing of the previous subframe. At 16.4 and 24.4 kbps it is bounded by [0.28, 0.56] and it computed as
()
Otherwise it is bounded by [0.0, 0.5] and is given by
()
where
and 
are the energies of the scaled pitch codevector and the scaled algebraic codevector of the previous subframe, respectively. The role of the tilt part is to reduce the excitation energy at low frequencies in case of voiced frames.
Depending on bitrates, coding mode and the estimated level of background noise, the adaptive pre-filter also includes a filter based on the spectral envelope, which colours the spectrum by damping frequencies between the formant regions. The final form of the adaptive pre filter 
is given by
(507)
where 
and 
if 
Hz and 
and 
if 
Hz.
The codebook search is performed in the algebraic domain by combining the pre-filter, 
, with the weighted synthesis filter prior to the codebook search. Thus, the impulse response 
of the weighted synthesis filter must be modified to include the pre-filter 
. That is, 
, where 
is the impulse response of the pre-filter.
5.2.3.1.5.2 Overview of Algebraic codebooks used in EVS
Depending on the bitrate and rendered bandwidth, algebraic codebooks of different sizes are used in the EVS codec. The following tables summarize the codebooks used in each subframe at different bitrates of the EVS codec
Table 38: NB Algebraic codebook configurations (bits/subframe)
|
Rate (kbps) |
IC |
UC |
VC |
GC |
|
7.2 |
n.a. |
n.a. |
12/12/12/20 |
12/12/12/20 |
|
8.0 |
n.a. |
n.a. |
12/20/12/20 |
12/20/12/20 |
|
9.6 |
30/32/32/32 |
30/32/32/32 |
28/28/28/28 |
24/26/24/26 |
|
13.2 |
n.a. |
n.a. |
36/43/36/43 |
36/36/36/43 |
|
16.4 |
56/58/56/58 |
56/58/56/58 |
56/56/56/58 |
55/56/55/56 |
|
24.4 |
96/98/96/98 |
96/98/96/98 |
96/96/96/98 |
94/96/96/96 |
Table 39: WB Algebraic codebook configurations (bits/subframe)
|
Rate (kbps) |
IC |
UC |
VC |
GC |
VC-FEC |
GC-FEC |
GSC |
|
7.2 |
n.a. |
n.a. |
12/12/12/20 |
12/12/12/20 |
n.a. |
n.a. |
n.a. |
|
8.0 |
n.a. |
n.a. |
12/20/12/20 |
12/20/12/20 |
n.a. |
n.a. |
n.a. |
|
9.6 |
28/28/28/28 |
28/28/28/28 |
26/26/26/28 |
20/26/24/24 |
n.a. |
n.a. |
n.a. |
|
13.2 |
n.a. |
n.a. |
28/36/36/36 (TD BWE) 36/36/36/43 (FD BWE) |
28/36/28/36 (TD BWE) 36/36/36/36 (FD BWE) |
n.a. |
n.a. |
n.a. |
|
16.4 |
43/43/43/43/43 |
43/43/43/43/43 |
40/43/43/43/43 |
40/43/40/43/43 |
n.a. |
n.a. |
n.a. |
|
24.4 |
75/75/75/75/75 |
75/75/75/75/75 |
73/75/73/75/75 |
73/73/73/75/73 |
73/73/73/73/75 |
70/75/73/73/73 |
n.a. |
|
32 |
12/12/12/12/12 |
n.a. |
n.a. |
36/36/36/36/36 |
n.a. |
n.a. |
n.a. |
|
64 |
12/12/12/12/12 |
n.a. |
n.a. |
36/36/36/36/36 |
n.a. |
n.a. |
n.a. |
Table 40: SWB Algebraic codebook configurations (bits/subframe)
|
Rate (kbps) |
IC |
UC |
VC |
GC |
VC-FEC |
GC-FEC |
GSC |
|
9.6 |
24/26/24/26 |
24/26/24/26 |
20/26/24/24 |
20/20/20/20 |
n.a. |
n.a. |
n.a. |
|
13.2 |
n.a. |
n.a. |
28/36/28/36 |
28/28/28/36 |
n.a. |
n.a. |
n.a. |
|
16.4 |
36/36/36/36/36 |
36/36/36/36/36 |
34/36/36/36/36 |
34/36/34/36/36 |
n.a. |
n.a. |
n.a. |
|
24.4 |
62/65/62/65/62 |
62/65/62/65/62 |
62/62/62/65/62 |
62/62/62/62/62 |
62/62/62/62/62 |
61/61/62/61/62 |
n.a. |
|
32 |
12/12/12/12/12 |
n.a. |
n.a. |
36/28/28/36/36 |
n.a. |
n.a. |
n.a. |
|
64 |
12/12/12/12/12 |
n.a. |
n.a. |
36/36/36/36/36 |
n.a. |
n.a. |
n.a. |
Table 41: FB Algebraic codebook configurations (bits/subframe)
|
Rate (kbps) |
IC |
UC |
VC |
GC |
VC-FEC |
GC-FEC |
|
16.4 |
36/36/36/36/36 |
36/36/36/36/36 |
34/36/36/34/36 |
34/34/36/34/36 |
n.a. |
n.a. |
|
24.4 |
62/62/65/62/65 |
62/62/65/62/65 |
62/62/62/62/62 |
62/62/62/62/62 |
61/62/61/62/62 |
61/61/61/61/61 |
|
32 |
12/12/12/12/12 |
n.a. |
n.a. |
36/28/28/36/36 |
n.a. |
n.a. |
|
64 |
12/12/12/12/12 |
n.a. |
n.a. |
36/36/36/36/36 |
n.a. |
n.a. |
VC-FEC and GC-FEC are specific configurations for which 4 bits are reserved to transmit LPC-based information exploited by the decoder in case of error of the previous frame.
5.2.3.1.5.3 Codebook structure and pulse indexing of the 7-bit codebook
In the 7-bit codebook, the algebraic vector contains only 1 non-zero pulse at one of 64 positions. The pulse position is encoded with 6 bits and the sign of the pulse is encoded with 1 bit. This gives a total of 7 bits for the algebraic code. The sign index here is set to 1 for positive signs and 0 for negative signs.
5.2.3.1.5.4 Codebook structure and pulse indexing of the 12-bit codebook
In the 12-bit codebook, the algebraic vector contains only 2 non-zero pulses. The 64 positions in a subframe are divided into 2 tracks, where each track contains one pulse, as shown in table 42.
Table 42: Potential positions of individual pulses in the 12-bit algebraic codebook
|
Track |
Pulse |
Positions |
|
1 |
0 |
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62 |
|
2 |
1 |
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63 |
Each pulse position in one track is encoded with 5 bits and the sign of the pulse in the track is encoded with 1 bit. This gives a total of 12 bits for the algebraic code. The sign index here is set to 0 for positive signs and 1 for negative signs.
The index of the signed pulse is given by
(508)
where 
is the position index, 
is the sign index, and 
is the number of bits per track. For example, a pulse at position 31 has a position index of 31/2 = 15 and it belongs to the track with index 1 (second track).
5.2.3.1.5.5 Codebook structure and pulse indexing of the 20-bit and larger codebooks
In the 20-bit or larger codebooks, the codevector contains 4 non-zero pulses. All pulses can have the amplitudes +1 or –1. The 64 positions in a subframe are divided into 4 tracks, where each track contains one pulse, as shown in table 43.
Table 43: Potential positions of individual pulses in the 20-bit algebraic codebook
|
Track |
Pulse |
Positions |
|
1 |
0 |
0, 4, 8, 12, 16, 20, 24, 28, 32 36, 40, 44, 48, 52, 56, 60 |
|
2 |
1 |
1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61 |
|
3 |
2 |
2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62 |
|
4 |
3 |
3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63 |
Each pulse position in one track is encoded with 4 bits and the sign of the pulse in the track is encoded with 1 bit. This gives a total of 20 bits for the algebraic code.
5.2.3.1.5.6 Pulse indexing of the algebraic codebook
The objective is to enumerate all possible constellations of pulses in a vector 
which corresponds to one track of length 
within a sub-frame. That is, vector 
has signed integer values such that its norm-1 is 
, whereby we say that 
contains 
pulses.
We can then partition the vector 
into two parts, 
such that the partitions are of length 
and 
and contain 
and 
pulses respectively. The number of different constellations for the original vector 
can then be determined by the recursive formulae:
()
For computational efficiency, the values of this function can be pre-calculated and placed in a table.
Above equation gives the number of possible states for given 
and 
. We can then enumerate a specific state, where 
and 
have 
and 
pulses respectively. The number of states that have less pulses than 
in partition 
is
()
We can then define that overall state has 
, whereby the overall state can be encoded with the recursion
()
where the boundary conditions are
()
The state can be decoded by the algorithm
- Set
and choose partitioning length 
and 
. - Calculate
with 
. - If
then 
. Otherwise, set 
and go to 2.
The states of the partitions 
and 
can then be calculated from the integer and reminder parts of the fraction 
We can then recursively determine the state of each position in the vector 
until a partition has 
, whereby
()
Observe that both the number of states 
as well as the state 
are integer numbers which can become larger than 32 bits. We must therefore employ arithmetic operations which support long integers throughout the algorithm.
5.2.3.1.5.7 Pulse indexing of the 43-bit codebook
The joint indexing encoding procedure of three pulses on two tracks is described as follows:
For 3 pulses on a track, the occurrence probability of 3 different pulse positions on a track is the highest, and the occurrence probability of 2 different pulse positions on a track is the second highest, and even the pulses have a higher occurrence probability on the left position of the track than on the right position of the track because the algebraic codebooks need to compensate for the boundary leap of adaptive codebooks between two neighbour sub-frame. So the case of the first pulse with lower position order will be encoded with a smaller index value and the case of more different pulse positions with higher occurrence probability will also be encoded with a smaller index value. The rule is same in case of more than 3 pulses on a track. This rule can be used to save bit in the multi-track joint indexing encoding.
- Firstly, the pulse information for each track is indexed as follows: (here we suppose that
pulses are assigned for each track, and the total quantity of positions on the track is 
) - Analyse the statistics about the positions of the
pulses to be encoded on a track and obtain pulse distribution on the track, it includes: quantity (namely 
) of pulse positions with pulses in it, the pulse position distribution which includes pulse position vector: 
, 
is the quantity of pulse positions , 
is the ith pulse positions with pulse in it on the track, and quantity of pulses in each pulse position with pulse in it which includes pulse number vector 
, 
, where 
is the number of pulses per track, 
is the number of pulses in position 
, and pulse sign vector 
, 
is the ith sign in position 
. If there are pulses having the same positions (pulses with the same positions have the same signs), they are merged into one pulse and the number of pulses for each pulse position as well as the pulse sign is saved. Pulse position are sorted in ascend order, the pulse sign is also adjusted based on the order of pulse position. - Compute the offset index
according to the quantity of pulse positions, the offset index is saved in a table and used in both encoder and decoder sides. Each offset index in the table indicate a unique number of pulse positions in the track, in case 
, the offset index only indicate a pulse distribution of pulse positions on the track 
, in case 
, the offset index indicate many 
which have a same pulse distribution of pulse positions on the track 
. - Compute the pulse- position index
according to the pulse distribution of pulse positions on the track (
). The 
only indicate a pulse distribution of pulse positions on the track 
among all the pulse distribution of 
. Permuting serial numbers of the positions 
and all possible values of 
are ordered from a smaller value to a greater value 
, 
refers to the quantity of positions with pulses in it, 
is the total quantity of positions on the track. Compute 
by using the permutation method as follows:
(514)
wherein 
represents a position serial number of an nth position that has pulses on it, 
, 
, 
, 
. For 43bit mode, 3 pulses on a track, 
, 
.
(515)
Compute the pulse-number index 
according to the quantity of pulses in each pulse position as follows:
is determined according to 
which represents the quantity of pulses in each position with pulses. In order to determine correspondence between 
and 
through algebraic calculation, a calculation method of the third index 
is provided below:
For a track, situations that a track with 
pulse positions and 
pulses are mapped to situations that a 
positions track have 
pulses, where 
represents the total number of pulses that are required to be encoded and on the track. For example, in the condition of 6-pulse 4-position (
=6, 
=4) situations, 
is {1, 2, 1, 2}, 1 is subtracted from the number of pulses in each position (because each position has at least one pulse) to obtain {0, 1, 0, 1}, that is, information of is mapped to a 2-pulse 4-position (
=2, 
=4) encoding situation. Figure 26 gives an example of the mapping for 
.
Figure 26: Example of mapping for 
According to set order, all possible distribution situations of 
pulses on 
positions are arrayed, and an arrayed serial number is used as the index
indicating the number of pulses on a position that has pulse.
A calculation formula reflecting the foregoing calculation method is:
()
wherein 
, 
represents a position serial number of an (h + 1)th pulse, 
, 
, 
, and ∑ indicates summation.
Compute the pulse-sign index
based on the 
pulse sign information.
The pulse sign represented by 
may be a positive value or a negative value. A simple coding mode is generally applied, 
represents a positive pulse and 
represents a negative pulse.
Generate the global index 
. Combine the indices 
, 
, 
and 
to get the global index 
as follows :
()
()
Here 
is the upper range of 
which is also the number of total permutations of 
pulses.
2. Combine the index of the two 3-pulse tracks together which is encoded as in step 1, suppose the indexes of the two tracks are 
and 
respectively, 
and 
, then the 
is as below:
()
3. Encode the joint index 
. (Suppose encode with 25 bits). In order to reduce the number of bits used for pulse indexing, a threshold 
is set at 3611648 for 3-pulses, according to the the pulse number, combination of the occurrence probability and the number of bits that may be saved. If the joint index 
is smaller than 
, 24 bits will be used to encode the joint index 
. If the joint index 
is bigger than or equal to 
, 
will be added into the joint index 
and 25 bits will be used to encode the joint index . This procedure is described as below:
If (
<
)
{
is encoded with 24 bits.
}
Else
{
is encoded with 25 bits.
}
For two pulses on the other track, the index for each track is encoded just as pulse indexing of the 20-bit codebook, but there is no joint indexing procedure, then the index for each track is transmitted one by one.
5.2.3.1.5.8 Multi-track joint coding of pulse indexing
The codebook for more than three pulses on a track have idle space in difference ratio, joint encoding for more than two tracks may enable idle codebook spaces in single-track encoding to be combined, and once combined idle spaces are sufficient, one actual encoding bit may be reduced. If several encoding indexes are directly combined, the final encoding length may be very large, or even may exceed the bit width (such as 64 bits) generally used for operating, so a general solution is to split each encoding index into two part and only all the high part is combined together in order to avoid directly combining.
