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+%% SYNTHÈSE ADDITIVE
+
+% Question 1.1 :
+% filename = '/Users/alexandredherissart/Desktop/SAR Audio/single_tone_clarinet-a3.wav';
+% figureTitle = 'Spectre en amplitude de clarinette';
+% plotColor = [1, 0.5, 0];
+%
+% [x, fe] = audioread(filename);
+% if size(x,2) > 1
+% x = x(:,1);
+% end
+% N = length(x);
+%
+% X = fft(x);
+% Xs = fftshift(X);
+% f = linspace(-fe/2, fe/2, N);
+% A_dB = 20*log10(abs(Xs) + eps);
+%
+% % Recherche de la fréquence fondamentale
+% [~, idx_max] = max(abs(Xs));
+% f1 = abs(f(idx_max));
+%
+% figure;
+% plot(f, A_dB, 'Color', plotColor, 'LineWidth', 1.5);
+% grid on;
+% title(figureTitle, 'Interpreter', 'none');
+% xlabel('Fréquence (Hz)');
+% ylabel('Amplitude (dB)');
+% hold on;
+%
+% % Annotation de la fréquence fondamentale
+% yl = ylim;
+% plot([f1 f1], yl, '--k', 'LineWidth', 1);
+% text(f1, yl(2)-5, sprintf('f1 = %.2f Hz', f1), ...
+% 'HorizontalAlignment', 'left', 'BackgroundColor', 'w', 'EdgeColor', 'k');
+%
+% hold off;
+
+% Question 1.2
+% nmax = 8;
+% pct = 0.05;
+%
+% [x1, fs] = audioread('/Users/alexandredherissart/Desktop/SAR Audio/single_tone_piano1.wav');
+% [x2, ~ ] = audioread('/Users/alexandredherissart/Desktop/SAR Audio/single_tone_piano2.wav');
+%
+% Nfft = 2^nextpow2( max(length(x1), length(x2)) );
+% X1 = fftshift( fft(x1, Nfft) );
+% X2 = fftshift( fft(x2, Nfft) );
+% f = linspace(-fs/2, fs/2, Nfft);
+%
+% figure;
+% plot(f, 20*log10(abs(X1)), 'b'); hold on;
+% plot(f, 20*log10(abs(X2)), 'r');
+% xlabel('Hz');
+% ylabel('dB');
+% legend('Piano 1','Piano 2');
+% title('Spectres comparés de piano1 et piano2');
+%
+% pos = f >= 0;
+% [fmax1, idx1] = max(abs(X1(pos)));
+% [fmax2, idx2] = max(abs(X2(pos)));
+% fp = f(pos);
+% f1_1 = fp(idx1);
+% f1_2 = fp(idx2);
+%
+% fh1 = zeros(1,nmax);
+% fh2 = zeros(1,nmax);
+% for n = 1:nmax
+% % Piano 1
+% mask1 = (f > n*f1_1*(1-pct)) & (f < n*f1_1*(1+pct));
+% [~, k1] = max(abs(X1(mask1)));
+% idx_m1 = find(mask1);
+% fh1(n) = f(idx_m1(k1));
+% % Piano 2
+% mask2 = (f > n*f1_2*(1-pct)) & (f < n*f1_2*(1+pct));
+% [~, k2] = max(abs(X2(mask2)));
+% idx_m2 = find(mask2);
+% fh2(n) = f(idx_m2(k2));
+% end
+%
+% n = 1:nmax;
+% xi1 = 1200 * log2( fh1 ./ (n * f1_1) );
+% xi2 = 1200 * log2( fh2 ./ (n * f1_2) );
+%
+% rms1 = sqrt(mean(xi1.^2));
+% rms2 = sqrt(mean(xi2.^2));
+% fprintf('\nRMS inharmonicité Piano1 : %.2f \n', rms1);
+% fprintf('RMS inharmonicité Piano2 : %.2f \n', rms2);
+%
+% if rms1 < rms2
+% fprintf('\n=> Le piano 1 est plus harmonieux .\n');
+% else
+% fprintf('\n=> Le piano 2 est plus harmonieux .\n');
