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PARTIE1.m

+%% ========================================================================
+%  PARTIE 1 — Synthese additive (Q 1.1 → Q 1.5)
+%  Poly « SAR – Traitements audio : partie signal »  v1.0 (23 avril 2025)
+%  ------------------------------------------------------------------------
+%  AUCUN caractere « _ » dans les noms de variables ou de fonctions.
+%  Les fichiers .wav peuvent garder leur nom d origine.
+%  ------------------------------------------------------------------------
+clear; close all; clc
+
+%% ------------------------------------------------------------------------
+%% Question 1.1  – Spectre et frequence fondamentale
+% -------------------------------------------------------------------------
+fichiers = { ...
+    "wav/piano_chord.wav", ...
+    "wav/nylon-guitar.wav", ...
+    "wav/single_tone_celtic-harp-a3.wav" };
+
+figure('Name','Q1-1 Spectres'); hold on
+fundamentale = zeros(numel(fichiers),1);
+nom = {"piano","guitare","harpe"}
+for k = 1:numel(fichiers)
+    [x, Fe] = audioread(fichiers{k});
+    x = mean(x,2);                          % mono
+    N = length(x);
+    X = fftshift( fft( x .* hann(N) ) );    % fenetrage Hann
+    f = linspace(-Fe/2, Fe/2, N);
+    amp = 20*log10( abs(X) + eps );
+
+    plot(f, amp, 'DisplayName', nom{k});
+
+    % premiere raie cote positif = fondamentale
+    [~, idx] = max( amp(f > 0) );
+    posVect = find(f > 0);
+    idxPos  = posVect(idx);
+    fondamentale(k) = f(idxPos);
+end
+grid on; xlabel('Frequence (Hz)'); ylabel('Amplitude (dB)');
+legend('Interpreter','none'); title('Q 1.1  Spectres normalises');
+
+%% ------------------------------------------------------------------------
+%% Question 1.2  – Inharmonicite de deux pianos
+% -------------------------------------------------------------------------
+[p1, Fe1] = audioread("wav/single_tone_piano1.wav");
+[p2, Fe2] = audioread("wav/single_tone_piano2.wav");
+
+analyse = @(x, Fe) ...
+    struct( ...
+        "N", length(x), ...
+        "f", linspace(-Fe/2, Fe/2, length(x)), ...
+        "amp", 20*log10( abs( fftshift( fft( mean(x,2) ) ) ) + eps ) );
+
+S1 = analyse(p1, Fe1);
+S2 = analyse(p2, Fe2);
+
+% fondamentale de chaque piano (pic principal > 0)
+[~, id1] = max( S1.amp( S1.f > 0 ) );
+[~, id2] = max( S2.amp( S2.f > 0 ) );
+idxPos1 = find(S1.f > 0); idxPos2 = find(S2.f > 0);
+f1P1 = S1.f( idxPos1(id1) );
+f1P2 = S2.f( idxPos2(id2) );
+
+% huit composantes dominantes
+kmax = 8;
+[pks1, locs1] = findpeaks( S1.amp(S1.f > 0), 'SortStr','descend', ...
+                           'NPeaks', kmax );
+[pks2, locs2] = findpeaks( S2.amp(S2.f > 0), 'SortStr','descend', ...
