Obisidian vault auto-backup: 06-01-2026 15:35:08 on . 1 files edited

.obsidian/workspace.json

@@ -37,10 +37,10 @@
             "state": {
               "type": "pdf",
               "state": {
-                "file": "ISEN/Réseau/CIPA4/TP/Module 4/M04 TP 01 - Communication.pdf"
+                "file": "ISEN/Réseau/CIPA4/TP/Module 5/M05 TP 01 - Les commandes.pdf"
               },
               "icon": "lucide-file-text",
-              "title": "M04 TP 01 - Communication"
+              "title": "M05 TP 01 - Les commandes"
             }
           }
         ],
@@ -219,18 +219,18 @@
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   "active": "8beea5ef99c3c6ed",
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-    "ISEN/Traitement du signal/CIPA4/TP/TP2/TP2cipa_MARQUET.pdf",
-    "ISEN/Traitement du signal/CIPA4/TP/TP2/~$P2cipa.docx",
-    "ISEN/Traitement du signal/CIPA4/TP/TP2/TP2_Experience7.m",
-    "ISEN/Traitement du signal/CIPA4/TP/TP2/TP2_Experience6.m",
-    "ISEN/Traitement du signal/CIPA4/TP/TP2/TP2_Experience5.m",
-    "ISEN/Réseau/CIPA4/TP/Module 4/M04 TP 02 -Packet_Tracer-La_communication.pka~",
-    "ISEN/Réseau/CIPA4/TP/Module 4/M04 TP 01 - Communication.pdf.sb-a92ffc2d-7qze7T",
+    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRL1687.tmp",
+    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRD1680.tmp",
+    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRL0051.tmp",
+    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRD0039.tmp",
+    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRL0467.tmp",
+    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRD0460.tmp",
+    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRL2779.tmp",
+    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRD2775.tmp",
+    "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/Réseau/CIPA4/TP/TP M02 Conversion.md",
-    "ISEN/Réseau/CIPA4/TP/Module 4/M04 TP 01 - Communication.pdf",
-    "ISEN/Réseau/CIPA4/TP/Module 5/M05 TP 01 - Les commandes.pdf",
-    "ISEN/Réseau/CIPA4/TP/Module 6/M06 TP 01 - IPv6.pdf",
-    "ISEN/Réseau/CIPA4/TP/Module 6",
     "Protocol Data Units (PDU).md",
     "ISEN/English/CIPA4/Elevator pitch.md",
     "ISEN/English/CIPA4/24 oct 2025.md",

ISEN/Traitement du signal/CIPA4/TP/TP3/TP3_Experience1.m

@@ -0,0 +1,71 @@
+%% Experiment 1 : Extract narrow-band jamming noise from Q2noisy
+% Objective:
+%   - Load noisy audio file 'Q2noisy.wav'
+%   - Plot magnitude spectrum to identify jamming frequency
+%   - Design a Butterworth bandstop (notch) filter around that frequency
+%   - Filter the signal and save result as 'E71yourname.wav'.
+
+clc;
+clear;
+close all;
+
+%% 1) Load the WAV file
+% Q2noisy.wav must be in the same folder as this script.
+
+[noisySig, Fs] = audioread('Q2noisy.wav');   % noisySig is a column vector, Fs in Hz
+
+% If stereo, convert to mono (average of channels)
+if size(noisySig,2) > 1
+    noisySig = mean(noisySig, 2);
+end
+
+N = length(noisySig);                        % Number of samples
+t = (0:N-1)/Fs;                              % Time axis (s)
+
+%% 2) Plot magnitude spectrum to locate jamming frequency
+
+% Compute FFT
+X = fft(noisySig);
+magX = abs(X);                               % Magnitude spectrum
+
+% Only positive frequencies (single-sided)
+halfN = floor(N/2) + 1;
+magX_half = magX(1:halfN);
+f = (0:halfN-1) * (Fs/N);                    % Frequency axis in Hz
+
+figure('Name','Q2noisy - Magnitude spectrum');
+plot(f, magX_half, 'g');
+xlabel('Frequency (Hz)');
+ylabel('|X(f)|');
+title('Magnitude spectrum of Q2noisy');
+grid on;
+xlim([0 Fs/2]);
+
+fJam = 5000;        
+
+%% 3) Design a suitable Butterworth bandstop (notch) filter
+
+% Choose a small stopband around the jamming frequency, e.g. ±50 Hz
+deltaF = 50;            % half-width of stopband (Hz) - adjust if needed
+
+f1 = (fJam - deltaF);   % lower edge of stopband (Hz)
+f2 = (fJam + deltaF);   % upper edge of stopband (Hz)
+
+% Normalise frequencies w.r.t Nyquist (Fs/2) for BUTTER.
+Wn = [f1 f2] / (Fs/2);   % normalized stopband [0..1]
+
+% Filter order (higher -> sharper notch but more phase distortion)
+Nfilt = 4;               % 4th-order Butterworth bandstop (typical choice)
+
+[b, a] = butter(Nfilt, Wn, 'stop');   % bandstop (notch) filter
+
+% (Optionnel) Afficher la réponse fréquentielle du filtre
+% figure; freqz(b,a,1024,Fs); grid on;
+
+%% 4) Filter the noisy signal
+
+cleanSig = filter(b, a, noisySig);    % Apply the filter to remove narrow-band noise
+
+%% 5) Save the result
+
+audiowrite('E71marquet.wav', cleanSig, Fs);   