The method is described as follows: the value range of the original index 
is divided into several intervals by a factor 
, correspondingly the original index 
is split into two indexes 
and 
by the factor 
, the length of each interval is not greater than 
, 
is a positive integer, 
denotes a serial number of an interval to which 
belongs, and 
denotes a serial number of 
in the interval to which 
belongs (apparently,
), and: 
;
The most economical case of splitting is performed as following:
, where 
denotes rounding down to an integer, and
, where 
denotes taking a remainder.
If a combined index needs to achieve better effect of saving encoding bits, it is needed to select a split index that retains the space characteristics of 
as much as possible, and therefore, for the track t providing a split index to participate in combination,
if 
, it is appropriate to select Indt0 to participate in combination, and
if 
, it is appropriate to select Indt1 to participate in combination.
Figure 27: The split factor selection and the corresponding codebook space section
Each track may adopt different 
, according to the pulse number on it
Table 44: the parameters for multi-track joint coding
|
pulse |
bits |
Codebook space |
Hi Bit |
effective ratio |
re-back bits |
|||||
|
Dec |
Hex |
value |
bits |
range |
8bit |
16bit |
24bit |
|||
|
1 |
5 |
32 |
||||||||
|
2 |
9 |
512 |
200 |
1 |
1 |
2 |
1.00 |
0 |
||
|
3 |
13 |
5472 |
1560 |
A8 |
8 |
172 |
0.6875 |
3 |
||
|
4 |
16 |
44032 |
AC00 |
AC |
9 |
345 |
0.67578125 |
1 |
9 |
|
|
5 |
19 |
285088 |
459A0 |
8B |
8 |
140 |
0.546875 |
5 |
||
|
6 |
21 |
1549824 |
17A600 |
BD |
8 |
190 |
0.7421875 |
3 |
||
|
7 |
23 |
7288544 |
6F36E0 |
DE |
8 |
223 |
0.875 |
1 |
9 |
|
|
8 |
25 |
30316544 |
1CE9800 |
1CE |
9 |
463 |
0.904297 |
8 |
||
|
9 |
27 |
113461024 |
6C34720 |
6C3 |
11 |
1732 |
0.845704 |
8 |
||
Multi-track joint coding processing is described as following:
Calculate an encoding index 
of each track, (subscript t denotes the tth track), split into two split indexes 
and 
according to a set factor 
combine a split index 
of each track to generate a combined index 
. The combined index 
is split into recombined indexes 
according to the re-back bits length, and each recombined index 
and an un-combined split index 
of a corresponding track are respectively combined, then obtain the final recombined index
with fixed length 8,16 or 24 bits.
For 4 track in a sub-frame, the algebraic codebook 94bit(8777)~108bit(9999) use 24 bits mode joint en/decoding，the algebraic codebook 62bit(4444)~92bit(7777) use 16 bits mode joint en/decoding，the algebraic codebook 40bit(3222)~61bit(4443) use 8 bits mode joint en/decoding.
All the encoding steps are described as following:
-
- Get the parameter from table 44 according to the pulse number of each track, include the index
, 
, 
, 
. And get the 8/16/24 mode also according to the pulse number of all track. - The index
of 
is split into 
and 
, the 
is 
, and length of 
is 
, length of 
is 
, - Combine the
and 
into 
as following:
- Get the parameter from table 44 according to the pulse number of each track, include the index
()
-
- Split the low part of
and get the 
, and the length of 
is 
,which get from table 44 in step 1, the 
and 
are combine into a 
with the length of 8,16 or 24 bits. - The high part
of 
continue combining with the next 
as following:
- Split the low part of
()
-
- Split the low part of
and get the 
, and the length of 
is 
,which get from table 44 in step 1, the 
and 
are combine into a 
with the length of 8,16 or 24 bits. - The high part
of 
continue combining with the next 
as following:
- Split the low part of
()
-
- Split the low part of
and get the 
, and the length of 
is 
,which get from table 44 in step 1, the 
and 
are combine into a 
with the length of 8,16 or 24 bits. - The high part
of 
is split into two parts. The low part of 
is used as the 
, and the length of 
is 
which is obtained from table 44 in step 1, the 
and 
are combined into a 
with the length of 8,16 or 24 bits. - Finally, the high part
of 
together with
, 
, 
and 
are the outputs of multi-track joint coding and stored into the stream in 16 bits unit.
- Split the low part of
Figure 28: Schematic diagram of 4-track joint coding
5.2.3.1.5.9 The search criterion at lower bitrates
The algebraic codebook is searched by minimizing the error between an updated target signal and a scaled filtered algebraic codevector. The updated target signal is given by
()
where 
is the filtered adaptive codevector and 
is the unquantized adaptive codebook gain. Thus, the updated target signal is obtained by subtracting the adaptive contribution from the initial target signal, 
.
Let a matrix 
be defined as a lower triangular Toeplitz convolution matrix with the main diagonal 
and lower diagonals 
, and 
(also known as the backward filtered target vector) be the correlation between the updated signal 
and the impulse response 
. Furthermore, let 
be the matrix of correlations of 
. Here, 
is the impulse response of the combination of the synthesis filter, the weighting filter and the pre-filter 
which includes a long-term filter.
The elements of the vector 
are computed by
()
and the elements of the symmetric matrix 
are computed by
()
Let 
the k-th algebraic codevector. The algebraic codebook is searched by maximizing the following criterion:
(526)
The vector 
and the matrix 
are usually computed prior to the codebook search.
The algebraic structure of the codebooks allows for very fast search procedures since the algebraic codevector, The algebraic structure of the codebooks allows for very fast search procedures since the algebraic codevector, 
, contains only a few non-zero pulses. The correlation in the numerator of equation () is given by
()
where 
is the position of the i-th pulse, 
is its amplitude (sign), and 
is the number of pulses. The energy in the denominator of equation () is given by
()
For saving the search load along with a better search result in the 12-bit codebook, the pulse amplitudes are predetermined based on a high-pass filtered 
. The high-pass filter is a three-tap MA (moving-average)-type filter, and its filter coefficients are { -0.35, 1.0, -0.35 }. The sign of a pulse in a position 
is set to negative when the high-pass filtered 
is negative, otherwise the sign is set to positive. To simplify the search, 
and 
are modified to incorporate the predetermined signs.
5.2.3.1.5.10 The search criterion at higher bitrates
The following search criterion is used for bit rates at and above 16.4 kbps. It allows limiting the increase of complexity for high number of pulses.
Let 
be the sub-frame length, and let matrices 
and 
, respectively, denote the 
lower triangular Toeplitz convolution matrix and the 
full-size convolution matrix, both defined for the filter 
. Here, 
is the length 
impulse response of the combination of the synthesis filter, the weighting filter and the pre-filter 
which includes a long-term filter. The target residual is 
and 
is the autocorrelation matrix of filter 
.
The elements of the autocorrelation matrix can be calculated by
()
and the target residual by
()
The final target is then 
which can be calculated by
()
Let 
be the kth algebraic codevector. The algebraic codebook is searched by maximizing the following criterion:
()
5.2.3.1.6 Combined algebraic codebook
In general the computational complexity of the algebraic codebook increases with the codebook size. In order to keep the complexity reasonable while providing better performance and scalability at high EVS ACELP bit-rates, an efficient combined algebraic codebook structure is employed. The combined algebraic codebook combines usually a frequency-domain coding in a first stage followed by a time-domain ACELP codebook in a second stage.
The frequency-domain coding of the first stage, denoted as a pre-quantizer in figure 29, uses a Discrete Cosine Transform (DCT) as the frequency representation and an Algebraic Vector Quantizer (AVQ) (see subclause 5.2.3.1.6.9) to quantize the frequency-domain coefficients of the DCT. The pre-quantizer parameters are set at the encoder in such a way that the ACELP codebook (second stage of the combined algebraic codebook) is applied to an excitation residual with more regular spectral dynamics than the pitch residual.
Figure 29: Schematic diagram of the ACELP encoder using a combined algebraic codebook in GC mode at high bit-rates
At the encoder, the first stage, or pre-quantizer, operates as follows. In a given subframe (aligned to the subframe of the ACELP codebook in the second stage) the excitation residual 
after applying the adaptive codebook is computed as
()
where r(n) is the target vector in residual domain. Further, v(n) is the adaptive codevector and gp the adaptive codevector gain.
The excitation residual 
after applying the adaptive codebook is de-emphasized with a filter 
. A difference equation for such a de-emphasis filter 
is given by
(534)
where 
is the de-emphasized residual and coefficient 
controls the level of de-emphasis.
Further a DCT is applied to the de-emphasized excitation residual 
using a rectangular non-overlapping window. Depending on the bit rate, all blocks or only some blocks of DCT coefficients 
usually corresponding to lower frequencies are quantized using the AVQ encoder. The other (not quantized) DCT coefficients 
are set to 0 (not quantized). To obtain the excitation residual for the second (ACELP) stage of the combined algebraic codebook, the quantized DCT coefficients 
are inverse transformed, and then a pre-emphasis filter 
is applied to obtain the time-domain contribution from the pre-quantizer 
. The pre-emphasis filter has the inverse transfer function of the de-emphasis filter 
.
5.2.3.1.6.1 Quantization
The AVQ encoder produces quantized transform-domain DCT coefficients 
. The indices of the quantized and coded DCT coefficients from the AVQ encoder are transmitted as a pre-quantizer parameters to the decoder.
In every sub-frame, a bit-budget allocated to the AVQ is composed as a sum of a fixed bit-budget and a floating number of bits. Depending on the used AVQ sub-quantizers of the encoder, the AVQ usually does not consume all of the allocated bits, leaving a variable number of bits available in each sub-frame. These bits are floating bits employed in the following sub-frame. The floating number of bits is equal to 0 in the first sub-frame and the floating bits resulting from the AVQ in the last sub-frame in a given frame remain unused when coding WB signals or are re-used in coding of upper band (see subclause 5.2.6.3).
5.2.3.1.6.2 Computation of pre-quantizer gain
Once the pre-quantizer contribution is computed, the pre-quantizer gain is obtained as
()
where 
are the AVQ input frequency coefficients and 
the AVQ output (quantized) frequency coefficients where 
is the transform-domain coefficient index and 
being the number of DCT transform coefficients.
5.2.3.1.6.3 Quantization of pre-quantizer gain
The pre-quantizer gain 
is quantized as follows. First, the gain is normalized by the predicted innovation energy 
as follows:
()
where the predicted innovation energy 
is obtained as described in subclause 5.2.3.1.7.1.
Then the normalized gain 
is quantized by a scalar quantizer in a logarithmic domain and finally de-normalized resulting in a quantized pre-quantizer gain. Specifically 6-bit scalar quantizer is used whereby the quantization levels are uniformly distributed in the log domain. The index of the quantized pre-quantizer gain is transmitted as a pre-quantizer parameter to the decoder.
5.2.3.1.6.4 Refinement of target vector
The pre-quantizer contribution 
is used to refine the original target vector for adaptive codebook search 
as
, (537)
and to refine the adaptive codebook gain using equation (502) with 
used instead of 
. When the pre-quantizer is used, the computation of the target vector for algebraic codebook search 
is done using
(538)
where 
is the filtered pre-quantizer contribution, i.e. the zero-state response of the weighted synthesis filter to the pre-quantizer contribution 
, and 
is the refined adaptive codebook gain.
Similarly, the target vector in residual domain 
is updated for the algebraic codebook search (the second-stage of the combined algebraic codebook) as
. (539)
5.2.3.1.6.5 Combined algebraic codebook in GC mode
In the EVS codec, the combined algebraic codebook structure as from figure 29 is used at bit-rates of 32 kbps and 64 kbps. In both cases the algebraic codebook search uses 36-bit codebooks and the rest of the bit-budget is employed by the AVQ to quantize the pre-quantizer coefficients.
At 32 kbps, the available fixed bit-budget for the AVQ (116, 115, 115, 115, 155 bits for every of five subframes) is sometimes too low to properly encode all input signal frames. Consequently in GC mode at 32kbps, the DCT and iDCT stages of pre-quantizer computation are omitted when the input signal is not classified as a harmonic one. The classification is based on a harmonicity counter 
updated every frame in the pre-processing module. If in a given frame the harmonicity counter 
the frame is classified as non-harmonic and the AVQ is applied directly on the time-domain signal 
and similarly producing directly the time-domain signal 
in figure 29.
5.2.3.1.6.6 Combined algebraic codebook in TC mode
The combined algebraic codebook structure is used also in TC mode at 32kbps and 64kbps. In this mode the algebraic codebook from figure 29 is replaced by glottal shape codebook but the structure of the pre-quantizer remains the same as in the GC mode. In TC mode @32kbps, the DCT and iDCT stages of the pre-quantizer are always employed.
Figure 30: Schematic diagram of the ACELP encoder using a combined algebraic codebook in IC mode at high bit-rates
5.2.3.1.6.7 Combined algebraic codebook in IC mode
Depending on the input signal characteristics, the ACELP encoder using a combined algebraic codebook from figure 29 is further adaptively changed. Specifically in coding of inactive speech segments, the order of the combined algebraic codebook stages is changed. I.e. the modified combined algebraic codebook combines a time-domain ACELP codebook in a first stage followed by a frequency-domain de-quantizer coding in a second stage as shown in figure 30. The first stage algebraic codebook employs very small codebooks, specifically 12 bits per subframe.
At the encoder, the de-quantizer in IC mode operates as follows. In a given subframe, the target signal 
after subtracting the scaled filtered adaptive excitation and the scaled filtered algebraic excitation is computed as
. ()
The target signal in speech domain 
is filtered through the inverse of the weighted synthesis filter with zero states resulting in the target in residual domain 
.
Similarly to the combined algebraic codebook in GC mode, the signal is first de-emphasized with a filter 
to enhance the low frequencies. A DCT is applied to the de-emphasized signal 
using rectangular non-overlapping window. Usually all blocks of DCT coefficients 
are quantized using the AVQ encoder. The quantized DCT coefficients 
in some bands can be however set to zero.
The quantized DCT coefficients 
are further inverse transformed using iDCT, and then a pre-emphasis filter 
is applied to obtain the time-domain contribution from the frequency-domain quantizer 
where the pre-emphasis filter has the inverse transfer function of the de-emphasis filter 
.
