## 5.2.5 Quantization of the ISP coefficients

26.1903GPPAdaptive Multi-Rate - Wideband (AMR-WB) speech codecSpeech codec speech processing functionsTranscoding functionsTS

The LP filter coefficients are quantized using the ISP representation in the frequency domain; that is

( 21 )

where *f _{i}* are the ISFs in Hz [0,6400] and

*f*=12800 is the sampling frequency. The ISF vector is given by = [

_{s}*f*

_{0}

*f*

_{1},…,

*f*

_{15}], with

*t*denoting transpose.

A 1st order MA prediction is applied, and the residual ISF vector is quantified using a combination of split vector quantization (SVQ) and multi-stage vector quantization (MSVQ). The prediction and quantization are performed as follows. Let denote the mean‑removed ISF vector at frame . The prediction residual vector **r**(*n*) is given by:

( 22 )

where **p**(*n*) is the predicted LSF vector at frame *n*. First order moving‑average (MA) prediction is used where:

, ( 23 )

where is the quantized residual vector at the past frame.

The ISF residual vector is quantized using split-multistage vector quantization S-MSVQ. The vector is split into 2 subvectors **r**_{1}(*n*) and **r**_{2}(*n*) of dimensions 9 and 7, respectively. The 2 subvectors are quantized in two stages. In the first stage **r**_{1}(*n*) is quantized with 8 bits and **r**_{2}(*n*) with 8 bits.

For 8.85 ,12.65, 14.25, 15.85, 18.25, 19.85, 23.05 or 23.85 kbit/s modes, the quantization error vectors are split in the next stage into 3 and 2 subvectors, respectively. The subvectors are quantized using the bit-rates described in Table 2.

Table 2. Quantization of ISP vector for the 8.85 ,12.65, 14.25, 15.85, 18.25, 19.85, 23.05 or 23.85 kbit/s modes

1. UNQUANTIZED 16-ELEMENT-LONG ISP VECTOR |
||||

2. STAGE 1 () 8 bits |
2. STAGE 1 () 8 bits |
|||

3. STAGE 2 () 6 bits |
3. STAGE 2 () 7 bits |
3. STAGE 2 () 7 bits |
3. STAGE 2 () 5 bits |
3. STAGE 2 () 5 bits |

For 6.60 kbit/s mode, the quantization error vectors are split in the next stage into 2 and 1 subvectors, respectively. The subvectors are quantized using the bit-rates described in Table 3.

Table 3. Quantization of ISP vector for the 6.60 kbit/s mode

1. UNQUANTIZED 16-ELEMENT-LONG ISP VECTOR |
|||

2. STAGE 1 () 8 bits |
2. STAGE 1 () 8 bits |
||

3. STAGE 2 () 7 bits |
3. STAGE 2 () 7 bits |
3. STAGE 2 () 6 bits |

A squared error ISP distortion measure is used in the quantization process. In general, for an input ISP or error residual subvector **r*** _{i}*,

*i*=1,2 and a quantized vector at index

*k*, , the quantization is performed by finding the index

*k*which minimizes

, ( 24 )

where *m* and *n* are the first and last elements of the subvector.