Obisidian vault auto-backup: 06-01-2026 13:44:16 on . 4 files edited

.obsidian/workspace.json

@@ -219,17 +219,17 @@
   },
   "active": "8beea5ef99c3c6ed",
   "lastOpenFiles": [
+    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRL2809.tmp",
+    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRD2801.tmp",
+    "ISEN/Traitement du signal/CIPA4/TP/TP3/TP3_Experience3.m",
+    "ISEN/Traitement du signal/CIPA4/TP/TP3/Copy_of_TP3_Experience2.m",
+    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRD2818.tmp",
     "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRL1378.tmp",
     "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRD1374.tmp",
     "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRL2201.tmp",
     "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRD2193.tmp",
     "ISEN/Traitement du signal/CIPA4/TP/TP3/TP3_Experience2.m",
     "ISEN/Traitement du signal/CIPA4/TP/TP3/Copy_of_TP3_Experience1.m",
-    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRL0005.tmp",
-    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRD0004.tmp",
-    "ISEN/Traitement du signal/CIPA4/TP/TP3/E71marquet.wav",
-    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRL0003.tmp",
-    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRD0002.tmp",
     "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/TP3/TP3_Experience2.m

@@ -3,7 +3,7 @@
 % - Sampling period Ts = 0.13*T
 % - Add narrowband jamming at 800 Hz and white noise
 % - Design IIR notch filter (order 15 then 5) to remove the jamming tone
-% - Use subplot to show time-domain signal and magnitude spectrum. [web:216][web:223]
+% - Use subplot to show time-domain signal and magnitude spectrum.
 
 clc;
 clear;
@@ -14,7 +14,7 @@ close all;
 T   = 2e-3;                % Symbol period (s)
 beta = 0.5;                % Roll-off factor
 Ts  = 0.13 * T;            % Sampling period (s)
-Fs  = 1 / Ts;              % Sampling frequency (Hz) [web:202]
+Fs  = 1 / Ts;              % Sampling frequency (Hz) 
 t   = -10*T : Ts : 10*T;   % Time vector
 N   = length(t);
 
@@ -23,11 +23,11 @@ f_axis = (-N/2 : N/2-1) * (Fs / N);   % Hz
 
 %% 2) Raised cosine pulse h(t)
 
-h = arrayfun(@(tt) raisedCosineSample(tt, T, beta), t);   % [web:223]
+h = arrayfun(@(tt) raisedCosineSample(tt, T, beta), t);  
 
 % Time-domain h(t) and magnitude spectrum
 H  = fft(h);
-magH = abs(fftshift(H));   % magnitude, zero frequency at center [web:202]
+magH = abs(fftshift(H));   % magnitude, zero frequency at center 
 
 figure('Name','Experiment 2 - h(t) and |H(f)|');
 subplot(2,1,1);
@@ -49,7 +49,7 @@ grid on;
 fJam = 800;                       % Jamming frequency (Hz)
 x = 0.2 * cos(2*pi*fJam*t);       % narrowband jamming (adjust amplitude if needed)
 
-n = 0.02 * randn(size(t));        % ambient white noise (low level) [web:223]
+n = 0.02 * randn(size(t));        % ambient white noise (low level) 
 
 z = h + x + n;                    % corrupted signal
 
@@ -74,7 +74,7 @@ grid on;
 
 %% 4) Design 15th-order notch (bandstop) filter at 800 Hz (no butter)
 % We build an IIR notch with zeros at exp(±j*w0) and poles at r*exp(±j*w0),
-% then cascade enough sections to reach an effective order ≈ 15. [web:238]
+% then cascade enough sections to reach an effective order ≈ 15.
 
 w0 = 2*pi*fJam/Fs;     % digital radian frequency
 r  = 0.98;             % pole radius (controls notch width)
@@ -150,7 +150,7 @@ grid on;
 function h = raisedCosineSample(t, T, beta)
     % Raised cosine pulse sample at time t (scalar).
     % h(t) = sinc(t/T) * cos(pi*beta*t/T) / (1 - (4*beta^2*t^2)/T^2)
-    % with sinc(x) = sin(pi*x)/(pi*x). [web:216][web:223]
+    % with sinc(x) = sin(pi*x)/(pi*x).
 
     x = t / T;
 
@@ -165,7 +165,7 @@ function h = raisedCosineSample(t, T, beta)
     if abs(t) < 1e-12
         h = 1;
     elseif beta ~= 0 && abs(abs(t) - T/(2*beta)) < 1e-12
-        h = (beta/pi) * sin(pi/(2*beta)); % limit at t = ±T/(2*beta) [web:223]
+        h = (beta/pi) * sin(pi/(2*beta)); % limit at t = ±T/(2*beta)
     else
         h = sx * cos(pi*beta*x) / (1 - (4*beta^2*x^2));
     end

