Obisidian vault auto-backup: 05-01-2026 15:08:40 on . 2 files edited

.obsidian/workspace.json

@@ -30,8 +30,21 @@
               "icon": "lucide-file",
               "title": "24 oct 2025"
             }
+          },
+          {
+            "id": "8beea5ef99c3c6ed",
+            "type": "leaf",
+            "state": {
+              "type": "pdf",
+              "state": {
+                "file": "ISEN/Réseau/CIPA4/TP/Module 4/M04 TP 01 - Communication.pdf"
+              },
+              "icon": "lucide-file-text",
+              "title": "M04 TP 01 - Communication"
+            }
           }
-        ]
+        ],
+        "currentTab": 1
       }
     ],
     "direction": "vertical"
@@ -204,11 +217,22 @@
       "obsidian-git:Open Git source control": false
     }
   },
-  "active": "f8adac6650611d50",
+  "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~",
+    "ISEN/Réseau/CIPA4/TP/Module 4/M04 TP 01 - Communication.pdf.sb-a92ffc2d-7qze7T",
+    "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",
+    "ISEN/Réseau/CIPA4/TP/dossier sans titre",
     "Protocol Data Units (PDU).md",
     "ISEN/English/CIPA4/Elevator pitch.md",
-    "Untitled.base",
     "ISEN/English/CIPA4/24 oct 2025.md",
     "ISEN/English/CIPA4/29 sept 2025.md",
     "ISEN/BDD/CIPA4/BDD Cours 1.md",
@@ -224,15 +248,6 @@
     "ISEN/Réseau/A2/CCNA Cours 3.md",
     "Elevator.md",
     "ISEN/JAVA/CIPA4/TP/TP2/TP2.md",
-    "ISEN/JAVA/CIPA4/CM/10_JDBC.pdf",
-    "ISEN/JAVA/CIPA4/CM/09-fichiers.pdf",
-    "ISEN/JAVA/CIPA4/CM/08-collections.pdf",
-    "ISEN/JAVA/CIPA4/CM/07-exceptions.pdf",
-    "ISEN/JAVA/CIPA4/CM/06-threads.pdf",
-    "ISEN/JAVA/CIPA4/CM/05-swing.pdf",
-    "ISEN/JAVA/CIPA4/CM/04-classes-abstraites-interfaces.pdf",
-    "ISEN/JAVA/CIPA4/CM/03-heritage.pdf",
-    "ISEN/JAVA/CIPA4/CM/02-classes.pdf",
     "ISEN/FHS/A1/Réunion stage associatif.md",
     "ISEN/FHS/A1/Démocratie/Démocracie cours 7.md",
     "ISEN/BDD/CIPA4/modelisation-cas-immo.md",
@@ -240,8 +255,6 @@
     "ISEN/BDD/CIPA4/BDD Cours 2.md",
     "ISEN/FHS/CIPA4/Anthropologie de l'entreprise/Mythe Horoquartz.md",
     "ISEN/FHS/CIPA4/Anthropologie de l'entreprise/Anthropologie de l'entreprise Cours 1.md",
-    "ISEN/BDD/CIPA4/Projet/Présentation projet.md",
-    "ISEN/Réunion/CIPA 4/Réunion international.md",
     "Pasted image 20251009192656.png",
     "src/Pasted image 20240130111505.png",
     "src/Pasted image 20240123120819.png",