5.2.3.1.6.8 Computation and quantization of de-quantizer gain
Once the de-quantizer contribution is computed, the de-quantizer gain is obtained as
()
where 
are the AVQ input transform-domain coefficients and 
are the AVQ output (quantized) transform-domain coefficients.
The de-quantizer gain 
is quantized using the normalization by the algebraic codebook gain 
. Specifically a 6-bit scalar quantizer is used whereby the quantization levels are uniformly distributed in the linear domain. The indice of the quantized de-quantizer gain 
is transmitted as a de-quantizer parameter to the decoder.
When coding the inactive signal segments the adaptive codebook excitation contribution is limited to avoid a strong periodicity in the synthesis. In practice a limiter is applied in the adaptive codebook search to constrain the adaptive codebook gain by 
.
5.2.3.1.6.9 AVQ quantization with split multi-rate lattice VQ
Prior to the AVQ quantization, the time domain or transform-domain 64 coefficients, here denoted as 
, are split into 8 consecutive sub‑bands of 8 coefficients each. The sub-bands are quantized with an 8-dimensional multi-rate algebraic vector quantizer. The AVQ codebooks are subsets of the Gosset lattice, referred to as the RE8 lattice.
5.2.3.1.6.9.1 Multi-rate AVQ with the Gosset Lattice RE8
5.2.3.1.6.9.1.1 Gosset Lattice RE8
The Gosset lattice RE8 is defined as the following union:
()
where 
is the 8-dimensional lattice composed of all points with integers components with the constraint that the sum of the 8 components is even. The lattice 
is simply the 
lattice scaled by 2. This implies that the sum of the components of a lattice point in 
is an integer multiple of 4. Therefore, the 8 components of a 
lattice point have the same parity (either all even or all odd) and their sum is a multiple of 4.
All points in the lattice RE8 lie on concentric spheres of radius 
, 
being the codebook number in sub-band 
. Each lattice point on a given sphere can be generated by permuting the coordinates of reference points called “leaders”. There are very few leaders on a sphere compared to the total number of lattice points which lie on the sphere.
5.2.3.1.6.9.1.2 Multi-rate codebooks in Gosset Lattice RE8
To form a vector codebook at a given rate, only lattice points inside a sphere in 8 dimensions of a given radius are taken. Codebooks of different bit rates can be constructed by including only spheres up to a given radius. Multi-rate codebooks are formed by taking subsets of lattice points inside spheres of different radii.
5.2.3.1.6.9.1.2.1 Base codebooks
First, base codebooks are designed. A base codebook contains all lattice points from a given set of spheres up to a number 
. Four base codebooks , noted 
, 
, 
, and 
, are used. There are 36 non-null absolute leaders plus the zero leader (the origin): Table 46 gives the list of these leaders and indicates to which codebook a leader belongs. 
, 
, 
, and 
are constructed with respectively 0, 8, 12, and 16 bits. Hence codebook 
requires 
bits to index any point in that codebook.
5.2.3.1.6.9.1.2.2 Voronoi extensions
From a base codebook 
(i.e. a codebook containing all lattice points from a given set of spheres up to a number 
), an extended codebook can be generated by multiplying the elements of 
by a factor 
, and adding a second-stage codebook called the Voronoi extension. This construction is given by
(543)
where 
is the scaling factor, 
is a point in a base codebook 
and 
is a point in the Voronoi extension. The extension is computed in such a way that any point 
from equation (543) is also a lattice point in 
. The scaling factor 
is a power of 2 (
), where 
is called the Voronoi extension order.
Such extended codebooks include lattice points that extend further out from the origin than the base codebook. When a given lattice point 
is not included in a base codebook 
(
, 
, 
or 
), the so-called Voronoi extension is applied, using the 
or 
base codebook part.
Giving the available bit-budget in particular layers, the maximum Voronoi extension order is 
. Therefore, for 
or 
, two extension orders are used: 
(
).
When 
, there is no Voronoi extension, and only a base codebook is used.
5.2.3.1.6.9.1.2.3 Codebook rates
There are 8 codebooks: the first 4 are base codebooks without Voronoi extension and the last four with Voronoi extension. The codebook number 
is encoded as a unary code with 
"1" bits and a terminating "0". Table 45 gives for each of the 8 codebooks, its base codebook, its Voronoi extension order (
indicates that there is not Voronoi extension), and its unary code.
Table 45: Multi-rate codebooks in RE8 lattice
|
Codebook |
Base Codebook |
Voronoi extension order |
Unary code for |
|---|---|---|---|
|
0 |
Q0 |
0 |
0 |
|
2 |
Q2 |
0 |
10 |
|
3 |
Q3 |
0 |
110 |
|
4 |
Q4 |
0 |
1110 |
|
5 |
Q3 |
1 |
11110 |
|
6 |
Q4 |
1 |
111110 |
|
7 |
Q3 |
2 |
1111110 |
|
8 |
Q4 |
2 |
11111110 |
For the base codebook 
, (
), there is only one point in the codebook and 1 bit is used to transmit the unary code corresponding to 
.
For the other three base codebooks 
(
) without Voronoi extension:
bits are used to transmit the unary code corresponding to ,,
bits are required to index a point in 
- thus
bits are used in total.
For codebooks with Voronoi extension (
):
bits are used to transmit the unary code corresponding to the base codebook number 
(respectively 
) if 
is even (respectively odd) and the Voronoi extension order 
is 1 if 
, or 2 otherwise),- 12 bits (respectively 16 bits) are required to index the point
in the base codebook 
(respectively 
) 
bits are required to index the 8-dimensional point 
in the Voronoi extension of order 
- thus,
bits are used in total.
In the codebook number encoding, a simple bit overflow check is performed: in case when the last AVQ coded sub-band of the spectrum 
is quantized, 
and only 
bits are available for the quantization, the terminating "0" in the codebook number coding is not encoded. At the decoder, the same bit overflow check enables the right decoding of the codebook number in this sub-band.
5.2.3.1.6.9.2 Quantization with RE8 lattice
In lattice quantization, the operation of finding the nearest neighbour of the input spectrum 
among all codebook points is reduced to a few simple operations, involving rounding the components of spectrum 
and verifying a few constraints. Hence, no exhaustive search is carried out as in stochastic quantization, which uses stored tables. Once the best lattice codebook point is determined, further calculations are also necessary to compute the index that will be sent to the decoder. The larger the components of the input spectrum 
, the more bits will be required to encode the index of its nearest neighbour in the lattice codebook. Hence, to remain within a pre-defined bit-budget, a gain-shape approach has to be used, where the input spectrum is first scaled down by the AVQ gain, then each 8-dimensional block of spectrum coefficients is quantized in the lattice and finally scaled up again to produce the quantized spectrum.
5.2.3.1.6.9.2.1 AVQ gain estimation
Prior to the quantization (nearest neighbour search and indexation of the nearest neighbour), the input spectrum has to be scaled down to ensure that the total bit consumption will remain within the available bit-budget.
A first estimation of the total bit-budget 
without scaling (i.e. with an AVQ gain equals to 1) is performed:
()
where 
is a first estimate of the bit budget to encode the sub-band 
given by:
()
with 
being the energy (with a lower limit set to 2) of each sub-band 
:
()
This gain estimation is performed in an iterative procedure described below.
Let NB_BITS be the number of bits available for the quantization process and NB_SBANDS the number of 8-dimensional sub-bands to be quantized:
|
Initialization: fac = 128, offset = 0, nbitsmax = 0.95 (NB_BITS – NB_SBANDS) for i = 1:10 offset = offset + fac if nbits ≤ nbitsmax, then offset = offset – fac fac = fac / 2 |
After the 10th iteration, the AVQ gain is equal to 
and is used to obtain the scaled spectrum 
:
()
5.2.3.1.6.9.2.2 Nearest neighbour search
The search of the nearest neighbour in the lattice RE8 is equivalent to searching for the nearest neighbour in the lattice 
and for the nearest neighbour in the lattice 
, and finally selecting among those two lattice points the closest to 
) as its quantized version 
.
Based on the definition of 
, the following fast algorithm is used to search the nearest neighbour of an 8-dimensional sub-band 
among all lattice points in 
:
|
Search of the nearest neighbour y1j in Compute Round each component of Compute Calculate the sum if
where Search of the nearest neighbour Compute Round each component of Compute Calculate the sum S of the 8 components of if S is not an integer multiple of 4 then modify its Ith component as follows:
where Compute Select between
where |
of 
:
.
to the nearest integer to generate 
.
.
of the 8 components of 
.
is not an integer multiple of 4, then modify its 
component as follows:
in 
of 
:
where 
denotes an 8-dimensional vector with all ones.
to the nearest integer to generate 
.
.
.
.
and 
as the closest point 
in 
to 
:
and 
.5.2.3.1.6.9.3 Indexation
The quantized scaled sub-band 
of 
) is a point 
in a RE8 lattice codebook, an index for each 
has to be computed and later inserted into the bitstream.
This index is actually composed of three parts:
- a codebook number
; - a vector index
, which uniquely identifies a lattice vector in a base codebook 
; - and if
, an 8-dimensional Voronoi extension index 
that is used to extend the base codebook when the selected point in the lattice is not in a base codebook 
.
The calculation of an index for a given point 
in the 
lattice is performed as follows:
First, it is verified whether 
is in a base codebook 
by identifying its sphere and its leader:
- if
is in a base codebook, the index used to encode 
is thus the codebook number 
plus the index 
of the lattice point 
in 
.
Otherwise, the parameters of the Voronoi extension (see equation (543)) have to determined: the scaling factor Mv, the base codebook 
(
or 
), the point 
in this base codebook, and the point 
in the Voronoi extension. Then, the index used to encode is composed of the codebook number 
(
) plus the index 
of the lattice point 
in the base codebook 
(
or 
), and the index 
of 
. in the Voronoi extension.
5.2.3.1.6.9.3.1 Indexing a codebook number
As explained in subclause 5.2.3.1.6.9.1.2.3 – Codebook rates, the codebook index 
is unary encoded with 
bits except for 
that is coded with one bit (see table 45).
5.2.3.1.6.9.3.2 Indexing of codevector in base codebook
The index Ij indicates the rank of codevector 
in j-th sub-band, i.e., the permutation to be applied to a specific leader to obtain . The index computation is done in several steps, as follows:
1) The input codevector 
is decomposed into a sign vector s0 and an absolute vector y0 following a two‑path procedure.
2) The sign vector is encoded, the associated index 
and the number of non-zero components in 
are obtained. More details are given in subsequent subclauses.
3) The absolute vector is encoded using a multi-level permutation-based index encoding method, and the associated index rank(y0) is obtained.
4) The absolute vector index 
and the sign index 
are added together in order to obtain the input vector rank: 
.
()
5) Finally, the offset 
is added to the rank. The index 
is obtained by
()
The indexing of codevector in base codebook is done in two steps. First the sign vector is encoded.
The number of bits required for encoding the sign vector elements is equal to the number of non‑zero elements in the codevector. "1" represents a negative sign and "0" a positive sign. As lattice 
quantization is used, the sum of all the elements in a codevector is an integer multiple of 4. If there is any change of sign in the non-zero element, the sum may not be a multiple of 4 anymore, in that case, the last element sign in the sign vector will be omitted. For example, the sign vector of the input vector (–1, –1, 1, 1, 1, 1, –1, –1) in leader 1 (see table 46) has seven bits and its value is 0x1100001.
In the second step the absolute vector and its position vector is encoded
The encoding method for the absolute vector works as follows. The absolute vector is first decomposed into MLmax levels. The highest-level vector 
is the original absolute vector. The 
value for 
is initialized to zero. Then:
1) First the intermediate absolute value vector of 
is obtained by removing the most frequent element as given in the decomposition order column of table 46 from the original absolute vector of
. Sequentially the remaining elements are built into a new absolute vector for
; it has a position order related to the level 
original absolute vector. All position values
of the remainder elements are used to build a position vector 
of
.
The relationship between the original absolute vector of
and the new absolute vector of
is that: the original absolute vector of
is the upper-level vector of the new absolute vector of
, and the new absolute vector ofis the lower-level vector of the original absolute vector of
.The relationship between any two neighbour level absolute vector is the same. The detail relationship is described as following:
Figure 31: Example processing of first level for
.
2) Then the position vector 
of the new absolute vector of
related to the original absolute vector of
is indexed based on a permutation and combination function, the indexing result being called the middle index 
. For the new absolute vector in
, the position vector indexing is computed as follows:
()
()
where 
is initialized to zero before the first step at the beginning of the procedure, 
is the dimension of the original absolute vector of
, 
is the dimension of the new absolute vector of
.
If there is more than one type of element in the new absolute vector, the new absolute vector, named the upper-level vector, will be encoded using the multi-level permutation-based index encoding method as following step:
3) Increment the n value. At level 
, 
, the intermediate absolute value vector is obtained by removing the most frequent element as given in the decomposition order column of table from the upper-level vector. Sequentially the remaining elements are built into a new absolute vector for the current level; it has a position order related to the level 
absolute vector. All position values of the remainder elements are used to build a position vector.
4) The position vector of the current lower-level vector related to its upper-level vector is indexed based on a permutation and combination function, the indexing result being called the middle index 
. For the absolute vector in the current lower level, the position vector indexing is computed as follows:
()
()
The elements 
are the element values in the 
level position vector ranged from left to right according to their level, 
is the dimension of the upper-level absolute vector, 
is the dimension of the current-level absolute vector, 
represents the permutation and combination formula 
, 
, and 
. All the values for
can be stored in a simple table in order to avoid calculation of factorials. The 
level final-index, 
, is multiplied by the possible index value number, 
, in the current level and is added to the index, 
, in the current level, to obtain the final index, 
, of the current level.
5) Repeat steps 3 and 4 until there is only one type of element left in the current absolute vector. The 
for the lowest level is the rank of the absolute vector called 
. Table 46 is a sample extracted from the 36 leader table case. The leaders are indexed by 
. The decomposition order corresponds to the level order. The decomposition order column gives the order in which the element will be removed from the higher level. The last column gives the three class parameters, the first one is the number of sign bits, 
, the second one is the number of decomposition levels and equals the number of element types in the leader, 
, from the third one to the last one they represent the absolute vector dimension in each lower level except the highest level, 
(note that the dimension for the highest level is eight, but is not listed in table 46).
