Obisidian vault auto-backup: 05-01-2026 14:48:31 on . 5 files edited

.obsidian/workspace.json

@@ -219,6 +219,8 @@
   },
   "active": "8beea5ef99c3c6ed",
   "lastOpenFiles": [
+    "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/Traitement du signal/CIPA4/TP/TP2/~$P2cipa.docx",
     "ISEN/Réseau/CIPA4/TP/Module 4/M04 TP 02 -Packet_Tracer-La_communication.pka~",
@@ -229,8 +231,6 @@
     "ISEN/Réseau/CIPA4/TP/Module 6/M06 TP 01 - IPv6.pdf",
     "ISEN/Réseau/CIPA4/TP/Module 6",
     "ISEN/Réseau/CIPA4/TP/dossier sans titre",
-    "ISEN/Réseau/CIPA4/TP/Module 5/M05 TP 01 - Packet_Tracer_Les_commandes.pka",
-    "ISEN/Réseau/CIPA4/TP/Module 5",
     "Protocol Data Units (PDU).md",
     "ISEN/English/CIPA4/Elevator pitch.md",
     "ISEN/English/CIPA4/24 oct 2025.md",

ISEN/Traitement du signal/CIPA4/TP/TP2/TP2_Experience5.m

@@ -0,0 +1,51 @@
+%% Experiment 5 : Magnitude spectrum of x(t)
+% x(t) = cos(2*pi + 20000*t) * sin(2*pi*30000*t) + 2*cos(22000*t)
+% Time interval: [0, 0.4 s]
+
+clc;
+clear;
+close all;
+
+%% 1) Define continuous-time parameters (for information)
+% Angular frequencies (rad/s)
+w1 = 20000;              % from cos(2*pi + 20000*t) -> cos(20000*t)
+w2 = 2*pi*30000;         % from sin(2*pi*30000*t)
+w3 = 22000;              % from cos(22000*t)
+
+% Corresponding frequencies (Hz)
+f1 = w1/(2*pi) + 30000;  % highest frequency component
+f2 = 30000 - w1/(2*pi);  % lower side frequency
+f3 = w3/(2*pi);          % from cos(22000*t)
+
+f_max = f1;              % maximum frequency in the signal
+
+%% 2) Choose sampling frequency Fs and period Ts
+Fs = 5 * 2 * f_max;      % Fs chosen well above 2*f_max (safety factor 5)
+Ts = 1 / Fs;             % Sampling period (s)
+
+%% 3) Build time vector on [0, 0.4 s]
+T_end = 0.4;             
+t = 0 : Ts : T_end;      % Time vector
+N = length(t);           % Number of samples
+
+%% 4) Generate sampled signal x[n] = x(t)
+x = cos(2*pi + 20000*t) .* sin(2*pi*30000*t) + 2*cos(22000*t);
+
+%% 5) Compute FFT and magnitude spectrum (single-sided)
+
+X = fft(x);                      % N-point FFT of x
+magX = abs(X);                   % Magnitude spectrum
+halfN = floor(N/2) + 1;          % First half (real signal -> symmetric) 
+magX_half = magX(1:halfN);
+
+% Frequency axis in Hz
+f = (0:halfN-1) * (Fs/N);        % f_k = k * Fs / N 
+
+%% 6) Plot magnitude spectrum
+
+figure;
+plot(f, magX_half, 'g');         % Green magnitude spectrum
+xlabel('Frequency (Hz)');
+ylabel('|X(f)|');
+title('Experiment 5 : Magnitude spectrum of x(t)');
+grid on;

ISEN/Traitement du signal/CIPA4/TP/TP2/TP2_Experience6.m

@@ -0,0 +1,37 @@
+%% Experiment 6 : Magnitude spectrum of x(t)
+% Sampling period Ts = 0.5 ms, time interval [0, 2 s]
+% x(t) = sin(4000 t) + 2 cos(4000 t - 32) + cos^2(2000 t)
+
+clc;
+clear;
+close all;
+
+%% 1) Sampling parameters
+
+Ts = 0.5e-3;              % Sampling period (s)
+Fs = 1 / Ts;              % Sampling frequency (Hz) -> 2000 Hz
+t  = 0 : Ts : 2;          % Time vector from 0 to 2 s
+N  = length(t);           % Number of samples
+
+%% 2) Generate the signal x(t)
+
+x = sin(4000*t) + 2*cos(4000*t - 32) + cos(2000*t).^2;
+
+%% 3) Compute FFT and magnitude spectrum (single-sided)
+
+X = fft(x);                       % N-point FFT of x(t) 
+magX = abs(X);                    % Magnitude spectrum
+halfN = floor(N/2) + 1;           % First half (real signal -> symmetric) 
+magX_half = magX(1:halfN);
+
+% Frequency axis in Hz
+f = (0:halfN-1) * (Fs/N);         % f_k = k * Fs / N  
+
+%% 4) Plot magnitude spectrum
+
+figure;
+plot(f, magX_half, 'g');          % Green magnitude spectrum
+xlabel('Frequency (Hz)');
+ylabel('|X(f)|');
+title('Experiment 6 : Magnitude spectrum of x(t)');
+grid on;