+% end
+
+% Question 1.3 :
+% filename = '/Users/alexandredherissart/Desktop/SAR Audio/single_tone_piano1.wav';
+% nmax = 8;
+% win_rel = 0.05;
+%
+% [x, fs] = audioread(filename);
+% x = x(:,1);
+% N = length(x);
+% Nfft = 2^nextpow2(N);
+% X = fft(x, Nfft);
+% Xs = fftshift(X);
+% f = linspace(-fs/2, fs/2, Nfft);
+%
+% % Détection de la fondamentale
+% pos = (f >= 0);
+% [~, ix0] = max(abs(Xs(pos)));
+% fp = f(pos);
+% f1 = fp(ix0);
+%
+% A = zeros(nmax,1);
+% for n = 1:nmax
+% f0 = n*f1;
+% mask = (f >= f0*(1-win_rel)) & (f <= f0*(1+win_rel));
+% [~, loc] = max(abs(Xs(mask)));
+% idx = find(mask);
+% idx_pk = idx(loc);
+% A(n) = 2*abs(Xs(idx_pk)) / Nfft;
+% end
+%
+% % Synthèse additive
+% t = (0:N-1)/fs;
+% x_synth = zeros(size(t));
+% for n = 1:nmax
+% x_synth = x_synth + A(n)*sin(2*pi*n*f1*t);
+% end
+%
+% % Écoute et sauvegarde
+% sound(x_synth, fs);
+% audiowrite('synth_piano1.wav', x_synth, fs);
+
+% Question 1.4
+% [y, fs] = audioread('/Users/alexandredherissart/Desktop/SAR Audio/synth_piano1.wav');
+% N = length(y);
+%
+% A = round(0.1 * N); % Attack = 10%
+% D = round(0.1 * N); % Decay = 10%
+% R = round(0.1 * N); % Release= 10%
+% S = N - (A + D + R); % Sustain
+%
+% % Enveloppe
+% env = [ ...
+% linspace(0, 1, A), ...
+% linspace(1, 0.7, D), ...
+% 0.7 * ones(1, S), ...
+% linspace(0.7, 0, R) ...
+% ];
+%
+% y_env = y(1:length(env)) .* env';
+%
+% t2 = (0:length(env)-1)/fs;
+% figure;
+% subplot(2,1,1);
+% plot(t2, env, 'LineWidth',1.2);
+% grid on;
+% title('Enveloppe ADSR simple');
+% xlabel('Temps (s)');
+% ylabel('Amplitude enveloppe');
+%
+% subplot(2,1,2);
+% plot(t2, y_env);
+% grid on;
+% title('Signal synthétisé avec ADSR');
+% xlabel('Temps (s)');
+% ylabel('Amplitude signal');
+%
+% soundsc(y_env, fs);
+% audiowrite('synth_ADSR_piano1.wav', y_env, fs);
+
+% Question 1.5 :
+% filename = '/Users/alexandredherissart/Desktop/SAR Audio/single_tone_piano1.wav';
+% nmax = 8;
+% win_rel = 0.05;
+%
+% [x, fs] = audioread(filename);
+% x = x(:,1);
+% N = length(x);
+% Nfft = 2^nextpow2(N);
+% X = fft(x, Nfft);
+% Xs = fftshift(X);
+% f = linspace(-fs/2, fs/2, Nfft);
+%
+% % Détection de la fondamentale
+% pos = (f >= 0);
+% [~, idx0] = max(abs(Xs(pos)));
+% fp = f(pos);
+% f1 = fp(idx0);
+%
+% % Méthode 1 : Synthèse par IFFT
+% Ys_trunc = zeros(size(Xs));
+% for n = 1:nmax
+% f0 = n * f1;
+% mask = abs(f - f0) <= f0 * win_rel;
+% idx_pos = find(mask, 1, 'first');
+% idx_neg = Nfft - idx_pos + 1;
+% Ys_trunc(idx_pos) = Xs(idx_pos);
+% Ys_trunc(idx_neg) = Xs(idx_neg);
+% end
+% Y_trunc = ifftshift(Ys_trunc);
+% y_ifft = real(ifft(Y_trunc, Nfft));