Table 46: List of leaders in base codebooks 
with their decomposition order and set parameter of multi-level permutation-based encoding
|
|
Leader |
Decomposition order |
|
Q0 |
Q2 |
Q3 |
Q4 |
|
{0,0,0,0,0,0,0,0} |
X |
||||||
|
0 |
{1,1,1,1,1,1,1,1} |
{1} |
{7,1} |
X |
X |
||
|
1 |
{2,2,0,0,0,0,0,0} |
{0,2} |
{2,2,2} |
X |
X |
||
|
2 |
{2,2,2,2,0,0,0,0} |
{0,2} |
{4,2,4} |
X |
|||
|
3 |
{3,1,1,1,1,1,1,1} |
{1,3} |
{7,2,1} |
X |
|||
|
4 |
{4,0,0,0,0,0,0,0} |
{0,4} |
{1,2,1} |
X |
X |
||
|
5 |
{2,2,2,2,2,2,0,0} |
{2,0} |
{6,2,2} |
X |
|||
|
6 |
{3,3,1,1,1,1,1,1} |
{1,3} |
{7,2,2} |
X |
|||
|
7 |
{4,2,2,0,0,0,0,0} |
{0,2,4} |
{3,3,3,1} |
X |
|||
|
8 |
{2,2,2,2,2,2,2,2} |
{2} |
{8,1} |
X |
|||
|
9 |
{3,3,3,1,1,1,1,1} |
{1,3} |
{7,2,3} |
X |
|||
|
10 |
{4,2,2,2,2,0,0,0} |
{2,0,4} |
{5,3,4,1} |
X |
|||
|
11 |
{4,4,0,0,0,0,0,0} |
{0,4} |
{2,2,2} |
X |
|||
|
12 |
{5,1,1,1,1,1,1,1} |
{1,5} |
{7,2,1} |
X |
|||
|
13 |
{3,3,3,3,1,1,1,1} |
{1,3} |
{7,2,4} |
X |
|||
|
14 |
{4,2,2,2,2,2,2,0} |
{2,0,4} |
{7,3,2,1} |
X |
|||
|
15 |
{4,4,2,2,0,0,0,0} |
{0,2,4} |
{4,3,4,2} |
X |
|||
|
16 |
{5,3,1,1,1,1,1,1} |
{1,3,5} |
{7,3,2,1} |
X |
|||
|
17 |
{ 6,2,0,0,0,0,0,0} |
{0,2,6} |
{2,3,2,1} |
X |
|||
|
18 |
{ 4,4,4,0,0,0,0,0} |
{0,4} |
{3,2,3} |
X |
|||
|
19 |
{ 6,2,2,2,0,0,0,0} |
{0,2,6} |
{4,3,4,1} |
X |
|||
|
20 |
{ 6,4,2,0,0,0,0,0} |
{0,2,4,6} |
{3,4,3,2,1} |
X |
|||
|
21 |
{ 7,1,1,1,1,1,1,1} |
{1,7} |
{7,2,1} |
X |
|||
|
22 |
{ 8,0,0,0,0,0,0,0} |
{0,8} |
{1,2,1} |
X |
|||
|
23 |
{6,6,0,0,0,0,0,0} |
{0,6} |
{2,2,2} |
X |
|||
|
24 |
{8,2,2,0,0,0,0,0} |
{0,2,8} |
{3,3,3,1} |
X |
|||
|
25 |
{8,4,0,0,0,0,0,0} |
{0,4, 8} |
{2,3,2,1} |
X |
|||
|
26 |
{9,1,1,1,1,1,1,1} |
{1,9} |
{7,2,1} |
X |
|||
|
27 |
{10,2,0,0,0,0,0,0} |
{0,2,10} |
{2,3,2,1} |
X |
|||
|
28 |
{8,8,0,0,0,0,0,0} |
{0,8} |
{2,2,2} |
X |
|||
|
29 |
{10,6,0,0,0,0,0,0} |
{0,6,10} |
{2,3,2,1} |
X |
|||
|
30 |
{12,0,0,0,0,0,0,0} |
{0,12} |
{1,2,1} |
X |
|||
|
31 |
{12,4,0,0,0,0,0,0} |
{0,4,12} |
{2,3,2,1} |
X |
|||
|
32 |
{10,10,0,0,0,0,0,0} |
{0,10} |
{2,2,2} |
X |
|||
|
33 |
{14,2,0,0,0,0,0,0} |
{0,2,14} |
{2,3,2,1} |
X |
|||
|
34 |
{12,8,0,0,0,0,0,0} |
{0,8,12} |
{2,3,2,1} |
X |
|||
|
35 |
{16,0,0,0,0,0,0,0} |
{0,16} |
{1,2,1} |
X |
, 
, 
The last value of the decomposition order for the leader 
is stored separately because this leader is the only one with 4 different values, the second dimension of the decomposition order being thus reduced from 4 to 3.
Figure 32 gives an encoding example for the leader 
.
|
|
Figure 32: Example processing for .
For example, in case the input vector is {0,–2,0,0,4,0,6,0}, the absolute input vector will be {0,2,0,0,4,0,6,0}, its associated leader can be found for Ka. The set of decomposition order is {0,2,4,6}. For the highest level L0, element "0" is removed first from the absolute vector. The first level 
absolute vector is {2,4,6}, its position vector is {1,4,6}. The second element which will be removed is "2", the second level 
absolute vector is {4,6}, its position vector is {1,2}. The third element which will be removed is "4", the third level 
absolute vector is {6}, its position vector is {1}.
The absolute vectors that have only two different values, out of which the most frequent is zero, are treated separately in a less complex procedure combining the encoding of the position vector with the sign encoding. These vectors have generally higher probability of occurrence. Example of such vectors are those derived for instance from the leaders: (2,2,0,0,0,0,0,0), (2,2,2,2,0,0,0,0). For these vectors there is a single level for the creation of the index and the first level remaining elements are the non-null components which are the significant elements for the sign encoding. The determination of the remaining elements and the creation of the sign index can be done thus in a single loop.
5.2.3.1.6.9.4 Voronoi extension determination and indexing
If the nearest neighbour 
is not in the base codebook, then the Voronoi extension has to be determined through the following steps.
(a) Set the Voronoi extension order 
and the scaling factor 
.
(b) Compute the Voronoi index 
of the lattice point 
that depends on the extension order 
and the scaling factor 
. The Voronoi index is computed via component-wise modulo operations such that 
depends only on the relative position of 
in a scaled and translated Voronoi region:
()
where 
is the 
generator matrix. Hence, the Voronoi index 
is a vector of integers with each component in 
.
(c) Compute the Voronoi codevector 
from the Voronoi index 
. The Voronoi codevector is obtained as
()
where 
is the nearest neighbour of 
in infinite 
(see subclause 5.2.3.1.6.9.2.2 for search details) and 
and 
are defined as
()
and
()
(d) Compute the difference vector 
. This difference vector 
always belongs to the scaled lattice 
. Compute 
, i.e. apply the inverse scaling to the difference vector 
. The codevector 
belongs to the lattice 
since 
belongs to 
lattice.
(e) Verify whether 
is in the base codebook 
(i.e. in 
or 
).
If 
is not in C, increment the extension order 
by 1, multiply the scaling factor 
by 2, and go back to sub-step (b).
Otherwise, if 
is in C, then the Voronoi extension order 
has been found and the scaling factor 
is sufficiently large to encode the index of 
.
5.2.3.1.6.9.3 Insertion of AVQ parameters into the bitstream
The parameters of the AVQ in each sub-band j consist of the codebook number 
, the vector index in base codebook 
and the 8-dimensional Voronoi index 
. The codebook numbers 
are in the set of integers {0, 2, 3, 4, 5, 6, 7, 8} and the size of its unary code representation is bits with the exception of 
that requires 1 bit and a possible overflow in the last AVQ coded sub-band. The size of each index 
and 
is given by 4nj bits and 
bits, respectively.
The AVQ parameters 
, 
, 
, are written sequentially in groups corresponding to the same sub‑band into the corresponding bitstream as
. ()
Note that if the lattice point in the block 
is in the base codebook 
, the Voronoi extension is not searched and consequently the index 
is not written into the bitstream in this group.
The actual bit-budget needed to encode AVQ parameters in current frame varies from sub-frame to sub-frame. The difference of bits between the allocated bits and actually spent bits are unused bits that can be employed in the subsequent sub-frame or high-rate higher band coding.
5.2.3.1.7 Gain quantization
5.2.3.1.7.1 Memory-less quantization of the gains
The adaptive codebook gain (pitch gain) and the algebraic codebook gain are quantized jointly in each subframe, using a 5-bit vector quantizer. While the adaptive codebook gain is quantized directly, the algebraic codebook gain is quantized indirectly, using a predicted energy of algebraic codevector. Note that, in this case, the prediction does not use any past information which limits the effect of frame-erasure propagation.
First, energy of residual signal in dB is calculated in each subframe as
(559)
where 
denotes the subframe and 
is the residual signal, defined in subclause 5.2.3.1.1. Then, average residual signal energy is calculated for the whole frame as
()
which is further modified by subtracting an estimate of the adaptive codebook contribution. That is
(561)
where
and 
, are as defined in subclause 5.1.10.4, are the normalized correlations of the first and the second half-frames, respectively. The result of equation (561), 
, serves as a prediction of the algebraic codevector energy and is quantized with 3 bits once per frame. The quantized value of the predicted algebraic codevector energy is defined as
()
where 
is the n-bit codebook for the predicted algebraic codevector energy and 
is the index minimizing the criterion above. The bit allocation 
is bit-rate and mode dependant and is given in Table 47
Table 47: Predictor energy codebook bit allocation
|
Rate (kbps) |
VC |
GC |
TC |
IC/UC |
|
7.2 |
n.a. |
n.a. |
4 |
n.a. |
|
8 |
n.a. |
n.a. |
4 |
n.a. |
|
9.6 |
3 |
3 |
n.a. |
n.a. |
|
13.2 |
5 |
4 |
4 |
n.a. |
|
16.4 |
3 |
3 |
n.a. |
3 |
|
24.4 |
3 |
3 |
n.a. |
3 |
|
32 |
n.a. |
5 |
5 |
5 |
|
64 |
n.a. |
5 |
5 |
5 |
Now, let 
denote the algebraic codebook excitation energy in dB in a given subframe, which is given by
(563)
In the equation above, 
is the filtered algebraic codevector, found in subclause 5.2.3.1.5.
Using the predicted algebraic codevector energy and the calculated algebraic codebook excitation energy, we may estimate the algebraic codebook gain as
(564)
A correction factor between the true algebraic codebook gain, 
, and the estimated one, 
, is given by
(565)
The pitch gain,
, and correction factor 
are jointly vector-quantized using a n-bit codebook, where n is dependent on the bit-rate and coding mode as shown in Table 48
Table 48: Gain codebook bit allocation per subframe
|
Rate (kbps) |
VC |
GC |
UC/IC |
|
7.2 |
7/6/6/6 |
6/6/6/6 |
n.a. |
|
8 |
8/7/6/6 |
8/7/6/6 |
n.a. |
|
9.6 |
5/5/5/5 |
5/5/5/5 |
n.a. |
|
13.2 |
6/6/6/6 |
6/6/6/6 |
n.a. |
|
16.4 |
7/7/7/7/7 |
7/7/7/7/7 |
6/6/6/6/6 |
|
24.4 |
7/7/7/7/7 |
7/7/7/7/7 |
6/6/6/6/6 |
|
32 |
6/6/6/6/6 |
6/6/6/6/6 |
6/6/6/6/6 |
|
64 |
12/12/12/12/12 |
12/12/12/12/12 |
6/6/6/6/6 |
The gain codebook search is performed by minimizing a mean-squared weighted error between the original and the reconstructed signal, which is given by
()
where 
is the target vector, 
is the filtered adaptive codevector, and 
is the filtered algebraic codevector. The quantized value of the pitch gain is denoted as
and the quantized value of the algebraic codebook gain is denoted as 
, where 
is the quantized value of the factor 
.
Furthermore, if pitch gain clipping is detected (as described in subclause 5.2.3.1.4.2), the last 13 entries in the codebook are skipped in the quantization procedure since the pitch gain in these entries is higher than 1.
5.2.3.1.7.2 Memory-less joint gain coding at lowest bit-rates
For the lowest bitrates of 7.2 and 8.0 kbps, slightly different memory-less joint gain coding scheme is used. This is due to the fact that there are not enough bits to cover the dynamic range of the target vector for algebraic search.
In the first subframe of the current frame, the estimated (predicted) gain of algebraic codebook is given by
()
where CT is a signal classification parameter (the coding mode), selected for the current frame in the pre-processing part, and 
is the energy of the filtered algebraic codevector, calculated in equation (). The inner term inside the logarithm corresponds to the gain of innovation vector. The constants a0 and a1 are found by means of MSE minimization on a large signal database. The only parameter in the equation above is the coding mode CT which is constant for all subframes of the current frame. The superscript [0] denotes the first subframe of the current frame. The estimation process for the first subframe is schematically depicted in the figure below.
Figure 33: Schematic description of the calculation process of algebraic gain in the first subframe
All subframes following the first subframes use slightly different estimation scheme. The difference is in the fact that in these subframes, the quantized gains of both the adaptive and the algebraic codebook from previous subframe(s) are used as auxiliary estimation parameters to increase the efficiency. The estimated value of the algebraic codebook gain in kth subframe, k>0 is given by
()
where k=1,2,3. Note, that the terms in the first and in the second sum of the exponent, there are quantized gains of algebraic and adaptive excitation of previous subframes, respectively. Note that the term including the gain of innovation vector 
is not subtracted. The reason is in the use of the quantized values of past algebraic codebook gains which are already close enough to the optimal gain and thus it is not necessary to subtract this gain again. The estimation constants b0,…,b2k+1 are found again through MSE minimization on a large signal database. The gain estimation process for the second and the following subframes is schematically depicted in the figure below.
Figure 34: Schematic description of the calculation process of algebraic gain in the following subframes
The gain quantization is done both at the encoder and at the decoder by searching the gain codebook and evaluating the MMSE between the target signal and the filtered adaptive codeword. In each subframe, the codebook is searched completely, i.e. for q=0,..,Q-1 where Q is the number of codebook entries. It is possible to limit the searching range in case ĝp is mandated to lie below certain threshold. To allow reducing the search range, the codebook entries are sorted in ascending order according to the value of ĝp.
The gain quantization is performed by calculating the following MMSE criterion for each codebook entry
()
where the constants c0, c1, c2, c3, c4 and c5 are calculated as
()
in which x(i) is the target signal, y(i) is the filtered adaptive excitation signal and z(i) is the filtered algebraic excitation signal. The codevector leading to the lowest energy is chosen as the winning codevector and its entries correspond to the quantized values of gp and .
