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rossignol/parametrique/mylevinsondurbin.m

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+%%% Algorithme de Levinson-Durbin pour la d\'etermination des param\`etres AR
+%%%
+%%% entr\'ees :
+%%%   - xx : signal
+%%%   - pp : ordre du mod\`ele AR (choisi de mani\`ere ind\'ependante)
+%%%   - fe : fr\'equence d'\'echantillonnage
+%%%
+%%% sorties :
+%%%   - aa     : les param\`etres AR
+%%%   - sigma2 : variance du bruit
+%%%   - ref    : coefficients de r\'eflexion
+%%%   - ff     : fr\'equences auxquelles la dsp a \'et\'e calcul\'ee
+%%%   - mydsp  : la dsp elle-m\^eme
+%%%
+%%% exemple : fe=32000;f0=440;xx=cos(2*pi*f0/fe*[1:1280]+2*pi*rand(1,1));mylevinsondurbin(xx,4,fe);
+%%%
+%%% S. Rossignol -- 2012
+
+function [aa, sigma2, ref, ff, mydsp] = mylevinsondurbin (xx, pp, fe)
+
+acf = xcorr(xx, pp+1, 'biased'); %% autocorr\'elation
+acf(1:pp+1) = [];                %% on enl\`eve la partie n\'egative
+acf(1) = real(acf(1));           %% Levinson-Durbin requiert c(1)==conj(c(1))
+
+ref = zeros(pp,1);
+gg = -acf(2)/acf(1);
+aa = [ gg ];
+sigma2 = real( ( 1 - gg*conj(gg)) * acf(1) ); %% real : enl\`eve une \'eventuelle
+                                              %%   partie imaginaire r\'esiduelle
+ref(1) = gg;
+for tt = 2 : pp
+  gg = -(acf(tt+1) + aa * acf(tt:-1:2)') / sigma2;
+  aa = [ aa + gg*conj(aa(tt-1:-1:1)), gg ];
+  sigma2 = sigma2 * ( 1 - real(gg*conj(gg)) );
+  ref(tt) = gg;
+end;
+aa = [1, aa];
+
+%%% densit\'e spectrale de puissance
+interm2=-j*2*pi/fe*[1:pp];
+df=0.9765625;      %%% la dsp est calcul\'ee tous les df Hz
+ff=-fe/2:df:fe/2;
+
+interm3=interm2'*ff;
+interm=1.+aa(2:pp+1)*exp(interm3);
+mydsp = sigma2./(interm.*conj(interm));
+
+% figure(1);
+% clf;
+% grid on;
+% hold on;
+% plot(ff,mydsp,'linewidth',2);
+% xlabel('frequency (in Hz)','fontsize',20);
+% ylabel('magnitude','fontsize',20);
+% hold off;
+% drawnow;
+

rossignol/parametrique/parametrique.m

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+clear;
+close all;
+
+% returns sampling frequency in Hz and data
+[y,Fs] = audioread('myson.wav');
+
+% Fs = sampling frequency, 32000 for fluteircam.wav
+lenW = 0.04*Fs; % window of lenW samples, i.e. 40 ms
+
+df=0.9765625;      %%% la dsp est calcul\'ee tous les df Hz
+ff=-Fs/2:df:Fs/2; % length 32769 for fluteircam.wav
+ffsub = ff(1:11:end); % compression x11, length 2979
+
+tt = (0:length(y)-1)/Fs;
+ttsub = (lenW/2:lenW:length(y))/Fs;
+
+dsps = zeros(length(ffsub), floor((length(y)-lenW+1)/lenW));
+
+% dsp fft
+T = 1/Fs; % Sampling period
+L = lenW; % Length of signal
+t = (0:L-1)*T; % Time vector
+fftsp = zeros(L/2+1, floor((length(y)-lenW+1)/lenW));
+fftspCpx = zeros(L/2+1, floor((length(y)-lenW+1)/lenW));
+f = Fs*(0:(L/2))/L;
+
+for i = 0:floor((length(y)-lenW+1)/lenW)
+    
+    % compute dsp AR
+    [~, ~, ~, ~, mydsp] = mylevinsondurbin(y(lenW*i+1:lenW*(i+1))',200,Fs);
+    dsps(:,i+1) = mydsp(1:11:end)'; % compression x11, length 2979
+    
+    % compute dsp fft
+    myfft = fft(y(lenW*i+1:lenW*(i+1)));
+    P2 = abs(myfft/L);
+    P1 = P2(1:L/2+1);
+    P1(2:end-1) = 2*P1(2:end-1);
+    fftsp(:,i+1) = P1;
+end
+
+% take only positive frequencies for dsp
+ffsubp = ffsub(1,(length(ffsub)-1)/2+1:end);
+dspsp = dsps((length(dsps)-1)/2+1:end,:);
+
+% plot
+figure()
+plot(tt,y)
+xlabel('temps (s)')
+ylabel('amplitude (u.a.)')
+title('signal fluteircam')
+
+% figure()
+% surf(ttsub,ffsub,dsps,'EdgeColor','None');
+% xlabel('temps (s)')
+% ylabel('fréquences (Hz)')
+% zlabel('amplitudes (u.a.)')
+% title('Full DSP AR signal fluteircam')
+
+figure()
+surf(ttsub,ffsubp,dspsp,'EdgeColor','None');
+xlabel('temps (s)')
+ylabel('fréquences (Hz)')
+zlabel('amplitudes (u.a.)')
+title('DSP AR signal fluteircam')
+
+figure()
+imagesc(ttsub,ffsubp,dspsp)
+xlabel('temps (s)')
+ylabel('fréquences (Hz)')
+title('Amplitude DSP AR signal fluteircam')
+
+figure()
+surf(ttsub,f,fftsp,'EdgeColor','None');
+xlabel('temps (s)')
+ylabel('fréquences (Hz)')
+zlabel('amplitudes (u.a.)')
+title('DSP FFT signal fluteircam')
+
+figure()
+imagesc(ttsub,f,fftsp)
+xlabel('temps (s)')
+ylabel('fréquences (Hz)')
+title('Amplitude DSP FFT signal fluteircam')
+
+
+% take max amplitude frequency
+[maxDspsp, maxIndDspsp] = max(dspsp);
+maxFfsubp = ffsubp(maxIndDspsp);
+figure
+plot(ttsub,maxFfsubp)
+xlabel('temps (s)')
+ylabel('fréquences (Hz)')
+title('Frequency max DSP AR signal fluteircam')
+
+[maxFftsp, maxIndFftsp] = max(fftsp);
+maxF = f(maxIndFftsp);
+figure
+plot(ttsub,maxF)
+xlabel('temps (s)')
+ylabel('fréquences (Hz)')
+title('Frequency max DSP FFT signal fluteircam')