## MATLAB Software for the Code Excited Linear Prediction by Karthikeyan Ramamurthy, Andreas Spanias

By Karthikeyan Ramamurthy, Andreas Spanias

This publication describes numerous modules of the Code Excited Linear Prediction (CELP) set of rules. The authors use the Federal Standard-1016 CELP MATLAB(r) software program to explain intimately a number of services and parameter computations linked to analysis-by-synthesis linear prediction. The ebook starts off with an outline of the fundamentals of linear prediction by way of an summary of the FS-1016 CELP set of rules. next chapters describe many of the modules of the CELP set of rules intimately. In each one bankruptcy, an total useful description of CELP modules is supplied in addition to special illustrations in their MATLAB(r) implementation. numerous code examples and plots are supplied to spotlight the various key CELP techniques. desk of Contents: advent to Linear Predictive Coding / Autocorrelation research and Linear Prediction / Line Spectral Frequency Computation / Spectral Distortion / The Codebook seek / The FS-1016 Decoder

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**Extra resources for MATLAB Software for the Code Excited Linear Prediction Algorithm: The Federal Standard-1016 (Synthesis Lectures on Algorithms and Software in Engineering)**

**Sample text**

Construction of LSP polynomials and computation of their zeros [62] by applying Descartes’ rule will be illustrated using MATLAB programs in the following sections. Correction of illconditioned cases that occur due to non-minimum phase LP polynomials and quantization of LSFs are also illustrated. 2) where P (z) is called the symmetric polynomial (palindromic) and Q(z) is called the anti-symmetric polynomial (anti-palindromic). This is because of the reason that P (z) has symmetric coefficients and Q(z) has anti-symmetric coefficients.

5: Inverse Levinson-Durbin recursion. 5 In order to keep the examples simple, we work with a reduced order LP polynomial. This is achieved by taking only the first four autocorrelation lags (r0_4, r_4) of the speech frame 28 2. AUTOCORRELATION ANALYSIS AND LINEAR PREDICTION (s) and forming a fourth order LP polynomial using Levinson-Durbin recursion. The coefficients are given as vectors below. Note that the vectors are given in MATLAB notation where separation using semicolon indicates a column vector.

7) j =1 −q , εi εi = εi−1 (1 − ki2 ) , ai+1 (j ) = ai (j ) + ki+1 ai (i + 1 − j ) . 4 are used to compute the coefficients of A(z). 4. 9: Frequency response of the linear prediction synthesis filter. 4 BANDWIDTH EXPANSION Bandwidth expansion by a factor of γ changes the linear predictor coefficients from a(i) to γ i a(i) and moves the poles of the LP synthesis filter inwards. 11) √ where 3 − 2 2 ≤ γ ≤ 1, and BW is the bandwidth expansion in radians. 994127 produces a bandwidth expansion of 15 Hz.