Before the gain quantization process it is assumed that both the filtered adaptive and innovation codewords are already known. The gain quantization at the encoder is performed by searching the designed gain codebook in the MMSE sense. Each entry in the gain codebook consists of two values: the quantized gain of the adaptive part and the correction factor 
for the algebraic part of the excitation. The estimation of the algebraic gain excitation is done beforehand and the resulting gc0 is used to multiply the correction factor selected from the codebook. In each subframe the gain codebook is searched completely, i.e. for q=0,..,Q-1. It is possible to limit the search range if the quantized gain of the adaptive part of the excitation is mandated to be below certain threshold. To allow for reducing the search range, the codebook entries are sorted in ascending order according to the value of gp. The gain quantization process is schematically depicted in the figure below.
Figure 35: Schematic diagram of the gain quantization process in the encoder
The gain quantization is performed by minimizing the energy of the error signal e(i) The error energy is given by
()
By replacing 
by 
we obtain
()
The constants c0, c1, c2, c3, c4 and c5 and the estimated gain 
are computed before the search of the gain codebook. The error energy E is calculated for each codebook entry. The codevector [
;
] leading to the lowest error energy is selected as the winning codevector and its entries correspond to the quantized values of gp and . The quantized value of the fixed codebook gain is then calculated as
()
In the decoder, the received index is used to retrieve the values of the quantized gain of the adaptive excitation and the quantized correction factor of the estimated gain of the algebraic excitation. The estimated gain for the algebraic part of the excitation is done in the same way as in the encoder.
5.2.3.1.7.3 Scalar gain coding at highest bit-rates
At the bit-rate of 64kbps and at the last subframe of TC7 and TC165 (see later in subclause 5.2.3.2.2), the adaptive codebook gain (pitch gain) and the algebraic codebook gain are quantized using a scalar quantizers. The adaptive codebook gain is quantized using a uniform scalar quantizer according to MMSE criterion in the range between [0; 1.22]. In contrast the quantized algebraic codebook gain is obtained as a product of a correction factor 
and the estimated algebraic codebook gain 
, see equation 565, where the correction factor is quantized in log domain in the range between [0.02; 5.0].
At 64 kbps, both the adaptive codebook gain and the algebraic codebook gain are quantized by means of 6 bits each. In the last subframe of TC configurations TC7 and TC165, they are quantized by means of 6-8 bits depending on the bit-rate.
5.2.3.1.8 Update of filter memories
An update of the states of the synthesis and weighting filters is needed in order to compute the target signal in the next subframe.
After the two gains have been quantized, the excitation signal,
, in the present subframe is found by
(574)
where 
and
are the quantized adaptive and algebraic codebook gains, respectively, 
is the adaptive codevector (interpolated, low-pass filtered past excitation), and 
is the algebraic codevector (including pre-filtering). The states of the filters can be updated by filtering the signal 
(difference between the residual signal and the excitation signal) through the filters 
and 
and saving the states of the filters. This would require 3 stages of filtering. A simpler approach, which requires only one filtering, is as follows. The local synthesis signal (without excitation post-processing) from layer 
is computed by filtering the excitation signal through
. The output of the filter due to the input 
is equivalent to
. So, the states of the synthesis filter
are given by 
.
The updating of the states of the filter
can be done by filtering the error signal 
through this filter to find the perceptually weighted error 
. However, the signal 
can be equivalently found by
(575)
where 
is the adaptive codebook search target signal, 
is the filtered adaptive codebook vector, and 
is the filtered algebraic codebook vector. Since the signals 
, 
, and 
are available, the states of the weighting filter are updated by computing 
as in equation 575 for 
. This saves two stages of filtering.
5.2.3.2 Excitation coding in TC mode
The principle of excitation coding in TC mode is shown on a schematic diagram in Figure 36. The individual blocks and operations are described in detail in the following clauses.
5.2.3.2.1 Glottal pulse codebook search
The TC mode improves the robustness of the codec to frame erasures. It also encodes frames with an outdated past excitation buffer, e.g. after switching from HQ core frame.
The TC mode in the current frame is selected based on the classification algorithm described in subclause 5.1.13. The increased robustness, or the excitation building when the past excitation is outdated, is achieved by replacing the adaptive codebook (inter-frame long-term prediction) with a codebook of glottal impulse shapes (glottal-shape codebook) [19], which is independent from past excitation. The glottal-shape codebook consists of quantized normalized shapes of the truncated glottal impulses placed at specific positions. The codebook search consists of both the selection of the best shape and the best position.
To select the best codevector, the mean-squared error between the target signal, 
(the same target signal as used for the adaptive codebook search described in subclause 5.2.3.1.2), and the contribution signal, 
, is minimized for all candidate glottal-shape codevectors. The glottal-shape codebook search has been designed in a similar way as the algebraic codebook search, described in subclause 5.2.3.1.5.9. In this approach, each glottal shape is represented as an impulse response of a shaping filter
. This impulse response can be integrated in the impulse response of the weighted synthesis filter 
prior to the search of the optimum impulse position. The searched codevectors can then be represented by vectors containing only one non-zero element corresponding to candidate impulse positions, and they can be searched very efficiently. Once selected, the position codevector is convolved with the impulse response of the shaping filter. This procedure needs to be repeated for all the candidate shapes and the best shape-position combination will form the excitation signal.
Figure 36: Schematic diagram of the excitation coding in TC mode
In the following, all vectors are supposed to be column vectors. Let 
be a position codevector with one non-zero element at a position
, and 
the corresponding glottal-shape codevector with index 
representing the centre of the glottal shape. Index 
is chosen from the range [0, 63], where 64 is the subframe length. Note that, due to the non-causal nature of the shaping filter, its impulse response is truncated for positions in the beginning and at the end of the subframe. The glottal shape codevector 
can be expressed in a matrix form as 
, where 
is a Toeplitz matrix representing the glottal impulse shape. Similarly to the algebraic codebook search, we can write
(576)
where 
is a lower triangular Toeplitz convolution matrix of the weighted synthesis filter. The rows of a convolution matrix 
correspond to the filtered shifted version of the glottal impulse shape or its truncated representation.
Because of the fact that the position codevector 
has only one non-zero sample, the computation of the criterion (576) is very simple and can be expressed as
(577)
As it can be seen from criterion (577), only the diagonal of the correlation matrix 
from criterion (576) needs to be computed.
The codebook consists of 8 prototype glottal impulse shapes of length 
samples placed at all subframe positions. Note that, since 
is shorter than the subframe length, the remaining samples in the subframe are set to zero.
In general, the coding efficiency of the glottal-shape codebook is lower than the efficiency of the long-term prediction, and more bits are generally needed to assure good synthesized speech quality.
However, the glottal-shape codebook does not need to be used in all subframes. First, there is no reason to use this codebook in subframes that do not contain any significant glottal impulse in the residual signal. Second, the glottal-shape codebook search is important only in the first pitch period in a frame. The following pitch periods can be encoded using the more efficient standard adaptive codebook search as it does not use the excitation of the past frame anymore. To satisfy the constant bit-rate requirement, the glottal-shape codebook is used in the EVS codec only in one of the four subframes in a frame. This leads to a highly structured coding mode where the bit allocation is dependent on the position of the first glottal impulse and the pitch period. The subframe where the glottal-shape codebook is used is chosen as the subframe with the maximum sample in the residual signal in the range 
, where 
is the open-loop pitch period estimated over the first half of the frame. The other subframes are processed as described in subclause 5.2.3.2.2.
Criterion (577) is typically used in the algebraic codebook search by pre-computing the backward filtered target vector 
and the correlation matrix 
. Given the non-causal nature of the filter 
, the matrix 
is not triangular and Toeplitz anymore, and this approach cannot be efficiently applied for the first 
positions in the glottal-shape codebook search.
Let 
be the 
th row of the matrix 
, where 
is computed in two steps to minimize the computational complexity. In the first step, the first 
rows of this matrix 
are calculated that correspond to the positions 
from the range 
. In the second step, the criterion (577) is used in a similar way as in the algebraic codebook search for the remaining part of 
(the last 
rows of the matrix 
).
In the first step, the convolution between the glottal-shape codebook entry for position 
and the impulse response 
is first computed using
(578)
where we take advantage of the fact that the filter 
has only 
non-zero coefficients.
Next, the convolution 
between the glottal-shape codebook entry for the position 
and the impulse response 
is computed, reusing the values of 
. For the following rows, the recursion is reused, resulting in
(579)
The recursion (579) is repeated for all
.
Now, the criterion (577) can be computed for all positions 
from the range 
in the form
(580)
In the second step, we take advantage of the fact that rows 
of the matrix 
are built using the coefficients of the convolution that are already computed as described by recursion (579) for 
. That is, each row corresponds to the previous row shifted to the right by 1 with a zero added at the beginning
(581)
and this is repeated for 
from the range 
.
Next, the target vector 
and the diagonal of the matrix 
need to be computed. First, we evaluate the numerator and the denominator of the criterion (577) for the last position 
(582)
and
(583)
For the remaining positions, the numerator is computed using equation (582), but with the summation index changed. In the computation of the denominator, some of the previously computed values can be reused. For example, for the position 
, the denominator of criterion (577) is computed using
(584)
Similarly, we can continue to compute the numerator and the denominator of criterion (577) for all positions 
.
The search continues using the previously described procedure for all other glottal impulse shapes and the codevector corresponding to the best combination of glottal-shape and position is selected. To maintain the complexity low, the computation described above is further reduced by limiting the position search to ±4 samples around the maximum absolute value of the residual signal.
The last parameter to be determined is the gain of the glottal-shape codebook excitation. The gain is quantized in two steps. First, a roughly quantized gain of the glottal-shape codevector, 
, is found. Then, after both the first-stage contribution (glottal-shape codevector) and the second-stage contribution (algebraic codevector) of the excitation signal are found, the gain 
of the first-stage contribution signal is jointly quantized with the second-stage contribution gain, 
. This is done using the memory-less gain vector quantization, as described in subclause 5.2.3.1.7.1. The found glottal shape codevector 
is thus the position codevector 
filtered through the shaping filter 
that represents the best found glottal shape. When scaling the glottal-shape codevector 
with the signed quantized gain
, we finally obtain the first stage excitation codevector, 
.
The glottal-shape gain 
is quantized using a quantization table as follows. First, an unquantized gain in the current glottal-shape subframe is found as
(585)
where 
is the subframe length, 
is the target signal and 
is the glottal-shape codevector 
filtered through the weighted synthesis filter
. Further, the sign of the glottal-shape gain is set to 0 if 
and 1 otherwise, and written to the bitstream. Finally, the glottal-shape gain quantization index 
is found as the maximum value of that satisfies 
, where 
is the glottal-shape gain quantization table of dimension 8. The signed quantized glottal-shape gain
is thus found as 
and its value is quantized using 4 bits (1 bit for sign, 3 bits for the value).
It should be noted that the closed-loop pitch period, 
, does not need to be transmitted anymore in a subframe which uses the glottal-shape codebook search with the exception of subframes containing more than one glottal impulse, i.e., when
. There are situations where the pitch period of the input signal is shorter than the subframe length and, in this case, we have to transmit its value. Given the pitch period length limitations and the subframe length, a subframe cannot contain more than two impulses. In the situation that the glottal-shape codevector contains two impulses, an adaptive codebook search is used in a part of the subframe. The first 
samples of the glottal-shape codevector 
are built using the glottal-shape codebook search and then the other samples in the subframe are built using the adaptive search as shown in Figure 37.
Figure 37: Glottal-shape codevector with two impulses construction
The described procedure is used even if the second glottal impulse appears in one of the first 
positions of the next subframe. In this situation, only a few samples (less than 
) of the glottal shape are used at the end of the current subframe. This approach has a limitation because the pitch period value transmitted in these situations is limited to 
, if it is bigger, it is not transmitted.
In order to enhance the coding performance, a low-pass filter is applied to the first stage excitation signal 
. In all subframes after the glottal-shape codebook subframe, the low-pass filtered first stage excitation is found as described in subclause 5.2.3.1.4.2.
5.2.3.2.2 TC frame configurations
5.2.3.2.2.1 TC frame configurations at 12.8 kHz internal sampling
At bit-rates with 12.8 kHz internal sampling rate the glottal-shape codebook is used in one out of four subframes. The other subframes in a TC frame (not encoded with the use of the glottal-shape codebook) are processed as follows. If the subframe with glottal-shape codebook search is not the first subframe in the frame, the excitation signal in preceding subframes is encoded using the algebraic CELP codebook only, this means that the first stage contribution signal is zero. If the glottal-shape codebook subframe is not the last subframe in the frame, the following subframes are processed by the standard CELP coding (i.e., using the adaptive and the algebraic codebook search). Thus, the first stage excitation signal is the scaled glottal-shape codevector, the adaptive codevector or the zero codevector.
In order to further increase encoding efficiency and to optimize bit allocation, different processing is used in particular subframes of a TC frame dependent on the pitch period. When the first subframe is chosen as a TC subframe, the subframe with the 2nd glottal impulse in the LP residual signal is determined. This determination is based on the pitch period value and the following four situations then can appear. In the first situation, the 2nd glottal impulse is in the 1st subframe, and the 2nd, 3rd and 4th subframes are processed using the standard CELP coding (adaptive and algebraic codebook search). In the second situation, the 2nd glottal impulse is in the 2nd subframe, and the 2nd, 3rd and 4th subframes are processed using the standard CELP coding again. In the third case, the 2nd glottal impulse is in the 3rd subframe. The 2nd subframe is processed using algebraic codebook search only as there is no glottal impulse in the 2nd subframe of the LP residual signal to be searched for using the adaptive codebook. The 3rd and 4th subframes are processed using the standard CELP coding. In the last (fourth) case, the 2nd glottal impulse is in the 4th subframe (or in the next frame), the 2nd and 3rd subframes are processed using the algebraic codebook search only, and the 4th subframe is processed using the standard CELP coding. Table 49 shows all possible coding configurations in the EVS codec at 12.8 kHz internal sampling rate.
The TC configuration is transmitted in the bit-stream using a Huffman-style coding and its bit sequence is show in the Table 49 in the column bitstream.
