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Commit 715812fe authored by Remi LELUAN's avatar Remi LELUAN
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ANNEXE_CODES_Matlab.m 0 → 100644
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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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