ISEN/Traitement du signal/CIPA4/TP/TP2/TP2_Experience7.m

@@ -0,0 +1,96 @@
+%% Experiment 7 : Spectral Analysis of the raised cosine waveform
+
+clc;
+clear;
+close all;
+
+%% Common parameters
+T   = 2e-3;                 % Symbol period (s)
+Ts  = 0.13 * T;             % Sampling period (s)
+Fs  = 1 / Ts;               % Sampling frequency (Hz)
+t   = -10*T : Ts : 10*T;    % Time vector from -10T to 10T
+N   = length(t);            % Number of samples
+
+%% Helper function: raised cosine pulse (inline)
+% We handle the singularities at t = 0 and t = ±T/(2*beta) using limits. 
+rc_pulse = @(beta) ...
+    arrayfun(@(tt) ...
+        raisedCosineSample(tt, T, beta), t);
+
+%% ===== a) & b) for beta = 0.5 =====
+beta1 = 0.5;
+
+h1 = rc_pulse(beta1);       % Time-domain raised cosine pulse
+
+% --- Time-domain plot (x-axis in ms) ---
+figure('Name','Experiment 7 - Time domain, beta = 0.5');
+plot(t*1e3, h1, 'g');       % t in ms
+xlabel('Time (ms)');
+ylabel('h(t)');
+title('Raised cosine pulse h(t), \beta = 0.5');
+grid on;
+
+% --- Frequency-domain magnitude spectrum ---
+H1 = fft(h1);               % FFT of the pulse
+magH1 = abs(fftshift(H1));  % Center zero frequency; take magnitude
+
+% Frequency axis in Hz, centered around 0
+f_axis = (-N/2:N/2-1) * (Fs/N);
+
+figure('Name','Experiment 7 - Frequency domain, beta = 0.5');
+plot(f_axis, magH1, 'g');
+xlabel('Frequency (Hz)');
+ylabel('|H(f)|');
+title('Magnitude spectrum of raised cosine pulse, \beta = 0.5');
+grid on;
+
+% --- c) Measure bandwidth (approximate)
+% For a raised cosine with symbol rate Rs = 1/T, ideal theoretical
+% baseband bandwidth is B = (Rs/2)*(1+beta). 
+Rs      = 1/T;                    % Symbol rate (Hz)
+BW_theo1 = (Rs/2) * (1 + beta1);  % Theoretical bandwidth (Hz)
+fprintf('Theoretical bandwidth for beta=0.5: %.2f Hz\n', BW_theo1);
+
+%% ===== d) Repeat for beta = 0.25 =====
+beta2 = 0.25;
+
+h2 = rc_pulse(beta2);
+
+% Time-domain plot
+figure('Name','Experiment 7 - Time domain, beta = 0.25');
+plot(t*1e3, h2, 'g');
+xlabel('Time (ms)');
+ylabel('h(t)');
+title('Raised cosine pulse h(t), \beta = 0.25');
+grid on;
+
+% Frequency-domain magnitude spectrum
+H2 = fft(h2);
+magH2 = abs(fftshift(H2));
+figure('Name','Experiment 7 - Frequency domain, beta = 0.25');
+plot(f_axis, magH2, 'g');
+xlabel('Frequency (Hz)');
+ylabel('|H(f)|');
+title('Magnitude spectrum of raised cosine pulse, \beta = 0.25');
+grid on;
+
+BW_theo2 = (Rs/2) * (1 + beta2);
+fprintf('Theoretical bandwidth for beta=0.25: %.2f Hz\n', BW_theo2);
+
+%% ===== Local function for one sample of raised cosine =====
+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)
+    % Special cases at t = 0 and t = ±T/(2*beta) use L'Hospital limits. 
+
+    if abs(t) < 1e-12
+        % Limit at t -> 0
+        h = 1;  % sinc(0) = 1 and cos(0)/(1-0) = 1
+    elseif beta ~= 0 && abs(abs(t) - T/(2*beta)) < 1e-12
+        % Singularities at t = ±T/(2*beta) -> use known limit value 
+        h = (beta/pi) * sin(pi/(2*beta));
+    else
+        x = t / T;
+        h = sinc(x) * cos(pi*beta*x) / (1 - (4*beta^2*x^2));
+    end
+end