+% y_ifft = y_ifft(1:N);
+%
+% % Méthode 2 : Synthèse additive
+% A = zeros(nmax,1);
+% for n = 1:nmax
+% f0 = n * f1;
+% mask = (f >= f0*(1-win_rel)) & (f <= f0*(1+win_rel));
+% [~, loc] = max(abs(Xs(mask)));
+% idx = find(mask);
+% A(n) = 2*abs(Xs(idx(loc))) / Nfft;
+% end
+%
+% t = (0:N-1)/fs;
+% x_synth = zeros(size(t));
+% for n = 1:nmax
+% x_synth = x_synth + A(n) * sin(2*pi*n*f1*t);
+% end
+%
+% figure;
+% subplot(3,1,1);
+% plot(t, x);
+% title('Signal original');
+% xlabel('Temps (s)'); ylabel('Amplitude'); grid on;
+%
+% subplot(3,1,2);
+% plot(t, y_ifft);
+% title('Synthèse IFFT (8 harmoniques)');
+% xlabel('Temps (s)'); ylabel('Amplitude'); grid on;
+%
+% subplot(3,1,3);
+% plot(t, x_synth);
+% title('Synthèse additive (8 harmoniques)');
+% xlabel('Temps (s)'); ylabel('Amplitude'); grid on;
+%
+% % Écoute et sauvegarde
+% soundsc(y_ifft, fs);
+% audiowrite('synth_ifft_8harm.wav', y_ifft, fs);
+%
+% sound(x_synth, fs);
+% audiowrite('synth_additive_8harm.wav', x_synth, fs);
+
+
+%% SYNTHÈSE SOUSTRACTIVE
+
+% Question 2.1 :
+% fs = 8000;
+% f0 = 440;
+% t = 0:1/fs:2/f0;
+%
+% % signaux
+% x_sq = square(2*pi*f0*t);
+% x_sd = sawtooth(2*pi*f0*t);
+%
+% % spectres
+% Nfft = 1024;
+% f = linspace(-fs/2, fs/2, Nfft);
+% Xsq = fftshift(fft(x_sq, Nfft));
+% Xsd = fftshift(fft(x_sd, Nfft));
+%
+% figure;
+% subplot(2,2,1);
+% plot(t, x_sq);
+% title('Signal carré'); xlabel('Temps (s)'); ylabel('Amplitude');
+% grid on;
+%
+% subplot(2,2,2);
+% plot(t, x_sd);
+% title('Signal dent de scie'); xlabel('Temps (s)'); ylabel('Amplitude');
+% grid on;
+%
+% S = abs(fft(x_sq));
+% D = abs(fft(x_sd));
+% f = (0:N-1)*fs/N;
+%
+% figure;
+% subplot(2,1,1);
+% stem(f(1:10), S(1:10));
+% title('Spectre signal carré'); xlabel('Hz'); ylabel('|S|');
+%
+% subplot(2,1,2);
+% stem(f(1:10), D(1:10));
+% title('Spectre dent de scie'); xlabel('Hz'); ylabel('|D|');
+
+% Question 2.2 :
+% fs = 8000;
+% f0 = 440;
+% t = 0:1/fs:2/f0;
+% Nfft = 1024;
+%
+% x_sq = square(2*pi*f0*t);
+% x_sd = sawtooth(2*pi*f0*t);
+%
+% % Définition du filtre y[k]
+% b = [1 1]/2;
+% a = 1;
+%
+% % Spectres d’entrée
+% f = linspace(-fs/2, fs/2, Nfft);
+% Xsq = fftshift(fft(x_sq, Nfft));
+% Xsd = fftshift(fft(x_sd, Nfft));
+%
+% % Réponse théorique du filtre
+% w = 2*pi * f / fs;
+% Hth = (1 + exp(-1j*w)) / 2;
+% Hmag = abs(Hth);
+%
+% % Spectres de sortie théoriques (|H|·|X|)
+% Ysq_th = Hmag .* abs(Xsq);
+% Ysd_th = Hmag .* abs(Xsd);
+%
+% % Simulation par filtrage et FFT des sorties
+% y_sq = filter(b, a, x_sq);
+% y_sd = filter(b, a, x_sd);
+% Ysq_im = fftshift(fft(y_sq, Nfft));
