Obisidian vault auto-backup: 06-01-2026 13:34:10 on . 5 files edited

.obsidian/workspace.json

@@ -219,17 +219,17 @@
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-    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRL0001.tmp",
-    "ISEN/Traitement du signal/CIPA4/TP/TP3/~WRD0000.tmp",
-    "ISEN/Traitement du signal/CIPA4/TP/TP3/TP3_Experience1.m",
-    "ISEN/Traitement du signal/CIPA4/TP/untitled.m",
-    "ISEN/Réseau/CIPA4/TP/Module 5/M05 TP 01 - Packet_Tracer_Les_commandes.pka~",
-    "ISEN/Réseau/CIPA4/TP/Module 4/M04 TP 01 - Communication.pdf",
-    "ISEN/Réseau/CIPA4/TP/Module 4/M04 TP 02 -Packet_Tracer-La_communication.pka~",
-    "ISEN/Traitement du signal/CIPA4/TP/TP3/~$P3cipa.docx",
-    "ISEN/Traitement du signal/CIPA4/TP/TP2/TP2cipa_MARQUET.pdf",
-    "ISEN/Traitement du signal/CIPA4/TP/TP2/~$P2cipa.docx",
-    "ISEN/Traitement du signal/CIPA4/TP/TP2/TP2_Experience7.m",
+    "ISEN/Traitement du signal/CIPA4/TP/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_Experience1.m

@@ -37,7 +37,7 @@ figure('Name','Q2noisy - Magnitude spectrum');
 plot(f, magX_half, 'g');
 xlabel('Frequency (Hz)');
 ylabel('|X(f)|');
-title('Magnitude spectrum of Q2noisy (use this to read jamming frequency)');
+title('Magnitude spectrum of Q2noisy');
 grid on;
 xlim([0 Fs/2]);
 

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. [web:216][web:223]
+
+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) [web:202]
+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);   % [web:223]
+
+% Time-domain h(t) and magnitude spectrum
+H  = fft(h);
+magH = abs(fftshift(H));   % magnitude, zero frequency at center [web:202]
+
+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) [web:223]
+
+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. [web:238]
+
+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;                         % adjust to get desired attenuation
+
+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). [web:216][web:223]
+
+    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) [web:223]
+    else
+        h = sx * cos(pi*beta*x) / (1 - (4*beta^2*x^2));
+    end
+end