Table 49: TC configurations used in the EVS codec at 12.8 kHz internal sampling rate
|
Coding configuration |
Bitstream |
Positions of the first (and the second, if relevant) glottal impulse(s) in the frame |
Type of codebook used (GS = glottal-shape, Ada = adaptive, Alg = algebraic) |
|||
|
1st subfr. |
2nd subfr. |
3rd subfr. |
4th subfr. |
|||
|
TC1 |
1 |
|
GS + Alg |
Ada + Alg |
Ada + Alg |
Ada + Alg |
|
TC2 |
0101 |
|
GS + Alg |
Ada + Alg |
Ada + Alg |
Ada + Alg |
|
TC3 |
0100 |
|
GS + Alg |
Alg |
Ada + Alg |
Ada + Alg |
|
TC4 |
011 |
|
GS + Alg |
Alg |
Alg |
Ada + Alg |
|
TC5 |
001 |
|
Alg |
GS + Alg |
Ada + Alg |
Ada + Alg |
|
TC6 |
0001 |
|
Alg |
Alg |
GS + Alg |
Ada + Alg |
|
TC7 |
0000 |
|
Alg |
Alg |
Alg |
GS + Alg |
5.2.3.2.2.2 TC frame configurations at 16 kHz internal sampling
At bit-rates with 16 kHz internal sampling rate the glottal-shape codebook is used in one out of five subframes. If the subframe with glottal-shape codebook search is not the first subframe in the frame, the excitation signal in preceding subframes is encoded using the algebraic CELP codebook only. If the glottal-shape codebook subframe is not the last subframe in the frame, the following subframes are processed by the standard CELP coding.
As the bit-rates with 16 kHz internal sampling rate are with high bit-budget, the number of TC configurations is reduced compared to the 12.8 kHz internal sampling rate. Table 50 shows all possible coding configurations in the EVS codec at 16 kHz internal sampling rate
Table 50: TC configurations used in the EVS codec at 16 kHz internal sampling rate
|
Coding configuration |
Bitstream |
Positions of the first glottal impulse in the frame |
Type of codebook used (GS = glottal-shape, Ada = adaptive, Alg = algebraic) |
||||
|
1st subfr. |
2nd subfr. |
3rd subfr. |
4th subfr. |
5th subfr. |
|||
|
TC161 |
00 |
|
GS + Alg |
Ada + Alg |
Ada + Alg |
Ada + Alg |
Ada + Alg |
|
TC162 |
01 |
|
Alg |
GS + Alg |
Ada + Alg |
Ada + Alg |
Ada + Alg |
|
TC163 |
10 |
|
Alg |
Alg |
GS + Alg |
Ada + Alg |
Ada + Alg |
|
TC164 |
110 |
|
Alg |
Alg |
Alg |
GS + Alg |
Ada + Alg |
|
TC165 |
111 |
|
Alg |
Alg |
Alg |
Alg |
GS + Alg |
5.2.3.2.2.3 Pitch period and gain coding in the TC mode
When using the TC, it is not necessary to transmit the pitch period for certain subframes. Further, it is not necessary to transmit both pitch gain, 
, and the algebraic codebook gain, 
, for subframes where there is no important glottal impulse, and only the algebraic codebook contribution is computed (the first stage excitation is the zero vector).
In subframes, where the glottal-shape, or adaptive, search is used, the first stage excitation gain (pitch gain), 
, and the second stage excitation gain (algebraic gain), 
, are quantized at bit-rates ≤ 32 kbps using the memory-less vector gain quantization described in subclause 5.2.3.1.7.1. At 64 kbps bit-rate, gains are scalar quantized as described in subclause 5.2.3.1.7.3. In glottal-shape subframes, the first stage gain, 
, is found in the same manner as described in subclause 5.2.3.1.4.2.
When only an algebraic gain is quantized in the current frame (the first stage excitation is the zero vector), the following scalar quantization process is used. First, an optimal algebraic gain in the current subframe is found as
(586)
where 
is the subframe length, 
is the target signal and 
is the algebraic codevector 
filtered through the weighted synthesis filter
with the pre-filter 
. The predictive algebraic energy calculated once per frame is employed as described in subclause 5.2.3.1.7. Further the algebraic codebook gain, 
, and the correction factor, 
, are given by equations () and (), respectively. Finally, the correction factor quantization index, 
, is found as the maximum value of 
that satisfies
()
where 
is the algebraic gain quantization table of dimension 8. The correction factor 
is quantized with 3 bits using the quantization table
and the quantized algebraic gain is obtained by
()
The following is a list of all TC configurations corresponding to Table 49 and Table 50.
Configuration TC1
In this configuration, two first glottal impulses appear in the first subframe that is processed using the glottal-shape codebook search. This means that the pitch period value in the 1st subframe can have the maximum value less than the subframe length, i.e., 
. Here, 
is the closed-loop pitch period and 
the subframe length. With the ½ sample resolution it can be coded with 6 bits. The pitch periods in the next subframes are found using – depending on the bit-rate – a 5- or 6-bit delta search with a fractional resolution.
Configuration TC2
When configuration TC2 is used, the first subframe is processed using the glottal-shape codebook search. The pitch period is not needed and all following subframes are processed using the adaptive codebook search. Because we know that the 2nd subframe contains the second glottal impulse, the pitch period maximum value holds 
. This maximum value can be further reduced thanks to the knowledge of the glottal impulse position value 
. The pitch period value in the 2nd subframe is then coded using 7 bits with a fractional resolution in the whole range of 
. In the 3rd and 4th subframes, a delta search using 6 bits is used with a fractional resolution.
Configuration TC3
When configuration TC3 is used, the first subframe is processed using the glottal-shape codebook search with no use of the pitch value again. But because the 2nd subframe of the LP residual signal contains no glottal impulse and the adaptive search is useless, the first stage contribution signal is replaced by zeros in the 2nd subframe. The adaptive codebook parameters (
and 
) are not transmitted in the 2nd subframe. The first stage contribution signal in the 3rd subframe is constructed using the adaptive codebook search with the pitch period maximum value 
and the minimum value 
, thus only a 7-bit coding of the pitch value with fractional resolution in all range is needed. The 4th subframe is processed using the adaptive search with – depending on the bit-rate – a 5- or 6-bit delta search coding of the pitch period value.
In the 2nd subframe, only the algebraic codebook gain, gc, is transmitted. Consequently, only 3 bits are needed for gain quantization in this subframe as described at the beginning of this subclause.
Configuration TC4
When configuration TC4 is used, the first subframe is processed using the glottal-shape codebook search. Again, the pitch period does not need to be transmitted. But because the LP residual signal contains no glottal impulse in the 2nd and also in the 3rd subframe, the adaptive search is useless for both these subframes. Again, the first stage excitation signal in these subframes is replaced by zeros. The pitch period value is transmitted only in the 4th subframe by means of 7 bits and its minimum value is 
.The maximum value of the pitch period is limited by the 
value only. It does not matter if the second glottal impulse will appear in the 4th subframe or not (the second glottal impulse can be present in the next frame if 
).
Note that the absolute value of the pitch period is necessary at the decoder for the frame concealment; therefore, it is transmitted also in the situation when the second glottal impulse appears in the next frame. When a frame 
preceding the TC frame 
is missing, the correct knowledge of the pitch period value from the frames 
and 
helps to reconstruct the missing part of the synthesis signal in the frame 
successfully.
The algebraic codebook gain,
, is quantized with 3 bits in the 2nd subframe and 3rd subframe.
Configuration TC5
When the first glottal impulse appears in the 2nd subframe, the pitch period is transmitted only for the 3rd and 4th subframe. 3rd subframe, the pitch value is coded using 9-bit absolute search while in the 4th subframe using – depending on the bit-rate – 5- or 6- bits delta search. In this case, only algebraic codebook parameters are transmitted in the 1st subframe (with the algebraic codebook gain, 
, quantized with 3 bits).
Configuration TC6
When the first glottal impulse appears in the 3rd subframe, the pitch period does not need to be transmitted for the TC technique. In this case, only algebraic codebook parameters are transmitted in the 1st and 2nd subframe with the algebraic codebook gain,
, quantized with 3 bits in both subframes. Nevertheless, the pitch period is transmitted in the 4th subframe by means of 9 bit absolute search coding for the reason of better frame erasure concealment in the frame after the TC frame. Also, the pitch period is transmitted for the 3rd subframe by means of 5 bit absolute search coding although it is not usually necessary.
Configuration TC7
When the first glottal impulse appears in the 4th subframe, the pitch period value information is not usually used in this subframe. However, its value is necessary for the frame concealment at the decoder (this value is used for the missing frame reconstruction when the frame preceding or following the TC frame is missing) or in case of strong onsets at the frame-end and very short pitch period. Thus, the pitch value is transmitted only in the 4th subframe by means of 9-bit absolute search coding and only algebraic codebook parameters are transmitted in the first three subframes (the gain pitch, 
, is not essential). The algebraic codebook gain, 
, is quantized with 3 bits in the 1st, 2nd and 3rd subframes. The scalar gain quantization is employed only at the 4th subframe in this configuration to encode the gain pitch and the algebraic codebook gain.
Configuration TC161
In this configuration, one or two first glottal impulses appear in the first subframe that is processed using the glottal-shape codebook search. This means that the pitch period value in the 1st subframe can have the maximum value less than the subframe length 
, i.e., 
and it is coded with 6 bits. Then the pitch period in the 2nd subframe is found using 8-bit absolute search on the interval 
. Finally the pitch period in the 3rd subframe is coded using 10-bit absolute search and in the 4th and 5th subframe using 6-bit delta search.
The gain pitch and the algebraic codebook gain are coded in all subframes using 6-bit VQ at 32 kbps resp. 12-bit SQ at 64 kbps.
Configuration TC162
The first glottal impulse appears in the 2nd subframe and the pitch period is transmitted for the 3rd, 4th and 5th subframe. In the 3rd subframe, the pitch value is coded using 10-bit absolute search while in the 4th and 5th subframe using 6- bits delta search. The pitch period is transmitted also in the 2nd subframe by means of 6 bits and serves in case when two first glottal impulses appears in the second subframe.
The gain pitch and the algebraic codebook gain are coded in the 2nd, 3rd, 4th and 5th subframe using 6-bit VQ at 32 kbps resp. 12-bit SQ at 64 kbps. The algebraic codebook gain,
, is quantized in the 1st subframe with 3 bits at 32 kbps resp. 6 bits at 64 kbps
Configuration TC163
The first glottal impulse appears in the 3rd subframe. In this case, only algebraic codebook parameters are transmitted in the 1st and 2nd subframe with the algebraic codebook gain,
, quantized in both subframes with 3 bits at 32 kbps resp. 6 bits at 64 kbps. Then the pitch period is coded by means of 10-bit absolute search in the 3rd subframe and by means of 6-bit delta search in the 4th and 5th subframe.
The gain pitch and the algebraic codebook gain are coded in the 3rd, 4th and 5th subframe using 6-bit VQ at 32 kbps resp. 12-bit SQ at 64 kbps.
Configuration TC164
The first glottal impulse appears in the 4th subframe. In this case, only algebraic codebook parameters are transmitted in the 1st, 2nd and 3rd subframe with the algebraic codebook gain,, quantized in all these subframes with 3 bits at 32kbps resp. 6 bits at 64kbps. Then the pitch period is coded by means of 10-bit absolute search in the 4th subframe and by means of 6-bit delta search in the 5th subframe.
The gain pitch and the algebraic codebook gain are coded in the 4th and 5th subframe using 6-bit VQ at 32 kbps resp. 12-bit SQ at 64 kbps.
Configuration TC165
When the first glottal impulse appears in the 5th subframe, the pitch period value information is not usually used in this subframe. However, its value is necessary for the frame concealment at the decoder (this value is used for the missing frame reconstruction when the frame preceding or following the TC frame is missing) or in case of strong onsets at the frame-end and very short pitch period. Thus, the pitch value is transmitted only in the 5th subframe by means of 10-bit absolute search coding and only algebraic codebook parameters are transmitted in the first four subframes. The algebraic codebook gain, 
, is quantized in the 1st, 2nd and 3rd subframes with 3 bits at 32kbps and 6 bits at 64 kbps. The gain pitch and the algebraic codebook gain are coded only in 5th subframe using a scalar gain quantizer.
5.2.3.2.2.4 Update of filter memories
In TC mode, the memories of the synthesis and weighting filter are updated as described in subclause 5.2.3.1.8. Note that signals in equation () are the first stage excitation signal 
(i.e., the glottal-shape codevector, the low-pass filtered adaptive codevector, or the zero codevector) and the algebraic codevector 
(including pre-filtering).
5.2.3.3 Excitation coding in UC mode at low rates
The principle of excitation coding in UC mode is shown in a schematic diagram in Figure 38. The individual operations are described in detail in the following clauses.
Figure 38: Schematic diagram of the excitation coding in UC mode
5.2.3.3.1 Structure of the Gaussian codebook
In UC mode, a Gaussian codebook is used for representing the excitation. To simplify the search and reduce the codebook memory requirement, an efficient structure is used whereby the excitation codevector is derived by the addition of 2 signed vectors taken from a table containing 64 Gaussian vectors of dimension 64 (the subframe size). Let 
denote the 
th 64-dimensional Gaussian vector in the table. Then, a codevector is constructed by
(589)
where 
and 
are the signs, equal to –1 or 1, and 
and 
are the indices of the Gaussian vectors from the table. In order to reduce the table memory, a shift-by-2 table is used, thus only 64 + 63 × 2 = 190 values are needed to represent the 64 vectors of dimension 64.
To encode the codebook index, one has to encode 2 signs, 
and 
, and two indices, 
and 
. The values of 
and 
are in the range 
, so they need 6 bits each, and the signs need 1 bit each. However, 1 bit can be saved since the order of the vectors 
and 
is not important. For example, choosing 
as the first vector and 
as the second vector is equivalent to choosing as the first vector and 
as the second vector. Thus, similar to the case of encoding two pulses in a track, only one bit is needed for both signs. The ordering of the vector indices is such that the other sign information can be easily deduced. This gives a total of 13 bits. To better explain this procedure, let us assume that the two vectors have the indices 
and 
with sign indices 
and 
, respectively (
if the sign is positive and 
if the sign is negative). The codevector index is given by
()
If 
then 
; otherwise 
is different from 
. Thus, when constructing the codeword (index of codevector), if the two signs are equal then the smaller index is assigned to 
and the larger index to 
, otherwise the larger index is assigned to 
and the smaller index to 
.