ISEN/Traitement du signal/CIPA4/TP/TP3/TP3_Experience3.m

@@ -0,0 +1,129 @@
+%% Experiment 3 : Modulation and demodulation of a guitar signal
+% Load guitar signal y(t) from 'guitar.wav'
+% Fmod = 8820 Hz
+% ym(t) = y(t) * sin(2*pi*Fmod*t)
+% ys(t) = ym(t) * sin(2*pi*Fmod*t)
+% yc(t) = ym(t) * cos(2*pi*Fmod*t)
+% Plot amplitude spectrum of y, ym, ys, yc and listen to each. 
+
+clc;
+clear;
+close all;
+
+%% 1) Load audio file
+
+[y, Fs] = audioread('guitar.wav');      % y: audio vector, Fs: sampling rate
+
+if size(y,2) > 1
+    y = mean(y,2);                      % convert to mono if stereo
+end
+
+N  = length(y);
+t  = (0:N-1)/Fs;                        % time vector
+
+Fmod = 8820;                            % modulation frequency in Hz
+
+%% 2) Generate modulated signals
+
+ym = y .* sin(2*pi*Fmod*t.');           % column vector; DSB-SC around ±Fmod
+
+ys = ym .* sin(2*pi*Fmod*t.');          % second multiplication by sin
+yc = ym .* cos(2*pi*Fmod*t.');          % multiplication by cos
+
+%% 3) Helper to compute single-sided amplitude spectrum |Y(f)|
+
+computeSpec = @(sig) ...
+    deal( ...
+        (0:floor(length(sig)/2)) * (Fs/length(sig)), ...   % f axis
+        abs(fft(sig)) / length(sig) ...                   % scale
+    );
+
+[f_y,  P_y]  = computeSpec(y);
+[f_ym, P_ym] = computeSpec(ym);
+[f_ys, P_ys] = computeSpec(ys);
+[f_yc, P_yc] = computeSpec(yc);
+
+P_y  = P_y(1:length(f_y));
+P_ym = P_ym(1:length(f_ym));
+P_ys = P_ys(1:length(f_ys));
+P_yc = P_yc(1:length(f_yc));
+
+%% 4) Plot amplitude spectra
+
+figure('Name','Amplitude spectra of y, ym, ys, yc');
+
+subplot(4,1,1);
+plot(f_y, P_y(1:numel(f_y)), 'g');
+xlim([0 Fs/2]);
+xlabel('Frequency (Hz)');
+ylabel('|Y(f)|');
+title('Original signal y(t) - spectrum');
+grid on;
+
+subplot(4,1,2);
+plot(f_ym, P_ym(1:numel(f_ym)), 'g');
+xlim([0 Fs/2]);
+xlabel('Frequency (Hz)');
+ylabel('|Y_m(f)|');
+title('ym(t) = y(t) * sin(2\pi F_{mod} t)');
+grid on;
+
+subplot(4,1,3);
+plot(f_ys, P_ys(1:numel(f_ys)), 'g');
+xlim([0 Fs/2]);
+xlabel('Frequency (Hz)');
+ylabel('|Y_s(f)|');
+title('ys(t) = ym(t) * sin(2\pi F_{mod} t)');
+grid on;
+
+subplot(4,1,4);
+plot(f_yc, P_yc(1:numel(f_yc)), 'g');
+xlim([0 Fs/2]);
+xlabel('Frequency (Hz)');
+ylabel('|Y_c(f)|');
+title('yc(t) = ym(t) * cos(2\pi F_{mod} t)');
+grid on;
+
+%% 5) Listen to the signals (uncomment in MATLAB to hear)
+% sound(y,  Fs);  pause(length(y)/Fs + 1);
+% sound(ym, Fs);  pause(length(y)/Fs + 1);
+% sound(ys, Fs);  pause(length(y)/Fs + 1);
+% sound(yc, Fs);
+
+%% 6) Demodulation to recover original sound
+% Theory:
+%   - ym(t) = y(t)*sin(2*pi*Fmod*t) is DSB-SC modulation.
+%   - Multiplying again by sin(2*pi*Fmod*t) gives:
+%       ys(t) = ym(t)*sin(2*pi*Fmod*t)
+%             = y(t)*sin^2(2*pi*Fmod*t)
+%             = 0.5*y(t) - 0.5*y(t)*cos(4*pi*Fmod*t)
+%     => low-frequency term 0.5*y(t) + high-frequency image around 2*Fmod.
+%   - A low-pass filter on ys(t) recovers a scaled version of y(t).
+%
+% So ys(t) is the best candidate for demodulation.
+
+% Simple low-pass filter: moving average (FIR) without toolboxes.
+% Choose window length so cut-off is << Fmod (keep audio band, remove 2*Fmod).
+LpOrder = 101;                      % odd length for symmetry
+h_lp = ones(LpOrder,1)/LpOrder;    % simple averaging filter
+
+y_rec = filter(h_lp, 1, ys);       % demodulated / low-passed version
+
+% Optionally compensate scaling (~0.5) by multiplying by 2
+y_rec = 2 * y_rec;
+
+%% 7) Spectrum of demodulated signal
+
+[f_rec, P_rec] = computeSpec(y_rec);
+P_rec = P_rec(1:length(f_rec));
+
+figure('Name','Demodulated signal spectrum');
+plot(f_rec, P_rec, 'g');
+xlim([0 Fs/2]);
+xlabel('Frequency (Hz)');
+ylabel('|Y_{rec}(f)|');
+title('Amplitude spectrum of demodulated signal (approx. original y(t))');
+grid on;
+
+%% 8) Listen to recovered sound (optional)
+% sound(y_rec, Fs);