ISEN/Traitement du signal/CIPA4/TP/TP2/TP2_Experience1.m

@@ -0,0 +1,80 @@
+%% Experiment 1 : FFT of sinusoidal mixtures (magnitude spectra only)
+
+clc;
+clear;
+close all;
+
+%% ========================== PART i ==========================
+%% i) Ts = 0.2 ms, t in [0, 4 s]
+
+Ts1   = 0.2e-3;               % Sampling period (s)
+Fs1   = 1 / Ts1;              % Sampling frequency (Hz)
+t1    = 0 : Ts1 : 4;          % Time vector
+N1    = length(t1);           % Number of samples
+
+fi1   = Fs1 / N1;             % Frequency resolution (Hz)
+k1    = 0 : (N1-1);           % FFT index vector
+f_full_1 = k1 * fi1;          % Full frequency axis
+
+% Signal: x(t) = sin(2000 t + 56) * sin(56 - 6000 t) + 2 cos(4000 t)
+x1 = sin(2000*t1 + 56) .* sin(56 - 6000*t1) + 2*cos(4000*t1);
+
+%% i-a) Magnitude spectrum of x(t)  (single-sided)
+
+X1 = fft(x1);                     % N-point FFT
+half_N1   = floor(N1/2) + 1;      % Length of single-sided spectrum
+X1_half   = X1(1:half_N1);        % Positive frequencies only
+f1_half   = f_full_1(1:half_N1);  % Frequency axis (Hz)
+magX1     = abs(X1_half);         % Magnitude of complex spectrum
+
+figure('Name','Part i-a: |X(f)| of x(t)');
+plot(f1_half, magX1, 'r-');
+title('Part i-a: magnitude spectrum |X(f)| of x(t)');
+xlabel('Frequency (Hz)');
+ylabel('|X(f)|');
+grid on;
+
+%% i-b) Magnitude spectrum of x^2(t)  (single-sided)
+
+x2 = x1.^2;                   % x^2(t)
+X2 = fft(x2);                 % FFT of x^2(t)
+
+X2_half   = X2(1:half_N1);
+magX2     = abs(X2_half);
+% Same frequency axis f1_half
+
+figure('Name','Part i-b: |X_2(f)| of x^2(t)');
+plot(f1_half, magX2, 'm-');
+title('Part i-b: magnitude spectrum |X_2(f)| of x^2(t)');
+xlabel('Frequency (Hz)');
+ylabel('|X_2(f)|');
+grid on;
+
+%% ========================== PART ii ==========================
+%% ii) Fs = 5 kHz, t in [0, 2 s]
+% x(t) = cos(2000 t^2) + 0.01 sin(2000 t) + 0.01 sin(10000 t)
+
+Fs2   = 5000;                % Sampling frequency (Hz)
+Ts2   = 1 / Fs2;             % Sampling period (s)
+t2    = 0 : Ts2 : 2;         % Time vector
+N2    = length(t2);          % Number of samples
+
+fi2   = Fs2 / N2;            % Frequency resolution
+k2    = 0 : (N2-1);
+f_full_2 = k2 * fi2;
+
+x3 = cos(2000*t2.^2) + 0.01*sin(2000*t2) + 0.01*sin(10000*t2);
+
+X3 = fft(x3);                % FFT
+
+half_N2   = floor(N2/2) + 1;
+X3_half   = X3(1:half_N2);
+f2_half   = f_full_2(1:half_N2);
+magX3     = abs(X3_half);
+
+figure('Name','Part ii: |X(f)| of chirp signal');
+plot(f2_half, magX3, 'b-');
+title('Part ii: magnitude spectrum |X(f)| of x(t)');
+xlabel('Frequency (Hz)');
+ylabel('|X(f)|');
+grid on;