5.2.3.3.2 Correction of the Gaussian codebook spectral tilt
In UC mode, the Gaussian codebook spectral tilt is corrected by a modification factor, which is encoded using 3 bits per subframe. First, the tilt of the target vector 
is computed as
()
and the tilt of the filtered Gaussian codebook 
is computed as
()
The filtered Gaussian codebook, 
, is the initial Gaussian codebook, 
, convolved with the weighted filter, 
. Note that vector 
represents the whole codebook, i.e., 
.
The spectral tilt modification factor is found by
()
and the integer quantization index is found by
()
where the operator 
returns the integer part of a floating point number. The integer quantization index is limited to [0, 7].
Finally, the quantized spectral tilt modification factor is used to adapt the tilt of the initial Gaussian codebook. That is
(595)
where the quantized spectral tilt modification factor is found as
()
In the following, the adapted Gaussian codebook 
, is searched to obtain the best two codevectors and signs which form the final codevector, 
, of dimension 64. In the following, we assume 
.
5.2.3.3.3 Search of the Gaussian codebook
The goal of the search procedure is to find the indices 
and 
of the two best random vectors and their corresponding signs, 
and 
. This is achieved by maximizing the following search criterion
(597)
where 
is the target vector and 
is the filtered final codevector. Note that in the numerator of the search criterion, the dot product between 
and 
, 
, is equivalent to the dot product between 
and 
, where 
is the backward filtered target vector which is also the correlation between 
and the impulse response 
. The elements of the vector 
are found by
()
Since 
is independent of the codevector 
, it is computed only once, which simplifies the computation of the numerator for different codevectors.
After computing the vector 
, a predetermination process is used to identify 
out of the 64 random vectors in the random table, so that the search process is then confined to those 
vectors. The predetermination is performed by testing the numerator of the search criterion 
for the 
vectors which have the largest absolute dot product (or squared dot product) between 
and 
, 
. That is, the dot products
that are given by
()
are computed for all random vectors 
and the indices of the 
vectors which result in the 
largest values of 
are retained. These indices are stored in the index vector 
, 
. To further simplify the search, the sign information corresponding to each predetermined vector is also preset. The sign corresponding to each predetermined vector is given by the sign of 
for that vector. These preset signs are stored in the sign vector 
, 
.
The codebook search is now confined to the pre-determined 
vectors with their corresponding signs. Here, the value 
is used, thus the search is reduced to finding the best 2 vectors among 8 random vectors instead of finding them among 64 random vectors. This reduces the number of tested vector combinations from 
to 
.
Once the most promising 
vectors and their corresponding signs are predetermined, the search proceeds with the selection of 2 vectors among those vectors which maximize the search criterion 
.
We first start by computing and storing the filtered vectors 
, 
corresponding to the 
predetermined vectors. This can be performed by convolving the predetermined vectors with the impulse response of the weighted synthesis filter, 
. The sign information is also included in the filtered vectors. That is
()
We then compute the energy of each filtered pre-determined vector as
()
and its dot product with the target vector
()
Note that 
and 
correspond to the numerator and denominator of the search criterion due to each predetermined vector. The search proceeds now with the selection of 2 vectors among the 
predetermined vectors by maximizing the search criterion 
. Note that the final codevector is given in equation ().
The filtered codevector 
is given by
()
Note that the predetermined signs are included in the filtered predetermined vectors 
. The search criterion in equation () can be expressed as
()
The vectors 
and the values of
and 
are computed before starting the codebook search. The search is performed in two nested loops for all possible positions 
and 
that maximize the search criterion 
. Only the dot products between the different vectors 
need to be computed inside the loop.
At the end of the two nested loops, the optimum vector indices 
and 
will be known. The two indices and the corresponding signs are then encoded as described above. The gain of the final Gaussian codevector is computed based on a combination of waveform matching and energy matching. The gain is given by
()
where 
is the gain that matches the waveforms of the vectors 
and 
and is given by
and 
is the gain that matches the energies of the vectors 
and 
and is given by 
. Here, 
is the target vector and 
is the filtered codevector 
, 
.
5.2.3.3.4 Quantization of the Gaussian codevector gain
In UC mode, the adaptive codebook is not used and only the Gaussian codevector gain needs to be quantized. The Gaussian codevector gain in dB is given by
(606)
is uniformly quantized between
and
with the step size given by
(607)
where 
is the number of quantization levels. The quantization index 
is given by the integer part of
(608)
Finally, the quantized gain in dB is given by
(609)
and the quantized gain is given by
(610)
In every subframe, 7 bits are used to quantize the gain. Thus, 
and the quantization step is 
dB with the quantization boundaries
and
. The quantized gain, 
, is finally used to form the total excitation in the UC mode by multiplying each sample of the codevector, 
, by
.
5.2.3.3.5 Other parameters in UC mode
In UC mode, the SAD and noisiness parameters are encoded to modify the excitation vector in stationary inactive segments. The noisiness parameter is required for an anti-swirling technique used in the decoder for enhancing the background noise representation during inactive speech.
The noisiness parameter is defined as the ratio between low- and high-order LP residual variances:
(611)
where 
and 
denote the LP residual variances for second-order and 16th-order LP filters, respectively. The LP residual variances are readily obtained as a by-product of the Levinson-Durbin procedure, described in subclause 5.1.9.4.
The noisiness parameter is normalized to the interval [0, 1] within which it is linearly quantized with 32 levels. That is
(612)
where 
is a normalization factor, which is different for WB and NB signals. For WB signals, 
, otherwise 
.
5.2.3.3.6 Update of filter memories
In UC mode, the memories of the synthesis and weighting filter are updated as described in subclause 5.2.3.1.8. Note that the excitation component 
is missing in equation () for UC mode.
5.2.3.4 Excitation coding in IC and UC modes at 9.6 kbps
At 9.6 kbps, the IC and UC modes are coded with a hybrid coding embedding two stages of innovative codebooks, the algebraic pulse codebook and a Gaussian noise-like excitation. Since the long term prediction gain is expected to be very low for such frames, the adaptive codebook is not used. The principle is depicted in figure 39.
Figure 39: Schematic diagram of the excitation coding in UC and IC modes at 9.6 kbps
5.2.3.4.1 Algebraic codebook
5.2.3.4.1.1 Adaptive pre-filter
For UC mode, the adaptive pre-filter is performed similarly as in subclause 5.2.3.1.5.1. Additional the pre-filter 
is amended with a phase scrambling filter as follows:
(613)
For NB IC mode, the filter is designed as follows:
(614)
where 
is defined in subclause 5.2.3.1.5.1 with 
, 
is also defined in subclause 5.2.3.1.5.1, and 
and 
.
For WB IC mode, 
is defined as:
(615)
where 
, 
, 
and 
represents the tilt of following filter:
(616)
The tilt is computed as:
(617)
is bounded by [0.25 0.5] and given is by:
(618)
where
and 
are the energies of the scaled pitch codevector and the scaled algebraic codevector of the previous subframe, respectively.
5.2.3.4.2 Gaussian noise generation
The Gaussian noise excitation is a second excitation added to the first innovative excitation from the algebraic codebook. This second contribution is only computed and added in WB.
The Gaussian noise excitation is produced by calling three times a random generator with a uniform distribution between -1 and +1. It follows the Central Limit Theorem.
(619)
The Gaussian noisy excitation 
is spectrally shaped by applying the pre-filter 
defined in subclause 5.2.3.4.1.1.
5.2.3.4.3 Gain coding
For NB only one gain has to be quantized, the gain of the algebraic codebook 
. It is quantized using a 6-bit quantizer.
For WB, the two gains 
and 
are quantized jointly in each subframe, using a 7-bit vector quantizer.
In both cases the optimal algebraic codeword gain is computed as follows:
(620)
In the equation above, 
is the algebraic codevector 
filtered through the weighted synthesis filter 
with the pre-filter 
.is the filtered algebraic codevector.
The algebraic codebook excitation energy in dB, 
, is also computed as follows:
(621)
5.2.3.4.3.1 Innovative codebook gain coding (NB)
The algebraic codevector gain in dB is given by
(622)
is uniformly quantized between -30 dB and 90dB with the step size of 1.9dB. The quantization index 
is given by the integer part of
(623)
Finally, the quantized gain in dB is given by
(624)
and the quantized gain is given by
(625)
5.2.3.4.3.2 Joint gain coding (WB)
The algebraic codebook gain is quantized indirectly, using a predicted energy of algebraic codevector. The energy of residual signal in dB is calculated.
Then, average residual signal energy is calculated for the whole frame and serves as a prediction of the algebraic codevector energy. It is quantized on 4 bits once per frame. The quantized value of the predicted algebraic codevector energy is defined as
(626)
where 
is the 4-bit codebook for the predicted algebraic codevector energy and 
is the index minimizing the criterion above.
Using the predicted algebraic codevector energy, we may estimate the algebraic codebook gain as
(627)
A correction factor between the true algebraic codebook gain, 
, and the estimated one, 
, is given by
(628)
The correction factor 
is uniformly quantized on 5 bits between -20 dB and 20dB with the step size of 1.25dB. The quantization index 
is given by the integer part of
(629)
Finally, the quantized gain in dB is given by
(630)
and the quantized gain is given by
(631)
The gain of Gaussian noise excitation is quantized on 2 bits. Unlike the algebraic codeword gain, the Gaussian noise excitation gain is optimized in order to minimize the energy mismatch between the target signal and reconstructed signal. The following criterion is minimized:
(632)
where 
is an attenuation factor set to 1 for clean speech, where high dynamic of energy is perceptually important and set to 0.8 for noisy speech where the noise excitation is made more conservative for avoiding fluctuation in the output energy between unvoiced and non-unvoiced frames
The quantized gain is expressed as follows where the index 
of the optimal gain is sent on 2 bits:
(633)
5.2.3.4.4 Memory update
The update of the filter memories is performed as described in subclause 5.2.3.1.8 except that there is no adaptive codebook contribution. The Gaussian noise excitation is not taken into account for the update and for computing the next subframe signal target.
5.2.3.5 Excitation coding in GSC mode
In the GSC mode, the excitation is encoded using mixed time-domain/frequency-domain coding technique. This mode is aimed at encoding generic audio signals at low bit rates without introducing more delay than the ACELP structure requires. The GSC mode is used only at 12.8 kHz internal sampling rate, and the excitation could be encoded with 4 subframes, 2 subframes, or 1 subframe per frame depending on the bit rate or the signal type.
Figure 40 is a schematic block diagram showing the general concept of coding the excitation in the GSC mode. The speech/music selector is used to choose between coding the excitation signal in the GSC mode or the other ACELP modes described above. The selector mainly consists of the speech music classification (as described in subclause 5.1.13.5), where GSC is used in case music signals are detected. A further detector (as described in subclause 5.1.13.5.3) is used to verify if a detected music contains a temporal attack. In such a case the time domain transient coding mode is used to code only the attack.
When encoding in the GSC mode, the time-domain excitation contribution is first computed. In case of 4 subframes, the time-domain excitation consists of both adaptive codebook and fixed codebook as in ordinary ACELP. In case 1 or 2 subframes are used, the time-domain excitation consists only of the adaptive codebook contribution. Then the time-domain contribution and residual signal are both converted to the transform domain (using DCT). The transform-domain signals are used to determine a cut-off frequency (the upper band still containing significant pitch contribution). The time-domain excitation contribution is then filtered by removing the frequency content above the cut-off frequency. The filtered time-domain contribution in the frequency domain is subtracted from the frequency-domain residual signal, and difference signal is quantized in the frequency domain using PVQ. The quantized difference signal is then added to the filtered transformed time-domain excitation contribution, and the resulting signal is converted back to the time domain to obtain the total excitation signal.
The GSC mode is used for encoding audio signals at 7.2, and 13.2 kbit/s for WB inputs. It is also used to encode unvoiced active speech and some audio signal at 13.2 kbit/s in case of SWB inputs. Further, the GSC mode is used to encode inactive signals in case of NB, WB, SWB, and FB signals (in case DTX is off) at 7.2, 8 and 13.2kbit/s.
Figure 40: GSC encoder overview
5.2.3.5.1 Determining the subframe length
The subframe length, or number of subframes per frame, is determined depending on the bit rate and nature of encoded signal. In case of SWB unvoiced mode at 13.2 kbit.s, 4 subframes are used. For NB and WB signals at 13.2 kbit/s, 2 subframes are used in case of inactive signals or when the high frequency dynamic range flag 
is 0, where 
is an indicator when set to 1 is indicates the presence of high frequency spectral correlation and is computed in subclause 5.1.11.2.6. Otherwise 1 subframe is used (audio signal where long-time support is needed to get better frequency resolution).
For the bit rates of 7.2 and 8 kbit/s, 1 subframe is always used (NB, WB, and SWB audio signals and inactive speech signals). The number of subframe information is encoded at 13.2 kbps with 1 bit.
5.2.3.5.2 Computing time-domain excitation contribution
For the SWB unvoiced mode at 13.2 kbit/s, 4 subframes are used and the excitation is computed similar to ACELP Generic coding mode using both adaptive and fixed codebooks (see subclause 5.2.3.1). The signal is encoded using GENERIC coding type at 7.2 kbit/s, and the remaining bits are used to encode the frequency domain contribution. The target signal for FCB search is computed without low-pass filtering of ACB excitation.
In other modes where 1 or 2 subframes are used the time-domain excitation contributions consists only of the adaptive codebook contribution. This is determined using ordinary closed-loop pitch search as in subclause 5.2.3.1.4.1.
When only 1 or 2 subframe are used, for example at 7.2 and 8 kbit/s rates, the adaptive codebook excitation and pitch gain quantization use the AUDIO coding type. The pitch found is quantized using 10 bits for the first subframe and 6 bit for the following subframe, if any. In these case, he pitch gain is quantized using a 4 bits vector quantizer.
The total excitation is finally constructed based on both ACB and FCB at 13.2 UC mode or only ACB contribution for other modes using a total between 14 and 24 bits in case of 1 or 2 subframe up to 106 bits for the 4 subframe case..
5.2.3.5.3 Frequency transform of residual and time-domain excitation contribution
In the frequency-domain coding of the mixed time-domain / frequency-domain GSC mode, the residual signal and the time-domain excitation contribution are transformed to frequency domain. The time-to-frequency transform is performed using a 256-point Type IV discrete cosine transform (DCTIV) giving a resolution of 25 Hz at the internal sampling frequency of 12.8 kHz.
The DCTIV, 
, of a signal 
of length 
is defined by the following equation:
(634)
Here 
and 
refers to either residual signal 
or time-domain excitation contribution 
with DCT output 
corresponding to frequency transformed signals 
and 
, respectively.
