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