From b6eb669249e260bfd44e1f45364b1493a1c0704f Mon Sep 17 00:00:00 2001
From: TeodoreAutuly <teodore@autuly.com>
Date: Fri, 16 May 2025 10:46:17 +0200
Subject: [PATCH] Part 2

---
 src/applicationSons.m      |  11 ++-
 src/comparaisonPianos.m    |  97 ++++++++++++++++----
 src/filtered_sawtooth.wav  | Bin 0 -> 176444 bytes
 src/filtered_square.wav    | Bin 0 -> 176444 bytes
 src/original_sawtooth.wav  | Bin 0 -> 176444 bytes
 src/original_square.wav    | Bin 0 -> 176444 bytes
 src/syntheseSoustractive.m | 176 +++++++++++++++++++++++++++++--------
 7 files changed, 230 insertions(+), 54 deletions(-)
 create mode 100644 src/filtered_sawtooth.wav
 create mode 100644 src/filtered_square.wav
 create mode 100644 src/original_sawtooth.wav
 create mode 100644 src/original_square.wav

diff --git a/src/applicationSons.m b/src/applicationSons.m
index 128cd9b..5635442 100644
--- a/src/applicationSons.m
+++ b/src/applicationSons.m
@@ -1,11 +1,20 @@
 fileName_cello = "wav/single_tone_cello-a3.wav";
 fileName_piano1 = "wav/single_tone_piano1.wav";
 fileName_piano2 = "wav/single_tone_piano2.wav";
+fileName_sax_alto = "wav/single_tone_sax-alto-a3.wav";
+fileName_sax_soprano = "wav/single_tone_sax-soprano-a3.wav";
+fileName_trumpet = "wav/single_tone_trumpet-a3.wav";
 
 [x_cello, fs_cello] = audioread(fileName_cello);
 [x_piano1, fs_piano1] = audioread(fileName_piano1);
 [x_piano2, fs_piano2] = audioread(fileName_piano2);
+[x_sax_alto, fs_sax_alto] = audioread(fileName_sax_alto);
+[x_sax_soprano, fs_sax_soprano] = audioread(fileName_sax_soprano);  
+[x_trumpet, fs_trumpet] = audioread(fileName_trumpet);
 