+                           'NPeaks', kmax );
+fMes1 = S1.f( S1.f > 0 );
+fMes1 = fMes1(locs1).';
+fMes2 = S2.f( S2.f > 0 );
+fMes2 = fMes2(locs2).';
+
+fTheo1 = f1P1*(1:kmax).';
+fTheo2 = f1P2*(1:kmax).';
+
+xi1 = 1200*abs( log2( fMes1 ./ fTheo1 ) );   % cents
+xi2 = 1200*abs( log2( fMes2 ./ fTheo2 ) );
+
+inharmTot1 = sum(xi1);
+inharmTot2 = sum(xi2);
+
+fprintf('\nInharmonicite totale Piano 1 : %.2f cents\n', inharmTot1);
+fprintf('Inharmonicite totale Piano 2 : %.2f cents\n', inharmTot2);
+
+figure('Name','Q1-2 Spectres pianos');
+plot(S1.f, S1.amp, 'b', S2.f, S2.amp, 'r'); grid on
+xlabel('Frequence (Hz)'); ylabel('Amplitude (dB)');
+legend('Piano 1','Piano 2'); title('Q 1.2  Comparaison spectrale');
+
+%% ------------------------------------------------------------------------
+%% Question 1.3  – Synthese additive (8 harmoniques)
+% -------------------------------------------------------------------------
+if inharmTot1 <= inharmTot2
+    fBase   = f1P1;
+    fMes    = fMes1;
+    ampLin  = 10.^(pks1/20);
+    FeSynt  = Fe1;
+    tag     = 'piano1';
+else
+    fBase   = f1P2;
+    fMes    = fMes2;
+    ampLin  = 10.^(pks2/20);
+    FeSynt  = Fe2;
+    tag     = 'piano2';
+end
+
+ampLin = ampLin(1:kmax);
+ampLin = ampLin / max(ampLin);            % normalisation
+
+dur = 2;                                  % secondes
+t = 0 : 1/FeSynt : dur - 1/FeSynt;
+yAdd = zeros(size(t));
+
+for n = 1:kmax
+    yAdd = yAdd + ampLin(n) * sin(2*pi*fMes(n)*t);
+end
+yAdd = yAdd.' / max(abs(yAdd));           % colonne + normalisation
+
+audiowrite("wav/" + tag + "_synth8h.wav", yAdd, FeSynt);
+soundsc(yAdd, FeSynt);
+
+%% ------------------------------------------------------------------------
+%% Question 1.4 – Application enveloppe ADSR
+% -------------------------------------------------------------------------
+clear t yAdd
+
+[ys, Fe] = audioread("wav/" + tag + "_synth8h.wav");
+Nsig = length(ys);
+
+tA = 0.03;       % Attack
+tD = 0.12;       % Decay
+sustainLvl = 0.7;
+tR = 0.30;       % Release
+
+nA = round(tA*Fe);
+nD = round(tD*Fe);
+nR = round(tR*Fe);
+nS = max(Nsig - nA - nD - nR, 0);
+
+env = [ linspace(0,1,nA), ...
+        linspace(1,sustainLvl,nD), ...
+        sustainLvl*ones(1,nS), ...
+        linspace(sustainLvl,0,nR) ];
+env = env(1:Nsig).';                       % mise a la meme taille
+
+yAdsr = ys .* env;
+yAdsr = yAdsr / max(abs(yAdsr));
+
+soundsc(yAdsr, Fe);
+audiowrite("wav/" + tag + "_synth8h_ADSR.wav", yAdsr, Fe);
+
+figure('Name','Q1-4 ADSR'); plot((0:Nsig-1)/Fe, env); grid on
+xlabel('Temps (s)'); ylabel('Amplitude');
+title('Enveloppe ADSR');
+
+%% ------------------------------------------------------------------------
+%% Question 1.5 – Synthese par IFFT
+% -------------------------------------------------------------------------
+clearvars -except tag FeSynt kmax fMes ampLin
+
+dur = 2;
+Nsyn = round(dur * FeSynt);
+Xspec = zeros(Nsyn,1);
+
+for n = 1:kmax
+    k = round(fMes(n) / FeSynt * Nsyn) + 1;
+    A = ampLin(n) / 2;
+    Xspec(k)          = A;
+    Xspec(Nsyn - k + 2) = conj(A);
+end
+
+yIdft = real( ifft( Xspec ) );
+yIdft = yIdft / max(abs(yIdft));
+
+audiowrite("wav/" + tag + "_synth8h_iDFT.wav", yIdft, FeSynt);
+soundsc(yIdft, FeSynt);
+
+% comparaison rapide
+[yt, ~] = audioread("wav/" + tag + "_synth8h.wav");
+Lcmp = min(length(yt), length(yIdft));
+errMax = max( abs( yt(1:Lcmp) - yIdft(1:Lcmp) ) );
+fprintf('\nErreur max entre somme sinus et IFFT : %.3e\n', errMax);
+
+%% ========================================================================
+%% === Fin PARTIE 1 =======================================================