+% Ysd_im = fftshift(fft(y_sd, Nfft));
+%
+% figure;
+%
+% % Carré
+% subplot(2,1,1);
+% plot(f, 20*log10(Ysq_th + eps), 'k-', 'LineWidth',1.3); hold on;
+% plot(f, 20*log10(abs(Ysq_im) + eps), 'r--','LineWidth',1.2);
+% xlim([-3000 3000]);
+% xlabel('Fréquence (Hz)');
+% ylabel('Amplitude (dB)');
+% title('Signal carré filtré : théorie vs simulation');
+% legend('Théorique |H|\cdot|X|','Simulation filter→FFT','Location','Best');
+% grid on;
+%
+% % Dent de scie
+% subplot(2,1,2);
+% plot(f, 20*log10(Ysd_th + eps), 'k-', 'LineWidth',1.3); hold on;
+% plot(f, 20*log10(abs(Ysd_im) + eps), 'r--','LineWidth',1.2);
+% xlim([-3000 3000]);
+% xlabel('Fréquence (Hz)');
+% ylabel('Amplitude (dB)');
+% title('Signal dent de scie filtré : théorie vs simulation');
+% legend('Théorique |H|\cdot|X|','Simulation filter→FFT','Location','Best');
+% grid on;
+
+% Question 2.3 :
+% fs = 8000;
+% f0 = 440;
+% T = 1;
+% t = 0:1/fs:T-1/fs;
+%
+% % Enveloppe ADSR identique pour tous
+% A = round(0.1*fs);
+% D = round(0.1*fs);
+% R = round(0.1*fs);
+% S = length(t) - (A+D+R);
+% env = [linspace(0,1,A), ...
+% linspace(1,0.7,D), ...
+% 0.7*ones(1,S), ...
+% linspace(0.7,0,R)];
+%
+% x_sq = square(2*pi*f0*t);
+% x_sd = sawtooth(2*pi*f0*t);
+%
+% % Synthèse soustractive (filtre passe-bas)
+% b = [1 1]/2; a = 1;
+% y_sq_sub = filter(b,a, x_sq .* env);
+% y_sd_sub = filter(b,a, x_sd .* env);
+%
+% % Synthèse additive
+% y_sq_add = zeros(size(t));
+% for n = 1:10
+% y_sq_add = y_sq_add + (4/(pi*(2*n-1))) * sin(2*pi*(2*n-1)*f0*t);
+% end
+% y_sq_add = y_sq_add .* env;
+%
+% y_sd_add = zeros(size(t));
+% for n = 1:10
+% y_sd_add = y_sd_add + (2/(pi*n)) * (-1)^(n+1) * sin(2*pi*n*f0*t);
+% end
+% y_sd_add = y_sd_add .* env;
+%
+% soundsc(y_sq_sub, fs); pause(T+0.5);
+% soundsc(y_sd_sub, fs); pause(T+0.5);
+% soundsc(y_sq_add, fs); pause(T+0.5);
+% soundsc(y_sd_add, fs);
+%
+% figure('Position',[100 100 900 600]);
+% subplot(2,2,1);
+% plot(t, y_sq_sub); title('Soustractive – Carré'); xlabel('Temps (s)'); ylabel('Amplitude');
+% subplot(2,2,2);
+% plot(t, y_sd_sub); title('Soustractive – Scie'); xlabel('Temps (s)');
+% subplot(2,2,3);
+% plot(t, y_sq_add); title('Additive – Carré'); xlabel('Temps (s)');
+% subplot(2,2,4);
+% plot(t, y_sd_add); title('Additive – Scie'); xlabel('Temps (s)');
+
+% Question 2.4 :
+% fs = 8000;
+% f0 = 440;
+% T = 1;
+% t = 0:1/fs:T-1/fs;
+% A = round(0.1*fs); D = A; R = A; S = length(t)-(A+D+R);
+% env = [linspace(0,1,A), linspace(1,0.7,D), 0.7*ones(1,S), linspace(0.7,0,R)];
+%
+% x = square(2*pi*f0*t).*env;
+%
+% d_fir4 = designfilt('lowpassfir', ...
