clc; close all; clear;
% Define parameters
T = 1/500; % Signal period
fm = 1/T; % Signal frequency
% Define sampling frequencies
fs1 = 500; % Fs < 2F (Aliasing case)
fs2 = 1000; % Fs = 2F (Critical Sampling)
fs3 = 10000; % Fs > 2F (Oversampling)
% Time vector (continuous)
t = 0:1e-6:10*T; % High resolution for visibility
% Continuous-time signal
x = cos(2*pi*fm*t);
% Define pulse width (short duration to approximate impulse)
pulse_width = 1e-5; % Very narrow pulse
% Create sample instants
t1 = 0:1/fs1:max(t); % Sample times for Fs < 2F
t2 = 0:1/fs2:max(t); % Sample times for Fs = 2F
t3 = 0:1/fs3:max(t); % Sample times for Fs > 2F
% Generate pulse trains
pulses1 = pulstran(t, t1, @rectpuls, pulse_width); % Sampling with Fs < 2F
pulses2 = pulstran(t, t2, @rectpuls, pulse_width); % Sampling with Fs = 2F
pulses3 = pulstran(t, t3, @rectpuls, pulse_width); % Sampling with Fs > 2F
% Sampled signals (multiplying by pulses)
sampled1 = x .* pulses1;
sampled2 = x .* pulses2;
sampled3 = x .* pulses3;
% Plot results
figure;
% Aliased signal (Fs < 2F)
subplot(3,1,1); plot(t, sampled1, 'r'); hold on;
xlabel('Time (s)'); ylabel('Amplitude'); title('Sampling with Fs < 2F (Aliasing)');
grid on;
% Nyquist rate sampling (Fs = 2F)
subplot(3,1,2); plot(t, sampled2, 'g'); hold on;
xlabel('Time (s)'); ylabel('Amplitude'); title('Sampling with Fs = 2F (Critical Sampling)');
grid on;
% Oversampling case (Fs > 2F)
subplot(3,1,3); plot(t, sampled3, 'b'); hold on;
xlabel('Time (s)'); ylabel('Amplitude'); title('Sampling with Fs > 2F (Oversampling)');
grid on;