ISEN/Traitement du signal/CIPA4/TP/TP2/TP2_Experience2.m

@@ -0,0 +1,49 @@
+%% Experiment 2 : Recreation of a signal
+
+clc;
+clear;
+close all;
+
+Fs = 4000;                 % Sampling frequency (Hz)
+N  = 2048;                 % Number of samples
+t  = (0:N-1)/Fs;           % Time vector (s)
+
+df = Fs/N;                 % Frequency resolution (Hz)
+
+% --- 1) Desired peak frequencies (Hz) ---
+f_target = [300 400 700 1300 1600 1700];
+
+% Align each frequency with the closest FFT bin to avoid spectral leakage.
+k = round(f_target/df);    % Integer FFT bin indices
+f = k * df;                % Actual frequencies used (bin-aligned)
+
+% --- 2) Desired peak heights in |FFT| ---
+H = [1000 2000 3250 3250 2000 1000];
+
+% --- 3) Amplitudes of the cosines for those peak heights ---
+% For a cosine perfectly aligned to a bin, the peak in |FFT| is about N*A/2,
+% so we choose A = 2*H/N to obtain the target height H. 
+A = 2*H / N;
+
+% --- 4) Build the time-domain signal y(t) as a sum of cosines ---
+% Random phases are used because the magnitude spectrum does not depend on phase.
+phi = 2*pi*rand(size(f));  % Random phase for each component
+y   = zeros(size(t));      % Initialize signal
+
+for i = 1:length(f)
+    y = y + A(i) * cos(2*pi*f(i)*t + phi(i));
+end
+
+% --- 5) Compute FFT and plot the magnitude spectrum ---
+Y  = fft(y);               % Complex FFT of y(t)
+Py = abs(Y);               % Magnitude of the FFT (two-sided, unnormalized) 
+
+f_axis = (0:N-1) * df;     % Frequency axis (Hz)
+
+figure;
+stem(f_axis, Py, 'g');     % Discrete spectrum as vertical lines
+xlim([0 Fs/2]);            % Show only positive frequencies up to Nyquist
+xlabel('Frequency (Hz)');
+ylabel('|Y(f)|');
+title('Magnitude spectrum with target peak heights');
+grid on;

ISEN/Traitement du signal/CIPA4/TP/TP2/TP2_Experience3.m

@@ -0,0 +1,31 @@
+%% Experiment 3 : Power spectrum of "holiday_offer"
+% Plot the power spectrum with the same style as the TP figure. [web:81][web:155]
+
+clc;
+clear;
+close all;
+
+% 1) Load signal from MAT-file
+data = load('holiday_offer.mat');
+varNames   = fieldnames(data);
+signalName = varNames{1};      
+x = data.(signalName);         % time-domain signal vector
+
+Fs = 11025;                    % Sampling frequency (Hz)
+
+% 2) FFT-based power spectrum (periodogram)
+N    = length(x);
+Xdft = fft(x);
+Pxx  = (1/N) * abs(Xdft).^2;   % power spectrum estimate [web:154]
+
+% We keep the FULL spectrum (both sides) as in the given figure
+f = (0:N-1) * (Fs/N);          % frequency axis from 0 to Fs (≈11025 Hz)
+
+% 3) Plot
+figure;                       
+plot(f, Pxx, 'g');            
+xlabel('Frequency (Hz)');
+ylabel('Power');
+title('Power spectrum of holiday\_offer signal');
+grid on;
+xlim([0 Fs]);                  

ISEN/Traitement du signal/CIPA4/TP/TP2/TP2_Experience4.m

@@ -0,0 +1,58 @@
+%% Experiment 4 : Magnitude spectra of composed signals
+
+clc;
+clear;
+close all;
+
+%% ========================== PART i ==========================
+% i) Set the sampling period to 0.5 ms and time interval [0, 2 s]
+%    x(t) = sin(4000 t) + 2 cos(4000 t - 32) + cos^2(2000 t)
+
+Ts1 = 0.5e-3;               % Sampling period (s)
+Fs1 = 1 / Ts1;              % Sampling frequency (Hz) -> 2000 Hz
+t1  = 0 : Ts1 : 2;          % Time vector (s)
+N1  = length(t1);           % Number of samples
+
+% Define the signal x1(t)
+x1 = sin(4000*t1) + 2*cos(4000*t1 - 32) + cos(2000*t1).^2;
+
+% FFT and magnitude spectrum (single-sided)
+X1    = fft(x1);                       % Complex FFT of x1
+magX1 = abs(X1);                       % Magnitude spectrum
+halfN1 = floor(N1/2) + 1;              % First half (real signal) [web:171]
+magX1_half = magX1(1:halfN1);
+f1 = (0:halfN1-1) * (Fs1/N1);          % Frequency axis in Hz
+
+figure('Name','Experiment 4 - Part i');
+plot(f1, magX1_half, 'g');             % Green magnitude spectrum
+xlabel('Frequency (Hz)');
+ylabel('|X_1(f)|');
+title('Experiment 4 - Part i : Magnitude spectrum of x(t)');
+grid on;
+
+%% ========================== PART ii ==========================
+% ii) Set the sampling frequency to 5 kHz and time interval [0, 2 s]
+%     x(t) = 0.1 sin(2000 * sqrt(t)) + 0.01 sin(4000 t) + 0.01 cos(7000 t)
+% Note: Interpret "2000 t1/2" as 2000 * sqrt(t), i.e., t^(1/2).
+
+Fs2 = 5000;                 % Sampling frequency (Hz)
+Ts2 = 1 / Fs2;              % Sampling period (s)
+t2  = 0 : Ts2 : 2;          % Time vector (s)
+N2  = length(t2);           % Number of samples
+
+% Avoid sqrt(0) issues in instantaneous frequency by allowing t = 0 (OK in MATLAB)
+x2 = 0.1 * sin(2000 * sqrt(t2)) + 0.01 * sin(4000*t2) + 0.01 * cos(7000*t2);
+
+% FFT and magnitude spectrum (single-sided)
+X2    = fft(x2);
+magX2 = abs(X2);
+halfN2 = floor(N2/2) + 1;
+magX2_half = magX2(1:halfN2);
+f2 = (0:halfN2-1) * (Fs2/N2);          % Frequency axis in Hz
+
+figure('Name','Experiment 4 - Part ii');
+plot(f2, magX2_half, 'g');             % Green magnitude spectrum
+xlabel('Frequency (Hz)');
+ylabel('|X_2(f)|');
+title('Experiment 4 - Part ii : Magnitude spectrum of x(t)');
+grid on;