 [amplitude_cello, f1_cello] = analyseSonHarmonique(x_cello, fs_cello);
 [amplitude_piano1, f1_piano1] = analyseSonHarmonique(x_piano1, fs_piano1);
-[amplitude_piano2, f1_piano2] = analyseSonHarmonique(x_piano2, fs_piano2);
\ No newline at end of file
+[amplitude_piano2, f1_piano2] = analyseSonHarmonique(x_piano2, fs_piano2);
+[amplitude_sax_alto, f1_sax_alto] = analyseSonHarmonique(x_sax_alto, fs_sax_alto);
+[amplitude_sax_soprano, f1_sax_soprano] = analyseSonHarmonique(x_sax_soprano, fs_sax_soprano);
+[amplitude_trumpet, f1_trumpet] = analyseSonHarmonique(x_trumpet, fs_trumpet);
\ No newline at end of file
diff --git a/src/comparaisonPianos.m b/src/comparaisonPianos.m
index 6f7dd11..160b4a4 100644
--- a/src/comparaisonPianos.m
+++ b/src/comparaisonPianos.m
@@ -29,14 +29,86 @@ legend('Piano 1', 'Piano 2');
 % Calcul des fondamentales
 [~, index1] = max(amplitude_piano1); % Trouver l'indice de la fréquence fondamentale
 [~, index2] = max(amplitude_piano2); % Trouver l'indice de la fréquence fondamentale
-f1 = f1(index1); % Fréquence fondamentale
-f2 = f2(index2); % Fréquence fondamentale
-disp(['Fréquence fondamentale Piano 1 : ', num2str(f1), ' Hz']);
-disp(['Fréquence fondamentale Piano 2 : ', num2str(f2), ' Hz']);
+ff1 = f1(index1); % Fréquence fondamentale
+ff2 = f2(index2); % Fréquence fondamentale
+disp(['Fréquence fondamentale Piano 1 : ', num2str(ff1), ' Hz']);
+disp(['Fréquence fondamentale Piano 2 : ', num2str(ff2), ' Hz']);
+
+% Index des harmoniques
+harmonic_indices1 = [index1, index1*2, index1*3, index1*4, index1*5, index1*6, index1*7];
+harmonic_indices2 = [index2, index2*2, index2*3, index2*4, index2*5, index2*6, index2*7];
+
+% Fréquences des harmoniques théoriques
+fh1theorique = ff1 * (1:7); % Fréquences théoriques des harmoniques
+fh2theorique = ff2 * (1:7); % Fréquences théoriques des harmoniques
+
+disp(['Fréquences harmoniques théoriques Piano 1 : ', num2str(fh1theorique)]);
+disp(['Fréquences harmoniques théoriques Piano 2 : ', num2str(fh2theorique)]);
+
+% Trouver les indices des harmoniques en cherchant les pics près des fréquences attendues
+window_width = 50; % Hz - largeur de recherche autour de la fréquence théorique
+
+% Mesure des harmoniques pour Piano 1
+ff1_harmonics = zeros(1, 7);
+for h = 1:7
+    expected_freq = fh1theorique(h);
+    % Trouver les indices proches de la fréquence harmonique théorique
+    [~, idx] = min(abs(f1 - expected_freq));
+    % Chercher le maximum local dans une fenêtre autour de cet indice
+    start_idx = max(1, idx - 10);
+    end_idx = min(length(f1), idx + 10);
+    [~, max_local_idx] = max(amplitude_piano1(start_idx:end_idx));
+    harmonics_idx1 = start_idx + max_local_idx - 1;
+    ff1_harmonics(h) = f1(harmonics_idx1);
+end
+
+% Mesure des harmoniques pour Piano 2
+ff2_harmonics = zeros(1, 7);
+for h = 1:7
+    expected_freq = fh2theorique(h);
+    % Trouver les indices proches de la fréquence harmonique théorique
+    [~, idx] = min(abs(f2 - expected_freq));
+    % Chercher le maximum local dans une fenêtre autour de cet indice
+    start_idx = max(1, idx - 10);
+    end_idx = min(length(f2), idx + 10);
+    [~, max_local_idx] = max(amplitude_piano2(start_idx:end_idx));
+    harmonics_idx2 = start_idx + max_local_idx - 1;
+    ff2_harmonics(h) = f2(harmonics_idx2);
+end
+
+% Assigner les harmoniques individuelles pour plus de clarté
+ff1_1 = ff1_harmonics(1);
+ff1_2 = ff1_harmonics(2);
+ff1_3 = ff1_harmonics(3);
+ff1_4 = ff1_harmonics(4);
+ff1_5 = ff1_harmonics(5);
+ff1_6 = ff1_harmonics(6);
+ff1_7 = ff1_harmonics(7);
+
+ff2_1 = ff2_harmonics(1);
+ff2_2 = ff2_harmonics(2);
+ff2_3 = ff2_harmonics(3);
+ff2_4 = ff2_harmonics(4);
+ff2_5 = ff2_harmonics(5);
+ff2_6 = ff2_harmonics(6);
+ff2_7 = ff2_harmonics(7);
 
 % Calcul des degrés d'inharmonicité pour 5 harmoniques
-deg1 = [1200*log2(f1/f1), 1200*log2(f1/2*f1), 1200*log2(f1/3*f1), 1200*log2(f1/4*f1), 1200*log2(f1/5*f1), 1200*log2(f1/6*f1), 1200*log2(f1/7*f1), 1200*log2(f1/8*f1)];
-deg2 = [1200*log2(f2/f2), 1200*log2(f2/2*f2), 1200*log2(f2/3*f2), 1200*log2(f2/4*f2), 1200*log2(f2/5*f2), 1200*log2(f2/6*f2), 1200*log2(f2/7*f2), 1200*log2(f2/8*f2)];
+deg1 = [abs(1200*(log2(ff1_1)-log2(ff1_1))), ...
+        abs(1200*(log2(ff1_2)-log2(2*ff1_1))), ...
+        abs(1200*(log2(ff1_3)-log2(3*ff1_1))), ...
+        abs(1200*(log2(ff1_4)-log2(4*ff1_1))), ...
+        abs(1200*(log2(ff1_5)-log2(5*ff1_1))), ...
+        abs(1200*(log2(ff1_6)-log2(6*ff1_1))), ...
+        abs(1200*(log2(ff1_7)-log2(7*ff1_1)))];
+deg2 = [abs(1200*(log2(ff2_1)-log2(ff2_1))), ...
+        abs(1200*(log2(ff2_2)-log2(2*ff2_1))), ...
+        abs(1200*(log2(ff2_3)-log2(3*ff2_1))), ...
+        abs(1200*(log2(ff2_4)-log2(4*ff2_1))), ...
+        abs(1200*(log2(ff2_5)-log2(5*ff2_1))), ...
+        abs(1200*(log2(ff2_6)-log2(6*ff2_1))), ...
+        abs(1200*(log2(ff2_7)-log2(7*ff2_1)))];
+
 disp(['Degré d inharmonicité Piano 1 : ', num2str(deg1)]);
 disp(['Degré d inharmonicité Piano 2 : ', num2str(deg2)]);
 