5.2.3.5.3.1 eDCT for DCTIV
The efficient eDCT is built upon a discrete cosine transform type IV (DCTIV) but the eDCT requires less storage and has lower complexity.
The DCTIV formula in above subclause can be rewritten as:
(635)
where the values 
are given by
(636)
and 
, 
, and 
.
Hence, the eDCT is computed using a Fast Fourier Transform (FFT) of 
points on the pre-rotated data 
:
A complex DFT with length 
is applied to the rotated data 
:
(637)
Here, when 
, a simple power-2 DFT is not suitable, so it is implemented with the following low complexity 2-dimensional (
) DFT, where 
and 
are coprime factors.
To reduce complexity, an address table is introduced. It can be calculated by:
(638)
where 
, 
are coprime and satisfy the condition 
.
Here, 
. The address table 
is stored for low complexity 2-dimentional DFT, and is used to indicate which samples are used for 
-point DFT or 
-point DFT following:
a) Applying 
-point DFT to 
for 
times based on the address table 
.
The input data to the i-th (
)
-point DFT is found by seeking their addresses stored in the address table 
. For the i-th 
-point DFT, the addresses of the input data are the 
continuous elements starting from the 
element in table 
. For every time of 
-point DFT, the resulting data need to be applied a circular shift with a step of 
, where 
is the re‑ordered index, which satisfies 
.
The output of step a) is:
(639)
For the i-th (
)
-point DFT, the addresses of the input data are the 
continuous elements starting from 
, and the results are circular shifted with 
. Here is an example of circular shift, the original vector is 
, the new vector with 2 circular shift is 
.
b) Applying 
-point DFT to 
for 
times based on the address table 
.
The input data to the i-th (
)
-point DFT is found by seeking their addresses stored in the address table 
. For the i-th 
-point DFT, the addresses of the input data are the elements starting from the i-th element in table 
, each of which separated by a step of 
. For every time of 
-point DFT, the resulting data need to be applied a circular shift with a step of 
. is the re-ordered index, which satisfies 
.
The output of step b) is:
(640)
For the i-th (
)
-point DFT, the addresses of the input data are the 
continuous elements starting from 
, each of which is separated by a step of 
, and the results are circular shifted with 
. Finally, the coefficients are output according to the stored address corresponding to the address table 
.
5.2.3.5.4 Computing energy dynamics of transformed residual and quantization of noise level
The DCT of the residual is divided into 16 bands (0 to 15) of length 16 bins. For bands 7 to 14, the energy dynamic per band is computed as the square of the maximum value divided by the average value per band, scaled by a factor 10. Then the average value 
over the 8 band (from 7 to 14) is computed.
A long-term dynamic 
is updated as
(641)
is quantized with 8 levels in the rage 50-82 (50, 54, 58, 62, 66, 70, 74, 78) with quantization index 
from 0 to 7.
The noise level is computed as 
For the bit rates of 7.2 and 8 kbit/s, the noise level is low limited to 12. Thus only values 12, 13, 14, 15 are permitted and 
is quantized with 2 bits). For UC SWB mode at 13.2 kbit/s is set to 15, otherwise 
is quantized with 3 bits (values 8 to 15).
5.2.3.5.6 Find and encode the cut-off frequency
The cut-off frequency consists of the last band with significant pitch contribution (the frequency after which coding improvement brought by the time-domain excitation contribution becomes too low to be valuable). Finding the cut-off frequency starts by computing the normalized cross-correlation for each frequency band between the frequency-transformed LP residual 
and the frequency-transformed time-domain excitation contribution 
. The 256-sample DCT spectrum is divided into the 16 bands with the following number of frequency bins per band
(642)
with cumulative frequency bins per band
(643)
The last frequency 
included in each of the 16 frequency bands are defined in Hz as:
(644)
The normalized correlation per band is defined as
()
Where 
and 
.
The cross-correlation vector is then smoothed between the different frequency bands using the following relation
()
where 
, 
and 
The average of the smoothed cross-correlation vector is computed over the first 13 bands (representing 5575 Hz). It is then limited to a minimum value of 0.5 normalised between 0 and 1.
A first estimate of the cut-off frequency is obtained by finding the last frequency of a frequency band 
which minimizes the difference between the last frequency of a frequency band 
and the normalized average 
of the smoothed cross-correlation vector multiplied by the width of the spectrum of the input sound signal. That is
()
and the first estimate of the cut-off frequency is given by
()
where 
Hz.
At 7.2 and 8 kbit/s, where the normalized average 
is never really high, or to artificially increase the value of 
to give a little more weight to the time domain contribution, the value of 
is upscaled with a factor of 2.
The 8th pitch harmonic is computed from the minimum or lowest pitch lag value of the time-domain excitation contribution of all sub-frames, and the frequency band containing the 8th harmonic is determined. The final cut-off frequency is given by the higher value between the first estimate of the cut-off frequency 
and the last frequency of the frequency band in which the 8th harmonic is located 
.
The cut-off frequency is quantized with a maximum of 4 bits using the values {0, 1175, 1575, 1975, 2775, 3175, 3575, 3975, 4375, 4775, 5175, 5575, 6375}.
Some hangover is added to stabilize the decision and prevent the cut-off frequency to switch between 0 (meaning no temporal contribution) and something else too often. First for the temporal contribution to be allowed, the average normalized correlation 
and the long-term correlation 
as computed in subclause 5.1.13.5.3, the long term average pitch gain of the GSC temporal contribution 
and the last value of the cut-off frequency are compared to some threshold to decide if it is allowed to remove all the temporal contribution (cut-off frequency would be 0). In addition a hangover logic is used to diminish any undesired switching to a complete frequency model where the cut-off frequency would be 0.
For the lowest bitrate, 7.2 and 8.0 kbit/s, only 1 bit is used to send the cut-off frequency information when the coding mode is INACTIVE otherwise, the cut-off frequency is considered as greater than 0 (meaning the temporal contribution is used) and the length of the contribution is deduced from the pitch information. At 13 kbps, 4 bits are used to send the cut-off frequency allowing all the possible cut-off frequency values.
Once the cut-off frequency is determined, the transform of the time-domain excitation contribution is filtered in the frequency domain by zeroing the frequency bins situated above the cut-off frequency supplemented with a smooth transition region. The transition region is situated above the cut-off frequency and below the zeroed bins, and it allows for a smooth spectral transition between the unchanged spectrum below 
and the zeroed bins in higher frequencies.
5.2.3.5.7 Band energy computation and quantization
The filtered time-domain contribution in the frequency domain 
is subtracted from the frequency-domain residual signal 
, and the resulting difference signal in the frequency domain
is quantized with the PVQ. Before the quantization is done, some gains per frequency band 
, as defined above, are computed and quantized using a split VQ. First the gain per band on the difference signal 
is computed as :
(649)
where 
and 
are defined in subclause 5.2.3.5.6.
In case of NB content, only the first 10 bands are quantized using a split VQ. For other bandwidth, the number of band quantized depends on the bitrate. At low bit rate only 12 bands are quantized, being the band 0 to 8 plus the bands 10, 12 and 14. The band 9, 11, 13 and 15 being interpolated based on the quantized bands 8, 10, 12, and 14. The codebook used for the vector quantization are different depending of the bitrate and the bandwidth of the input signal giving a total 4 different set of codebooks.
In all cases, prior to the vector quantitation of the bands, the average gain of all the bands is subtract from the bands and vector quantized as well using 6 bits. In total between 21 and 26 bits are used to get the gain per band quantized 
depending of the bitrate.
5.2.3.5.8 PVQ Bit allocation
The PVQ is a coding technic that is flexible in its bit allocation. To decide where bits should be allocated inside the difference spectrum to quantize, some parameters are analyse as the bitrate, the cut-off frequency
, the noise level
, the coding mode (INACTIVE, AUDIO or active UC), the bit budget available and the bandwidth.
First, only a subset of bands will be sent to the PVQ for quantization. The minimum number of band is 5 out of 16. To determine the number of band, a first criteria is the bit rate, a second criteria is the cut-off frequency and another criteria is noise level. When the number of band is decided, a minimum amount of bit is spread over the number of band decided with an emphasis on the low frequencies. If some bits remain after the minimum bit allocation, then the remaining bits are split among the bands. When the number of bands and its bit allocation are found, the bands are picked from the initial spectrum of the difference signal 
based on the quantized gain of this band. The 5 first bands are always sent to the PVQ, the choice of the other bands on the energy associated to that band and the high frequency flag indicator
.
5.2.3.5.9 Quantization of difference signal
Once the bit allocation the number of band to quantize and their position in the spectrum is defined, a new vector is concatenated containing all the chosen bands. The values are then passed to the PVQ for quantization to obtain the quantized difference spectrum
. The PVQ quantization scheme is described in subclause 5.3.4.2.7.
5.2.3.5.10 Spectral dynamic and noise filling
After the quantization by the PVQ, some band are empty and many more bins are zeroed due to the low inherent to the GSC technology available. To make the frequency model as robust as possible on speech like content, the spectral dynamic is revised and some noise filling is added to the difference spectrum.
For INACTIVE content below 13.2 kbit/s, the quantized spectrum above 1.6kHz is multiplied by a factor of 0.15. For INACTIVE content at 13.2 kHz, the quantized spectrum above 2.0kHz is multiplied by a factor of 0.25. Otherwise the scaling factor for the spectral dynamic
and the frequency bin where the scaling of the spectral dynamic 
is applied is computed as follow:
()
and
()
Furthermore, for frequencies above 3.2 kHz, the spectral dynamic is limited to an amplitude of ±1 for bitrate below 13.2 kbit/s and to ± 1.5 otherwise.
This scaling is then applied to the quantized difference spectrum
, to obtain its scaled version
.
A noise filling is then applied to the whole difference spectrum. The noise level added is based on the bitrate, the coding mode and the spectral dynamic
to obtain the scaled difference spectrum with noise
on which the gain will be applied on.
5.2.3.5.11 Quantized gain addition, temporal and frequency contributions combination
Once dynamic of the quantized difference spectrum has been scaled and the noise fill has be performed, the gain of each bands is computed exactly as in subclause 5.2.3.5.7 to get gain of the quantized spectrum
. The gain per band to apply 
consists as:
()
This gain is applied to both the scaled difference spectrum with noise
and the scaled difference spectrum
and both vectors are added to the temporal contribution to get two different spectral representation of the quantized excitation in the frequency domain, one with noise fill
and the other without
as shown below.
()
and
()
5.2.3.5.12 Specifics for wideband 8kbps
The available bits are allocated to the bands of the frequency excitation signal according to the bit allocation algorithm as described in subclause 5.2.3.5.8, where the frequency excitation signal is the output of DCTIV as described in subclause 5.2.3.5.3. If the index 
of the highest frequency band with bit allocation is more than a given threshold, the bit allocation for the frequency excitation bands will be adjusted: Decrease the number of the allocated bits of the bands with more bits, and increase the number of the allocated bits of the band 
and the bands near to 
. And then, encode the frequency excitation signal with the allocated bits, where the given threshold is determined by the available bits and the resolution of the frequency excitation signal.
The details are described as follows:
- Allocate most of the available bits to the 5 lower frequency bands by the pre-determined bit allocation table;
- Allocate the remaining bits to those bands excluding the lower frequency 5 bands which have the largest band energy, if there are remaining bits after the first step;
- Search the index
of the highest frequency band with bit allocation.
If the index of the highest frequency band with bit allocation is more than a given threshold
, the bit allocation for the frequency excitation bands will be adjusted:
- Allocate bits to some more bands whose index is above
. The number of the newly bit allocated bands
is determined by the noise level
and the coding mode. - For the newly bit allocated bands, allocate 5 bits to each band. If the number of the newly bit allocated bands
, allocate 1 more bit to each band whose index starts from 4 to 
. - The total number of newly allocated bits
is 
. 
is obtained by decreasing the number of the bits allocated to the 4 lower frequency bands.
Otherwise, the original number of allocated bits to each band is not changed.
Finally, quantize and encode the frequency excitation signal according to the allocated bits.
Then, reconstruct the frequency excitation signal based on the quantized parameters. The reconstructed frequency excitation signal is corresponding to the decoded frequency excitation signal in decoder.
For the reconstructed frequency excitation signal, if the index 
of the highest frequency band with bit allocation is more than a given threshold, or there is the temporal contribution in the reconstructed frequency excitation signal, the frequency excitation signal above 
will be reconstructed by the reconstructed frequency excitation signal; otherwise, the frequency excitation signal above 
will be reconstructed by noise filling.
The detailed descriptions are as follows:
When the coding mode of previous frame is AC mode, if the last sub-band index of bit allocation 
is larger than 
or there is the temporal contribution in the reconstructed frequency excitation signal, the BWE flag 
is set to 1. It should be noted that the BWE flag 
is initialized to 0 and calculated for every frame. 
is then refined by:
()
If 
, the frequency excitation signal below 
will be reconstructed as described in subclause 5.2.3.5.11, and the frequency excitation signal above 
will be reconstructed as follows:
()
And then the frequency excitation signal 
is scaled by the quantized gains to obtain the scaled frequency excitation signal 
.
When the energy ratio between the current frame and the previous frame is in the range (0.5, 2), for any band with index range is [4, 9], if the band is bit allocated in the current frame or in the previous frame, the coefficients in the band are smoothed by weighting the coefficients of the current frame and the previous frame.
For the scaled frequency excitation signal above 
, estimate the position of the formant by LSF parameters. If the magnitudes of the coefficients near to the formant are larger than a threshold, the magnitudes are decreased to improve the perceptual quality.
Otherwise, If 
, the un-quantized coefficients, i.e. un-decoded coefficients at the decoder side will be reconstructed by noise filling as described in subclause 5.2.3.5.10.
5.2.3.5.13 Inverse DCT
After the gain has been applied and the combination in the frequency domain done, both frequency representations of the coded excitation are convert back to time domain using the exact same DCT as in subclause 5.2.3.5.3. The inverse transform is performed to get the quantized excitation 
which is the temporal representation of 
and 
which is the temporal representation of
. 
will be used to update the TDBWE while 
is used to update the internal CELP state as the adaptive codebook memory.
5.2.3.5.14 Remove pre-echo in case of onset detection
Compute the energy of the excitation 
over each 4 samples using a 4-sample sliding window, and find the more energetic section to determine a possible attack (onset). If the attack is larger than the previous frame energy plus 6 dB, the algorithm finds the energy before the attack (excluding the section where the attack has been detected) and it scales it to the level of the previous frame energy plus 6dB.