sampling and filtering in discrete time modulation

Sampling converts continuous-time signals to discrete-time, following Nyquist-Shannon theorem for fidelity.

1. The project will comprehensively cover sampling techniques (uniform, non-uniform, oversampling) and filtering methods (FIR, IIR), elucidating their theoretical underpinnings and practical applications.

2. Practical demonstrations, simulations, and hands-on experiments will be employed to illustrate the principles and real-world significance of sampling and filtering in digital signal processing systems, fostering practical skills and insights among participants.

% Define parameters
Fs = 1000; % Sampling frequency (Hz)
T = 1/Fs; % Sampling period
t = 0:T:1; % Time vector (1 second duration)
f1 = 10; % Frequency of the original signal (Hz)
A = 1; % Amplitude of the original signal

% Generate original signal (sine wave)
x = A*sin(2*pi*f1*t);

% Plot original signal
subplot(3,1,1);
plot(t, x);
title('Original Signal');
xlabel('Time (s)');
ylabel('Amplitude');

% Sample the signal
Fs_new = 50; % New sampling frequency (Hz)
T_new = 1/Fs_new; % New sampling period
n = 0:T_new:1; % New time vector
x_sampled = A*sin(2*pi*f1*n); % Sampled signal

% Plot sampled signal
subplot(3,1,2);
stem(n, x_sampled);
title('Sampled Signal');
xlabel('Time (s)');
ylabel('Amplitude');

% Apply low-pass filtering (simple moving average)
N = 10; % Filter length (number of samples)
b = ones(1, N)/N; % Filter coefficients (moving average)
x_filtered = filter(b, 1, x_sampled); % Filtered signal

% Plot filtered signal
subplot(3,1,3);
stem(n, x_filtered);
title('Filtered Signal');
xlabel('Time (s)');
ylabel('Amplitude');

% Display original and filtered signal frequency content
figure;
freqz(b, 1, length(x_sampled), Fs_new);
title('Frequency Response of Filter');