ISEN/Traitement du signal/CIPA4/TP/TP3/TP3_Experience2.m

@@ -0,0 +1,172 @@
+%% Experiment 2 : Raised cosine with jamming and ambient noise
+% - Generate raised cosine h(t) on [-10T, 10T], T = 2 ms, beta = 0.5
+% - 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.
+
+clc;
+clear;
+close all;
+
+%% 1) Parameters and time vector
+
+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) 
+t   = -10*T : Ts : 10*T;   % Time vector
+N   = length(t);
+
+% Frequency axis for spectra (centered)
+f_axis = (-N/2 : N/2-1) * (Fs / N);   % Hz
+
+%% 2) Raised cosine pulse h(t)
+
+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 
+
+figure('Name','Experiment 2 - h(t) and |H(f)|');
+subplot(2,1,1);
+plot(t*1e3, h, 'g');
+xlabel('Time (ms)');
+ylabel('h(t)');
+title('Raised cosine pulse h(t), \beta = 0.5');
+grid on;
+
+subplot(2,1,2);
+plot(f_axis, magH, 'g');
+xlabel('Frequency (Hz)');
+ylabel('|H(f)|');
+title('Magnitude spectrum |H(f)| of raised cosine');
+grid on;
+
+%% 3) Generate jamming and ambient noise, build z(t)
+
+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) 
+
+z = h + x + n;                    % corrupted signal
+
+% Time-domain and magnitude spectrum of z(t)
+Z  = fft(z);
+magZ = abs(fftshift(Z));
+
+figure('Name','Experiment 2 - z(t) and |Z(f)|');
+subplot(2,1,1);
+plot(t*1e3, z, 'g');
+xlabel('Time (ms)');
+ylabel('z(t)');
+title('Noisy signal z(t) = h(t) + jamming + white noise');
+grid on;
+
+subplot(2,1,2);
+plot(f_axis, magZ, 'g');
+xlabel('Frequency (Hz)');
+ylabel('|Z(f)|');
+title('Magnitude spectrum |Z(f)| with jamming at 800 Hz');
+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.
+
+w0 = 2*pi*fJam/Fs;     % digital radian frequency
+r  = 0.98;             % pole radius (controls notch width)
+
+% One second-order notch section:
+b_sec = [1, -2*cos(w0), 1];          % zeros at e^{±jw0}
+a_sec = [1, -2*r*cos(w0), r^2];      % poles at r*e^{±jw0}
+
+% Approximate 15th-order by cascading 8 sections (~16th order)
+sections = 8;                        
+
+b15 = 1;
+a15 = 1;
+for k = 1:sections
+    b15 = conv(b15, b_sec);
+    a15 = conv(a15, a_sec);
+end
+
+% Filter output zz(t) and its spectrum
+zz15 = filter(b15, a15, z);
+
+ZZ15   = fft(zz15);
+magZZ15 = abs(fftshift(ZZ15));
+
+figure('Name','Experiment 2 - Order ~15 notch filter');
+subplot(2,1,1);
+plot(t*1e3, zz15, 'g');
+xlabel('Time (ms)');
+ylabel('zz_{15}(t)');
+title('Filtered signal (notch order ≈ 15)');
+grid on;
+
+subplot(2,1,2);
+plot(f_axis, magZZ15, 'g');
+xlabel('Frequency (Hz)');
+ylabel('|ZZ_{15}(f)|');
+title('Magnitude spectrum after order ≈ 15 notch filter');
+grid on;
+
+%% 5) Modify filter order to ~5 and update plot
+
+% Fewer cascaded sections (e.g. 3 -> ~6th order)
+sections2 = 3;
+
+b5 = 1;
+a5 = 1;
+for k = 1:sections2
+    b5 = conv(b5, b_sec);
+    a5 = conv(a5, a_sec);
+end
+
+zz5 = filter(b5, a5, z);
+
+ZZ5   = fft(zz5);
+magZZ5 = abs(fftshift(ZZ5));
+
+figure('Name','Experiment 2 - Order ~5 notch filter');
+subplot(2,1,1);
+plot(t*1e3, zz5, 'g');
+xlabel('Time (ms)');
+ylabel('zz_{5}(t)');
+title('Filtered signal (notch order ≈ 5)');
+grid on;
+
+subplot(2,1,2);
+plot(f_axis, magZZ5, 'g');
+xlabel('Frequency (Hz)');
+ylabel('|ZZ_{5}(f)|');
+title('Magnitude spectrum after order ≈ 5 notch filter');
+grid on;
+
+%% ===== Local function: one sample of raised cosine pulse =====
+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).
+
+    x = t / T;
+
+    % Manual sinc(x)
+    if abs(x) < 1e-12
+        sx = 1;                           % limit at x -> 0
+    else
+        sx = sin(pi*x) / (pi*x);
+    end
+
+    % Handle critical points of the raised cosine denominator
+    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)
+    else
+        h = sx * cos(pi*beta*x) / (1 - (4*beta^2*x^2));
+    end
+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);