+% 'FilterOrder',4, ...
+% 'CutoffFrequency',2000, ...
+% 'SampleRate',fs);
+%
+% d_fir16 = designfilt('lowpassfir', ...
+% 'FilterOrder',16, ...
+% 'CutoffFrequency',1500, ...
+% 'SampleRate',fs);
+%
+% [bb2, aa2] = butter(2, 0.25);
+%
+% [bc4, ac4] = cheby2(4, 40, 0.2);
+%
+% filterAnalyzer( d_fir4, ...
+% d_fir16, ...
+% bb2, aa2, ...
+% bc4, ac4 );
+
+
+%% EFFETS AUDIO-NUMÉRIQUES
+
+% Certaines questions ne figurent pas ici étant donné que l'entièreté du
+% code est donnée sur le livrable
+
+% Question 3.3 :
+% xe1 = randn(1, 1000);
+% xe2_full = conv(rectwin(200), rectwin(200));
+% xe2 = xe2_full(1:min(1000, length(xe2_full)));
+% xe2 = xe2 / max(abs(xe2));
+%
+% % Autocorrélations normalisées
+% r1 = xcorr(xe1, 'coeff');
+% r2 = xcorr(xe2, 'coeff');
+%
+% lags1 = (-length(xe1)+1):(length(xe1)-1);
+% lags2 = (-length(xe2)+1):(length(xe2)-1);
+% fs = 44100;
+% t1 = lags1 / fs;
+% t2 = lags2 / fs;
+%
+% % Largeur à -3 dB
+% idx1 = find(r1 >= 0.5);
+% idx2 = find(r2 >= 0.5);
+% L1 = (idx1(end) - idx1(1)) / fs;
+% L2 = (idx2(end) - idx2(1)) / fs;
+%
+% figure;
+%
+% subplot(2,1,1);
+% plot(t1, r1, 'b'); grid on;
+% xlabel('Décalage (s)'); ylabel('R_{x_1x_1}');
+% title('Autocorrélation normalisée de xe1');
+% text(0.01, 0.8, sprintf('largeur_{R1 @0.5} = %.5f s', L1), 'BackgroundColor','w');
+%
+% subplot(2,1,2);
+% plot(t2, r2, 'r'); grid on;
+% xlabel('Décalage (s)'); ylabel('R_{x_2x_2}');
+% title('Autocorrélation normalisée de xe2');
+% text(0.01, 0.8, sprintf('largeur_{R2 @0.5} = %.5f s', L2), 'BackgroundColor','w');
+
+% Question 3.4 :
+% data = load('/Users/alexandredherissart/Desktop/SAR Audio/signal_excitation.mat');
+% xe = data.xe1;
+% fs = data.fe;
+%
+% % Simulation de la propagation dans la pièce
+% ye = simule_piece(xe, fs);
+%
+% [Ryx, lags] = xcorr(ye, xe);
+%
+% idx = (lags >= 0);
+% h_est = Ryx(idx);
+% t = lags(idx) / fs;
+% h_est = h_est / max(abs(h_est));
+%
+% figure;
+% plot(t, h_est, 'LineWidth',1.5);
+% grid on;
+% xlabel('Temps (s)');
+% ylabel('Amplitude normalisée');
+% title('Réponse impulsionnelle estimée via corrélation croisée');
+% xlim([0 t(end)]);
+
+% Question 3.12 :
+% Fe = 44100;
+%
+% % Parametres du delay
+% tau_s = 0.25;
+% g = 0.9;
+%
+% tau = round(tau_s * Fe);
+%
+% % Coefficients du filtre de Delay
+% b = 1;
+% a = [1, zeros(1, tau-1), g];
+%
+% N_imp = 5 * tau;
+% imp = [1; zeros(N_imp, 1)];
+%
+% % Application du filtre pour obtenir h[k]
+% h = filter(b, a, imp);
+%
+% k = (0:length(h)-1) / Fe;
+% figure;
+% stem(k, h, 'filled');
+% grid on;
+% xlabel('Temps (s)');
+% ylabel('h(k)');
