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