#### Spectral Envelope by Linear Prediction

Finally, let's do an LPC window. It had better be good because the LPC model is exact for this example.

M = 6; % Assume three formants and no noise % compute Mth-order autocorrelation function: rx = zeros(1,M+1)'; for i=1:M+1, rx(i) = rx(i) + speech(1:nsamps-i+1) ... * speech(1+i-1:nsamps)'; end % prepare the M by M Toeplitz covariance matrix: covmatrix = zeros(M,M); for i=1:M, covmatrix(i,i:M) = rx(1:M-i+1)'; covmatrix(i:M,i) = rx(1:M-i+1); end % solve "normal equations" for prediction coeffs: Acoeffs = - covmatrix \ rx(2:M+1) Alp = [1,Acoeffs']; % LP polynomial A(z) dbenvlp = 20*log10(abs(freqz(1,Alp,nspec)')); dbsspecn = dbsspec + ones(1,nspec)*(max(dbenvlp) ... - max(dbsspec)); % normalize plot(f,[max(dbsspecn,-100);dbenv;dbenvlp]); grid;

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Spectral Envelope by the Cepstral Windowing Method