+% title('Reponse impulsionnelle du filtre de delay (\tau = 0.25s, g = 0.9)');
+
+% Question 3.14 :
+% load('h_delay.mat','h');
+% Fe = 44100;
+%
+% % FFT
+% NFFT = 2^nextpow2(length(h)*4);
+% f = (0:NFFT/2)*(Fe/NFFT);
+%
+% H_num = fft(h, NFFT);
+% H_num = abs(H_num(1:NFFT/2+1));
+%
+% % Reponse theorique du delay
+% tau = round(0.25 * Fe);
+% g = 0.9;
+% w = 2*pi*f/Fe;
+% H_th = 1 ./ sqrt(1 + 2*g*cos(w*tau) + g^2);
+%
+% figure;
+% plot(f, 20*log10(H_th+eps), 'k-', 'LineWidth',1.5); hold on;
+% plot(f, 20*log10(H_num+eps), 'r--','LineWidth',1.2);
+% grid on;
+% xlim([0 25]);
+% xlabel('Frequence (Hz)');
+% ylabel('Gain (dB)');
+% title('Reponse frequentielle du filtre de delay : theorie vs FFT');
+% legend('Theorique','Par FFT de h','Location','Best');
+
+% Question 3.15 :
+% function y = effet_delay(x, tau, g, Fe)
+% % vecteurs de coefficients pour filter
+% b = 1;
+% a = [1, zeros(1, tau-1), g];
+%
+% % application du filtre IIR
+% y = filter(b, a, x);
+% end
+
+% Question 3.16 :
+% [x, Fe] = audioread('/Users/alexandredherissart/Desktop/SAR Audio/piano_chord.wav');
+%
+% tau_s = 0.25;
+% tau = round(tau_s * Fe);
+% g = 0.9;
+%
+% % Application de l'effet delay
+% y_delay = effet_delay(x, tau, g, Fe);
+%
+% % Lecture des sons
+% soundsc(x, Fe);
+% pause(length(x)/Fe + 0.5); % signal sec
+% soundsc(y_delay, Fe); % signal avec delay
+%
+% % Affichage des signaux
+% t = (0:length(x)-1)/Fe; % axe temporel
+%
+% figure;
+% subplot(2,1,1);
+% plot(t, x);
+% title('Signal original');
+% xlabel('Temps (s)');
+% ylabel('Amplitude');
+%
+% subplot(2,1,2);
+% plot(t, y_delay);
+% title('Signal avec effet delay');
+% xlabel('Temps (s)');
+% ylabel('Amplitude');
+
+% Question 3.18 :
+% [x, Fe] = audioread('/Users/alexandredherissart/Desktop/SAR Audio/piano_chord.wav');
+%
+% % Parametres du delay
+% tau_s = 0.25;
+% tau = round(tau_s * Fe);
+% g = 0.9;
+% K = 10;
+%
+% % Application de l'effet
+% y_del_filt = effet_delay_filtre(x, tau, g, K, Fe);
+%
+% soundsc(x, Fe);
+% pause(length(x)/Fe + 0.5);
+% soundsc(y_del_filt, Fe);
+%
+% audiowrite('piano_chord_delay_filtre.wav', y_del_filt, Fe);
+
+% Question 3.19 :
+% [x, Fe] = audioread('/Users/alexandredherissart/Desktop/SAR Audio/piano_chord.wav');
+%
+% % Paramètres du delay
+% tau_s = 0.25;
+% tau = round(tau_s * Fe);
+% g = 0.9;
+% K = 10;
+%
+% % Application de l’effet
+% y_del_filt = effet_delay_filtre(x, tau, g, K, Fe);
+%
+% soundsc(x, Fe);
+% pause(length(x)/Fe + 0.5);
+% soundsc(y_del_filt, Fe);
+%
+% audiowrite('piano_chord_delay_filtre.wav', y_del_filt, Fe);
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