@@ -51,10 +123,10 @@ legend('Piano 1', 'Piano 2');
 
 % Récupérer les amplitudes des 8 premières harmoniques du piano1
 harmonic_amplitudes = zeros(1, 8);
-harmonic_frequencies = f1 * (1:8); % Fréquences des 8 premières harmoniques
+harmonic_frequencies = ff1 * (1:8); % Fréquences des 8 premières harmoniques
 
 for k = 1:8
-    [~, idx] = min(abs(f1 - harmonic_frequencies(k))); % Trouver l'indice de la fréquence harmonique
+    [~, idx] = min(abs(ff1 - harmonic_frequencies(k))); % Trouver l'indice de la fréquence harmonique
     harmonic_amplitudes(k) = abs(singalFFTpiano1(idx)); % Amplitude correspondante
 end
 
@@ -70,9 +142,6 @@ end
 % Normaliser le signal synthétisé
 synthesized_signal = synthesized_signal / max(abs(synthesized_signal));
 
-% Écouter le son généré
-sound(synthesized_signal, fs_piano1);
-
 % Sauvegarder le son généré dans un fichier
 audiowrite('synthesized_piano1.wav', synthesized_signal, fs_piano1);
 
@@ -100,9 +169,6 @@ envelope = envelope(1:length(t));
 % Appliquer l'enveloppe au signal synthétisé
 synthesized_signal = synthesized_signal .* envelope;
 
-% Écouter le son avec l'enveloppe ADSR
-sound(synthesized_signal, fs_piano1);
-
 % Sauvegarder le son avec l'enveloppe ADSR dans un fichier
 audiowrite('synthesized_piano1_with_adsr.wav', synthesized_signal, fs_piano1);
 
@@ -123,9 +189,6 @@ synthesized_signal_ifft = real(ifft(spectrum));
 % Normaliser le signal synthétisé
 synthesized_signal_ifft = synthesized_signal_ifft / max(abs(synthesized_signal_ifft));
 
-% Écouter le son généré
-sound(synthesized_signal_ifft, fs_piano1);
-
 % Sauvegarder le son généré dans un fichier
 audiowrite('synthesized_piano1_ifft.wav', synthesized_signal_ifft, fs_piano1);
 
diff --git a/src/filtered_sawtooth.wav b/src/filtered_sawtooth.wav
new file mode 100644
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diff --git a/src/syntheseSoustractive.m b/src/syntheseSoustractive.m
index 4cf6fd0..bfd94e1 100644
--- a/src/syntheseSoustractive.m
+++ b/src/syntheseSoustractive.m
@@ -56,57 +56,161 @@ xlabel('Fréquence (Hz)');
 ylabel('Amplitude');
 
 % Filtrage passe-bas d'ordre 1
-% y(k) = 0.5 * (x(k) + x(k-1))
+% Implémentation du filtre y(k) = 0.5 * (x(k) + x(k-1))
+b = [0.5, 0.5]; % Coefficients du numérateur
+a = [1]; % Coefficients du dénominateur
+% Application du filtre aux signaux
+filtered_square = filter(b, a, square_signal);
+filtered_sawtooth = filter(b, a, sawtooth_signal);
 
