Linear prediction of audio signals

audio signal : speech.wav, handel.wav ** lab11_5.m * mw * 04/25/2007

Contents

Input dialog

prompt = {'Order of predictor p'};
dlg_title = 'lab11_4'; num_lines = 1; def = {'3'};
answer = inputdlg(prompt,dlg_title,num_lines,def);
if isempty(answer)
    Np = 3;                     % default
else
    Np = str2num(answer{1});    % prediction order
end
[x,fs,bits]=wavread('speech');  % speech signal
% [x,fs,bits]=wavread('handel'); % audio signal
Lx = length(x);                 % number of samples
soundsc(x,fs,bits);

MATLAB Signal Processing Toolbox

[bp E] = lpc(x,Np);
disp('lpc : Prediction filter coefficients')
disp(bp)
disp('lpc : Variance of prediction error')
disp(E)
k = tf2latc(bp);
disp('lpc : Reflection coefficients')
disp(k)

lpc : Prediction filter coefficients
    1.0000   -1.2238    0.2551   -0.1177    0.0778   -0.3082    0.3622    0.0136

lpc : Variance of prediction error
  6.4467e-004

lpc : Reflection coefficients
   -0.9828
    0.4721
    0.1603
    0.2181
    0.1796
    0.3789
    0.0136

Linear prediction (long term)

Rxx = xcorr(x,'unbiased'); % estimate mean autocorrelation sequence
r = Rxx(Lx:Lx+Np+1);       % relevant coefficients for Levinson-Durbin alg. Rxx[0],Rxx[1],...
[a,E,k] = levinson(r,Np);  % Levinson-Durbin alg. (Signal Processing Toolbox)
[e g] = latcfilt(k,x);     % residuum e[n] (prediction error) (Signal Processing Toolbox)
clear g;                   % delete backward lattice filter output signal
Ree = xcorr(e,'unbiased'); % estimate autocorrelation sequence of residuum
fprintf('lab11_4 : Reflection coefficients\n')
for m=1:Np
    fprintf([' k',num2str(m),' = %g \n'],k(m))
end
fprintf('Audio signal        Rxx[0] = %g \n',Rxx(Lx))
fprintf('Residual signal     Ree[0] = %g \n',Ree(Lx))
fprintf('Prediction error    E      = %g \n',E)
fprintf('Prediction gain     Gp     = %g dB\n\n',10*log10(Rxx(Lx)/Ree(Lx)))
pause(1+Lx/fs)
soundsc(e,fs,bits);        % residuum

lab11_4 : Reflection coefficients
 k1 = -0.982861 
 k2 = 0.47298 
 k3 = 0.16021 
 k4 = 0.218412 
 k5 = 0.179777 
 k6 = 0.37979 
 k7 = 0.0129872 
Audio signal        Rxx[0] = 0.031681 
Residual signal     Ree[0] = 0.00064467 
Prediction error    E      = 0.000642065 
Prediction gain     Gp     = 16.9146 dB

Inverse filtering (all-pole filter)

[y g] = latcfilt(k,1,e);    % all-pole filter (Signal Processing Toolbox)
Ryy = xcorr(y,'unbiased');  % estimate mean autocorrelation sequence
pause(1+Lx/fs)
soundsc(y,fs,bits);         % reconstructed signal

Graphics

figure('Name',['lab11_4 : pth order linear prediction with lattice structure -> p = ',...
    num2str(Np),' , fs = ',num2str(fs)],'NumberTitle','off');
L2 = 400;
t1 = (0:Lx-1)/fs; t2 = 1e3*(0:L2)/fs;
subplot(3,2,1), plot(t1,x(1:Lx)),grid
xlabel('t in s \rightarrow'), ylabel('x(t) \rightarrow')
title('Audio signal (original)')
subplot(3,2,2), plot(t2,Rxx(Lx:Lx+L2)/Rxx(Lx)),grid
xlabel('\tau in ms \rightarrow'), ylabel('R_{xx}(\tau) / R_{xx}(0) \rightarrow')
title('ACF')
subplot(3,2,3), plot(t1,e(1:Lx)),grid
xlabel('t in s \rightarrow'), ylabel('e(t) \rightarrow')
title('Prediction error')
subplot(3,2,4), plot(t2,Ree(Lx:Lx+L2)/Rxx(Lx),0,Ree(Lx)/Rxx(Lx),'o'),grid
xlabel('\tau in ms \rightarrow'), ylabel('R_{ee}(\tau) / R_{xx}(0) \rightarrow')
title('ACF')
subplot(3,2,5), plot(t1,y(1:Lx)),grid
xlabel('t in s \rightarrow'), ylabel('y(t) \rightarrow')
title('Audio signal (restored)')
subplot(3,2,6), plot(t2,Ryy(Lx:Lx+L2)/Rxx(Lx)),grid
xlabel('\tau in ms \rightarrow'), ylabel('R_{yy}(\tau) / R_{xx}(0) \rightarrow')
title('ACF')

Published with MATLAB® 7.3