3.2 Symbols
26.1903GPPAdaptive Multi-Rate - Wideband (AMR-WB) speech codecSpeech codec speech processing functionsTranscoding functionsTS
For the purposes of this TS, the following symbols apply:
The inverse filter with unquantized coefficients
The inverse filter with quantized coefficients
The speech synthesis filter with quantized coefficients
The unquantized linear prediction parameters (direct form coefficients)
The quantified linear prediction parameters
The order of the LP model
The perceptual weighting filter (unquantized coefficients)
The perceptual weighting factor
The integer pitch lag nearest to the closed‑loop fractional pitch lag of the subframe
The adaptive pre‑filter coefficient (the quantified pitch gain)
Pre‑processing high‑pass filter
LP analysis window
Length of the first part of the LP analysis window 
Length of the second part of the LP analysis window 
The auto‑correlations of the windowed speech 
Lag window for the auto‑correlations (60 Hz bandwidth expansion)
The bandwidth expansion in Hz
The sampling frequency in Hz
The modified (bandwidth expanded) auto‑correlations
The prediction error in the ith iteration of the Levinson algorithm
The ith reflection coefficient
The jth direct form coefficient in the ith iteration of the Levinson algorithm
Symmetric ISF polynomial
Antisymmetric ISF polynomial
Polynomial 
Polynomial 
with roots 
and 
eliminated
The immittance spectral pairs (ISPs) in the cosine domain
An ISP vector in the cosine domain
The quantified ISP vector at the ith subframe of the frame n
The immittance spectral frequencies (ISFs)
A mth order Chebyshev polynomial
The coefficients of the polynomials 
and 
The coefficients of the polynomials 
and 
The coefficients of either 
or 
Sum polynomial of the Chebyshev polynomials
Cosine of angular frequency 
Recursion coefficients for the Chebyshev polynomial evaluation
The immittance spectral frequencies (ISFs) in Hz
The vector representation of the ISFs in Hz
The mean‑removed ISF vector at frame n
The ISF prediction residual vector at frame n
The predicted ISF vector at frame n
The quantified residual vector at the past frame
The quantified ISF subvector 
at quantization index k
The distance between the immittance spectral frequencies 
and 
The impulse response of the weighted synthesis filter
The weighted synthesis filter
The integer nearest to the fractional pitch lag of the previous (1st or 3rd) subframe
The windowed speech signal
The weighted speech signal
Reconstructed speech signal
The target signal for adaptive codebook search
, 
The target signal for algebraic codebook search
The LP residual signal
The fixed codebook vector
The adaptive codebook vector
The filtered adaptive codebook vector
The past filtered excitation
The excitation signal
The gain‑scaled emphasized excitation signal
The best open‑loop lag
Minimum lag search value
Maximum lag search value
Correlation term to be maximized in the adaptive codebook search
The interpolated value of 
for the integer delay k and fraction t
Correlation term to be maximized in the algebraic codebook search at index k
The correlation in the numerator of 
at index k
The energy in the denominator of 
at index k
The correlation between the target signal 
and the impulse response 
, i.e., backward filtered target
The lower triangular Toepliz convolution matrix with diagonal 
and lower diagonals 
The matrix of correlations of 
The elements of the vector d
The elements of the symmetric matrix 
The innovation vector
The correlation in the numerator of 
The position of the ith pulse
The amplitude of the ith pulse
The number of pulses in the fixed codebook excitation
The energy in the denominator of 
The normalized long‑term prediction residual
The signal used for presetting the signs in algebraic codebook search
The sign signal for the algebraic codebook search
Sign extended backward filtered target
The modified elements of the matrix 
, including sign information
, 
The fixed codebook vector convolved with 
The mean‑removed innovation energy (in dB)
The mean of the innovation energy
The predicted energy
The MA prediction coefficients
The quantified prediction error at subframe k
The mean innovation energy
The prediction error of the fixed‑codebook gain quantization
The quantization error of the fixed‑codebook gain quantization
The states of the synthesis filter 
The perceptually weighted error of the analysis‑by‑synthesis search
The gain scaling factor for the emphasized excitation
The fixed‑codebook gain
The predicted fixed‑codebook gain
The quantified fixed codebook gain
The adaptive codebook gain
The quantified adaptive codebook gain
A correction factor between the gain 
and the estimated one 
The optimum value for 
Gain scaling factor