-% Application du filtre au signal carré
-square_filtered = filter([0.5, 0.5], 1, square_signal);
+% Calcul du spectre des signaux filtrés
+filtered_square_fft = fftshift(fft(filtered_square));
+filtered_square_magnitude = abs(filtered_square_fft) / N;
+
+filtered_sawtooth_fft = fftshift(fft(filtered_sawtooth));
+filtered_sawtooth_magnitude = abs(filtered_sawtooth_fft) / N;
+
+% Calcul de la réponse en fréquence théorique du filtre
+omega = 2 * pi * f / Fs; % Fréquences normalisées
+H = 0.5 * (1 + exp(-1j * omega)); % Réponse en fréquence théorique
+H_magnitude = abs(H);
+
+% Application de la réponse théorique aux spectres originaux
+theoretical_filtered_square = square_magnitude .* H_magnitude;
+theoretical_filtered_sawtooth = sawtooth_magnitude .* H_magnitude;
 
-% Application du filtre au signal dent de scie
-sawtooth_filtered = filter([0.5, 0.5], 1, sawtooth_signal);
+% Affichage de la réponse en fréquence du filtre
+figure;
+plot(f, H_magnitude);
+title('Réponse en fréquence du filtre passe-bas d''ordre 1');
+xlabel('Fréquence (Hz)');
+ylabel('Gain');
+grid on;
+xlim([-100, 100]);
 
-% Affichage des signaux filtrés
+% Affichage des résultats du filtrage
 figure;
 
 % Signal carré filtré
-subplot(2, 1, 1);
-plot(t, square_filtered);
-title('Signal carré filtré (passe-bas)');
+subplot(2, 2, 1);
+plot(t, square_signal, 'b');
+hold on;
+plot(t, filtered_square, 'r');
+title('Signal carré original et filtré');
 xlabel('Temps (s)');
 ylabel('Amplitude');
-xlim([0 5*T]); % Limiter l'axe des x pour une meilleure visualisation
+xlim([0 5*T]);
+legend('Original', 'Filtré');
+
+% Comparaison des spectres théorique et réel du signal carré filtré
+subplot(2, 2, 2);
+plot(f, filtered_square_magnitude, 'r');
+hold on;
+plot(f, theoretical_filtered_square, 'g--');
+title('Spectres du signal carré filtré');
+xlabel('Fréquence (Hz)');
+ylabel('Amplitude');
+legend('Spectre réel', 'Spectre théorique');
+xlim([-100, 100]); % Zoom sur les basses fréquences
 
 % Signal dent de scie filtré
-subplot(2, 1, 2);
-plot(t, sawtooth_filtered);
-title('Signal dent de scie filtré (passe-bas)');
+subplot(2, 2, 3);
+plot(t, sawtooth_signal, 'b');
+hold on;
+plot(t, filtered_sawtooth, 'r');
+title('Signal dent de scie original et filtré');
 xlabel('Temps (s)');
 ylabel('Amplitude');
-xlim([0 5*T]); % Limiter l'axe des x pour une meilleure visualisation
-
-% Calcul du spectre des signaux filtrés
-square_filtered_fft = fftshift(fft(square_filtered));
-square_filtered_magnitude = abs(square_filtered_fft) / N;
-sawtooth_filtered_fft = fftshift(fft(sawtooth_filtered));
-sawtooth_filtered_magnitude = abs(sawtooth_filtered_fft) / N;
-
+xlim([0 5*T]);
+legend('Original', 'Filtré');
 