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 +1,117 @@
+%% Experiment 7 : Spectral Analysis of the raised cosine waveform
+% Raised cosine pulse:
+%   h(t) = sinc(t/T) * cos(pi*beta*t/T) / (1 - (4*beta^2*t.^2)/T^2)
+% where sinc(x) = sin(pi*x)/(pi*x).
+%
+% For this experiment:
+%   T   = 2 ms
+%   beta = 0.5 (then 0.25)
+%   t in [-10T, 10T]
+%   Ts  = 0.13*T  (sampling period)
+%
+% We generate the pulse h(t), plot it in time (ms) and frequency (Hz),
+% and compute the theoretical bandwidth B = (1/(2T))*(1+beta). 
+
+clc;
+clear;
+close all;
+
+%% 1) 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
+
+% Frequency axis for FFT (centered around 0)
+f_axis = (-N/2 : N/2-1) * (Fs / N);   % Hz
+
+% Inline handle to generate the pulse for any beta value
+rc_pulse = @(beta) arrayfun(@(tt) raisedCosineSample(tt, T, beta), t);
+
+%% ===================== beta = 0.5 =====================
+
+beta1 = 0.5;
+
+% Time-domain pulse
+h1 = rc_pulse(beta1);
+
+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));      % Magnitude, zero frequency centered
+
+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;
+
+% Theoretical bandwidth
+Rs       = 1 / T;                      % Symbol rate (Hz)
+BW_theo1 = (Rs/2) * (1 + beta1);       % B = (Rs/2)*(1+beta)
+fprintf('Theoretical bandwidth for beta = 0.5 : %.2f Hz\n', BW_theo1);
+
+%% ===================== beta = 0.25 =====================
+
+beta2 = 0.25;
+
+% Time-domain pulse
+h2 = rc_pulse(beta2);
+
+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;
+
+% Theoretical bandwidth
+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)
+    % with sinc(x) = sin(pi*x)/(pi*x).
+    % Special cases at t = 0 and t = ±T/(2*beta) use limit values. 
+    x = t / T;
+
+    % Manual definition of sinc(x) = sin(pi*x)/(pi*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
+        % At t -> 0, h(0) = 1 (sinc(0)=1 and cos(0)/(1-0)=1)
+        h = 1;
+    elseif beta ~= 0 && abs(abs(t) - T/(2*beta)) < 1e-12
+        % Limit at t = ±T/(2*beta)
+        h = (beta/pi) * sin(pi/(2*beta));
+    else
+        h = sx * cos(pi*beta*x) / (1 - (4*beta^2*x^2));
+    end
+end