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

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Félix MARQUET
2026-01-05 15:08:40 +01:00
parent 63ae5c2a9a
commit d7867f2850
2 changed files with 6 additions and 7 deletions
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13
ISEN/Traitement du signal/CIPA4/TP/TP2/TP2_Experience7.m
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@@ -10,7 +10,7 @@
% Ts = 0.13*T (sampling period) % Ts = 0.13*T (sampling period)
% %
% We generate the pulse h(t), plot it in time (ms) and frequency (Hz), % We generate the pulse h(t), plot it in time (ms) and frequency (Hz),
% and compute the theoretical bandwidth B = (1/(2T))*(1+beta). [web:222][web:228] % and compute the theoretical bandwidth B = (1/(2T))*(1+beta).
clc; clc;
clear; clear;
@@ -45,8 +45,8 @@ title('Raised cosine pulse h(t), \beta = 0.5');
grid on; grid on;
% Frequency-domain magnitude spectrum % Frequency-domain magnitude spectrum
H1 = fft(h1); % FFT of the pulse [web:8] H1 = fft(h1); % FFT of the pulse
magH1 = abs(fftshift(H1)); % Magnitude, zero frequency centered [web:202] magH1 = abs(fftshift(H1)); % Magnitude, zero frequency centered
figure('Name','Experiment 7 - Frequency domain, beta = 0.5'); figure('Name','Experiment 7 - Frequency domain, beta = 0.5');
plot(f_axis, magH1, 'g'); plot(f_axis, magH1, 'g');
@@ -57,7 +57,7 @@ grid on;
% Theoretical bandwidth % Theoretical bandwidth
Rs = 1 / T; % Symbol rate (Hz) Rs = 1 / T; % Symbol rate (Hz)
BW_theo1 = (Rs/2) * (1 + beta1); % B = (Rs/2)*(1+beta) [web:222][web:228] BW_theo1 = (Rs/2) * (1 + beta1); % B = (Rs/2)*(1+beta)
fprintf('Theoretical bandwidth for beta = 0.5 : %.2f Hz\n', BW_theo1); fprintf('Theoretical bandwidth for beta = 0.5 : %.2f Hz\n', BW_theo1);
%% ===================== beta = 0.25 ===================== %% ===================== beta = 0.25 =====================
@@ -94,8 +94,7 @@ function h = raisedCosineSample(t, T, beta)
% Raised cosine pulse sample at time t (scalar). % 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) % 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). % with sinc(x) = sin(pi*x)/(pi*x).
% Special cases at t = 0 and t = ±T/(2*beta) use limit values. [web:223] % Special cases at t = 0 and t = ±T/(2*beta) use limit values.
x = t / T; x = t / T;
% Manual definition of sinc(x) = sin(pi*x)/(pi*x) % Manual definition of sinc(x) = sin(pi*x)/(pi*x)
@@ -110,7 +109,7 @@ function h = raisedCosineSample(t, T, beta)
% At t -> 0, h(0) = 1 (sinc(0)=1 and cos(0)/(1-0)=1) % At t -> 0, h(0) = 1 (sinc(0)=1 and cos(0)/(1-0)=1)
h = 1; h = 1;
elseif beta ~= 0 && abs(abs(t) - T/(2*beta)) < 1e-12 elseif beta ~= 0 && abs(abs(t) - T/(2*beta)) < 1e-12
% Limit at t = ±T/(2*beta) [web:223] % Limit at t = ±T/(2*beta)
h = (beta/pi) * sin(pi/(2*beta)); h = (beta/pi) * sin(pi/(2*beta));
else else
h = sx * cos(pi*beta*x) / (1 - (4*beta^2*x^2)); h = sx * cos(pi*beta*x) / (1 - (4*beta^2*x^2));

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ISEN/Traitement du signal/CIPA4/TP/TP2/~$P2cipa.docx
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