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PARTIE2.m

+%% ========================================================================
+%  PARTIE 2 — Synthese soustractive  (Q 2.1 → Q 2.4)
+%  Poly « SAR – Traitements audio : partie signal »  v1.0 (23 avril 2025)
+%  ------------------------------------------------------------------------
+%  Script sans caractere underscore, corrige pour l erreur designfilt.
+%  ------------------------------------------------------------------------
+clear; close all; clc
+Fe = 44100;                     % frequence d echantillonnage (Hz)
+addpath(pwd)                    % acces aux fichiers wav
+
+%% ========================================================================
+%% Q 2.1 — Spectres carre et dent de scie
+% -------------------------------------------------------------------------
+dur = 0.1;  f0 = 440;
+t = (0:1/Fe:dur - 1/Fe).';
+xCarre = square(2*pi*f0*t);
+xScie  = sawtooth(2*pi*f0*t);
+
+figure('Name','Q2-1 Spectres'); hold on
+plotSpectrum(xCarre,Fe,'b','Carre FFT');
+plotSpectrum(xScie ,Fe,'r','Scie  FFT');
+
+nH = 20;
+stem(f0*(1:2:(2*nH-1)), 20*log10(abs(4./(pi*(1:2:(2*nH-1))))), ...
+     'k.','DisplayName','Carre theorie');
+stem(f0*(1:nH),        20*log10(abs(2./(pi*(1:nH)))         ), ...
+     'm.','DisplayName','Scie  theorie');
+xlim([0 8*f0]); grid on; legend
+xlabel('Frequence (Hz)'); ylabel('|X| (dB)');
+title('Q 2.1  Spectres normalises');
+
+%% ========================================================================
+%% Q 2.2 — Filtre passe-bas ordre 1 : theorie et test
+% -------------------------------------------------------------------------
+dur = 0.1;  t = (0:1/Fe:dur - 1/Fe).';
+x = sawtooth(2*pi*f0*t);
+b = [0.5 0.5];  a = 1;
+
+[H,w] = freqz(b,a,4096,'whole',Fe);
+figure('Name','Q2-2 Filtre ordre 1');
+subplot(2,1,1)
+plot(w,20*log10(abs(H))); grid on
+title('|H| theorique  cos(w/2)'); xlabel('f (Hz)'); ylabel('dB')
+
+y = filter(b,a,x);
+subplot(2,1,2); hold on
+plotSpectrum(x,Fe,'k','Entree');
+plotSpectrum(y,Fe,'g','Sortie');
+xlim([0 6*f0]); grid on; legend
+title('Spectre dB  verification');
+
+soundsc([x y],Fe);               % gauche brut, droite filtre
+
+%% ========================================================================
+%% Q 2.3 — Ecoute comparative  (sources + LPF)
+% -------------------------------------------------------------------------
+forms = {'square','sawtooth','triangle'};
+fprintf('\n===== Q 2.3  ecoute comparative =====\n');
+pause(0.4)
+for k = 1:numel(forms)
+    dur = 0.5; t = (0:1/Fe:dur - 1/Fe).';
+    switch forms{k}
+        case 'triangle'
+            x = sawtooth(2*pi*f0*t,0.5).^2 .* sign(sin(2*pi*f0*t));
+        otherwise
+            x = feval(forms{k},2*pi*f0*t);
+    end
+    y = filter(b,a,x);
+    fprintf('-- %s  non filtre ...\n',forms{k});   soundsc(x,Fe); pause(dur+0.25)
+    fprintf('-- %s  filtre ...\n',forms{k});        soundsc(y,Fe); pause(dur+0.25)
+end
+fprintf('===== fin Q 2.3 =====\n');
+
+%% ========================================================================
+%% Q 2.4 — Variation Fc, ordre, FIR ou IIR
+% -------------------------------------------------------------------------
+dur = 1;  t = (0:1/Fe:dur - 1/Fe).';
+x = sawtooth(2*pi*110*t);        % scie grave (La1)
+
+% Parametres adaptes pour eviter l erreur designfilt
+dFIR8  = designfilt('lowpassfir','FilterOrder',8,  'HalfPowerFrequency',0.30);
+dFIR30 = designfilt('lowpassfir','FilterOrder',30, 'HalfPowerFrequency',0.15);
+dIIR   = designfilt('lowpassiir','FilterOrder',8,  'HalfPowerFrequency',0.20,...
+                    'DesignMethod','butter');
+
+bank = {dFIR8 ,'FIR N=8  Fc=0.30' ; ...
+        dFIR30,'FIR N=30 Fc=0.15' ; ...
+        dIIR  ,'IIR Butter N=8 Fc=0.20'};
+
+fprintf('\n===== Q 2.4  ecoute des filtres =====\n');
+for k = 1:size(bank,1)
+    y = filter(bank{k,1},x);
+    fprintf('-- %s ...\n',bank{k,2});
+    soundsc(y,Fe); pause(dur+0.35)
+end
+
+figure('Name','Q2-4 Reponses en frequence'); hold on
+for k = 1:size(bank,1)
+    [h,w] = freqz(bank{k,1},4096,Fe);
+    plot(w,20*log10(abs(h)),'DisplayName',bank{k,2});
+end
+grid on; xlabel('f (Hz)'); ylabel('dB'); legend
+title('Filtres FIR et IIR  influence de Fc et de l ordre');
+
+fprintf('===== fin Q 2.4 =====\n');
+
+%% ========================================================================
+%% === Fonction locale =====================================================
+function plotSpectrum(x,Fe,color,label)
+N = length(x);
+f = (-N/2:N/2-1)*Fe/N;
+X = fftshift(fft(x .* hann(N)));
+SdB = 20*log10(abs(X)/max(abs(X))+eps);
+plot(f,SdB,color,'LineWidth',1.2,'DisplayName',label);
+end