Obisidian vault auto-backup: 07-01-2026 14:02:01 on . 4 files edited

.obsidian/workspace.json

@@ -219,6 +219,10 @@
   },
   "active": "8beea5ef99c3c6ed",
   "lastOpenFiles": [
+    "ISEN/Traitement du signal/CIPA4/TP/TP4/TP4_Experience3.m",
+    "ISEN/Traitement du signal/CIPA4/TP/TP4/Copy_of_TP4_Experience2.m",
+    "ISEN/Traitement du signal/CIPA4/TP/TP4/~WRL1606.tmp",
+    "ISEN/Traitement du signal/CIPA4/TP/TP4/~WRD1606.tmp",
     "ISEN/Traitement du signal/CIPA4/TP/TP4/~WRL0238.tmp",
     "ISEN/Traitement du signal/CIPA4/TP/TP4/~WRD0235.tmp",
     "ISEN/Traitement du signal/CIPA4/TP/TP4/~WRL1355.tmp",
@@ -226,10 +230,6 @@
     "ISEN/Traitement du signal/CIPA4/TP/TP4/TP4_Experience2.asv",
     "ISEN/Traitement du signal/CIPA4/TP/TP4/TP4_Experience2.m",
     "ISEN/Traitement du signal/CIPA4/TP/TP4/Copy_of_TP4_Experience1.m",
-    "ISEN/Traitement du signal/CIPA4/TP/TP4/~WRL3213.tmp",
-    "ISEN/Traitement du signal/CIPA4/TP/TP4/~WRD3209.tmp",
-    "ISEN/Traitement du signal/CIPA4/TP/TP4/TP4_Experience1.m",
-    "ISEN/Traitement du signal/CIPA4/TP/TP4/TP3_Experience1.m",
     "ISEN/Réseau/CIPA4/TP/TP M02 Conversion.md",
     "Protocol Data Units (PDU).md",
     "ISEN/English/CIPA4/Elevator pitch.md",

ISEN/Traitement du signal/CIPA4/TP/TP4/TP4_Experience2.asv

@@ -1,55 +0,0 @@
-%% Experiment 2 : Baseband recovery from TP4cipaQ2.wav
-
-clc;
-clear;
-close all;
-
-%% Load the audio
-[y, Fs] = audioread('TP4cipaQ2.wav');
-if size(y,2) > 1
-    y = mean(y,2);                      % 
-end
-
-N  = length(y);
-
-%% i) Spectre d'amplitude en kHz
-Y  = fft(y);
-magY = abs(Y);
-halfN = floor(N/2)+1;
-magY_half = magY(1:halfN);
-f = (0:halfN-1)*(Fs/N);     % Hz
-f_kHz = f/1000;             % kHz
-
-figure;
-plot(f_kHz, magY_half,'g');
-xlabel('Frequence (kHz)');
-ylabel('|Y(f)|');
-title('Spectre amplitude du signal TP4cipaQ2');
-grid on;
-xlim([0 Fs/2000]);
-
-%% Filtre passe-bas Butterworth pour recuperer la bande de base
-% Choisir une frequence de coupure Fc (en Hz) apres avoir regarde le spectre.
-Fc = 3000;                   % exemple : 3 kHz (a adapter si besoin)
-Wn = Fc/(Fs/2);              % normalisation par Fs/2 [web:237]
-ordre = 4;                   % ordre du filtre (simple mais efficace)
-
-[b,a] = butter(ordre, Wn, 'low');   % filtre passe-bas Butterworth
-
-y_filt = filter(b,a,y);            % signal filtre
-
-%% ii) Spectre du signal filtre
-Yf = fft(y_filt);
-magYf = abs(Yf);
-magYf_half = magYf(1:halfN);
-
-figure;
-plot(f_kHz, magYf_half,'g');
-xlabel('Frequence (kHz)');
-ylabel('|Y_f(f)|');
-title('Spectre amplitude du signal filtre');
-grid on;
-xlim([0 Fs/2000]);
-
-%% iii) Ecouter le signal filtre (a lancer dans MATLAB)
-% sound(y_filt, Fs);

ISEN/Traitement du signal/CIPA4/TP/TP4/TP4_Experience3.m

@@ -0,0 +1,71 @@
+%% Experiment 3 : Recovery of a(t) from y1(t) and y2(t)
+
+clc;
+clear;
+close all;
+
+%% Load data from MAT-file
+
+donnees3 = load('TP4cipaQ3.mat');
+y1 = donnees3.y1;
+y2 = donnees3.y2;
+y1 = y1(:);                     
+y2 = y2(:);
+
+Fs = 96000;                      % Sampling frequency (Hz)
+Ts = 1/Fs;                       % Sampling period (s)
+N  = length(y1);                 % Number of samples
+t  = (0:N-1)*Ts;                 % Time axis (s)
+
+%% Recover a(t) using the hint cos^2 + sin^2 = 1
+% a(t) is the envelope common to y1 and y2.
+
+a = sqrt( y1.^2 + y2.^2 );   
+
+%% Plot y1(t) and y2(t) in time domain
+
+figure('Name','y1(t) and y2(t)');
+subplot(2,1,1);
+plot(t, y1, 'g');
+xlabel('Time (s)');
+ylabel('Amplitude');
+title('y1(t) = a(t) cos(2\pi 30000 t + A)');
+grid on;
+
+subplot(2,1,2);
+plot(t, y2, 'g');
+xlabel('Time (s)');
+ylabel('Amplitude');
+title('y2(t) = a(t) sin(2\pi 30000 t + A)');
+grid on;
+
+%% Plot a(t) in time domain
+
+figure('Name','a(t)');
+plot(t, a, 'g');
+xlabel('Time (s)');
+ylabel('Amplitude');
+title('Recovered envelope a(t) = sqrt(y1(t)^2 + y2(t)^2)');
+grid on;
+
+%% Amplitude spectrum of a(t) in kHz and in dB
+
+A_fft = fft(a);                  
+magA   = abs(A_fft);             
+
+halfN = floor(N/2) + 1;          % Positive frequencies only
+magA_half = magA(1:halfN);
+
+f_Hz  = (0:halfN-1)*(Fs/N);      % Frequency axis (Hz)
+f_kHz = f_Hz / 1000;             % Convert to kHz
+
+% Convert magnitude to dB scale (20*log10), avoid log(0) using eps
+magA_dB = 20*log10(magA_half + eps);
+
+figure('Name','Amplitude spectrum of a(t)');
+plot(f_kHz, magA_dB, 'g');
+xlabel('Frequency (kHz)');
+ylabel('Amplitude (dB)');
+title('Single-sided amplitude spectrum of a(t)');
+grid on;
+xlim([0 Fs/2000]);               % From 0 to Nyquist frequency in kHz