-% Affichage des spectres des signaux filtrés
+% Comparaison des spectres théorique et réel du signal dent de scie filtré
+subplot(2, 2, 4);
+plot(f, filtered_sawtooth_magnitude, 'r');
+hold on;
+plot(f, theoretical_filtered_sawtooth, 'g--');
+title('Spectres du signal dent de scie filtré');
+xlabel('Fréquence (Hz)');
+ylabel('Amplitude');
+legend('Spectre réel', 'Spectre théorique');
+xlim([-100, 100]); % Zoom sur les basses fréquences
+
+% Synthèse sonore pour écoute et comparaison
+% Paramètres pour la synthèse audio
+duration = 2; % Durée en secondes
+audio_Fs = 44100; % Fréquence d'échantillonnage pour l'audio (standard)
+
+% Paramètres des signaux
+freq = 440; % Fréquence fondamentale en Hz (La4)
+audio_t = 0:1/audio_Fs:duration-1/audio_Fs; % Vecteur temps pour l'audio
+
+% Génération des signaux source à fréquence audible
+audio_square = A * square(2 * pi * freq * audio_t);
+audio_sawtooth = A * sawtooth(2 * pi * freq * audio_t);
+
+% New filter
+d = designfilt('lowpassfir','FilterOrder',2,'HalfPowerFrequency',0.25)
+filterAnalyzer(d)
+
+% Création d'une enveloppe ADSR simple
+attack_time = 0.1; % secondes
+decay_time = 0.2; % secondes
+sustain_level = 0.7; % niveau de sustain (0-1)
+release_time = 0.3; % secondes
+sustain_time = duration - (attack_time + decay_time + release_time);
+
+% Nombre d'échantillons pour chaque phase
+attack_samples = round(attack_time * audio_Fs);
+decay_samples = round(decay_time * audio_Fs);
+sustain_samples = round(sustain_time * audio_Fs);
+release_samples = round(release_time * audio_Fs);
+
+% Création des segments de l'enveloppe
+attack = linspace(0, 1, attack_samples);
+decay = linspace(1, sustain_level, decay_samples);
+sustain = ones(1, sustain_samples) * sustain_level;
+release = linspace(sustain_level, 0, release_samples);
+
+% Assemblage de l'enveloppe complète
+envelope = [attack, decay, sustain, release];
+
+% Application du filtre passe-bas existant et de l'enveloppe
+filtered_square = filter(d, audio_square) .* envelope;
+filtered_sawtooth = filter(d, audio_sawtooth) .* envelope;
+
+% Normalisation pour éviter l'écrêtage
+audio_square = audio_square / max(abs(audio_square));
+audio_sawtooth = audio_sawtooth / max(abs(audio_sawtooth));
+filtered_square = 0.9 * filtered_square / max(abs(filtered_square));
+filtered_sawtooth = 0.9 * filtered_sawtooth / max(abs(filtered_sawtooth));
+
+% Application de l'enveloppe aux signaux audio
+audio_square = audio_square .* envelope;
+audio_sawtooth = audio_sawtooth .* envelope;
+
+% Stocker les signaux audio dans des fichiers
+audiowrite('filtered_square.wav', filtered_square, audio_Fs);
+audiowrite('filtered_sawtooth.wav', filtered_sawtooth, audio_Fs);
+audiowrite('original_square.wav', audio_square, audio_Fs);
+audiowrite('original_sawtooth.wav', audio_sawtooth, audio_Fs);
+
+% Affichage des FFT des signaux audio sur le même graphique	
 figure;
-
-
-% Spectre du signal carré filtré
-subplot(2, 2, 1);
-plot(f, square_filtered_magnitude);
-title('Spectre du signal carré filtré');
+subplot(2, 1, 1);
+plot(f, abs(fftshift(fft(audio_square)))/N);
+hold on;
+plot(f, abs(fftshift(fft(filtered_square)))/N);
+title('FFT du signal carré et du signal carré filtré');
 xlabel('Fréquence (Hz)');
 ylabel('Amplitude');
-xlim([-Fs/2 Fs/2]); % Limiter l'axe des x pour une meilleure visualisation
-
-
-% Spectre du signal dent de scie filtré
-subplot(2, 2, 2);
-plot(f, sawtooth_filtered_magnitude);
-title('Spectre du signal dent de scie filtré');
+legend('Signal carré', 'Signal carré filtré');
+xlim([-100, 100]); % Zoom sur les basses fréquences
+subplot(2, 1, 2);
+plot(f, abs(fftshift(fft(audio_sawtooth)))/N);
+hold on;
+plot(f, abs(fftshift(fft(filtered_sawtooth)))/N);
+title('FFT du signal dent de scie et du signal dent de scie filtré');
 xlabel('Fréquence (Hz)');
 ylabel('Amplitude');
-xlim([-Fs/2 Fs/2]); % Limiter l'axe des x pour une meilleure visualisation
+legend('Signal dent de scie', 'Signal dent de scie filtré');
+xlim([-100, 100]); % Zoom sur les basses fréquences
-- 
GitLab