sampling and filtering in continuous time modulation

Explores the fundamental techniques of sampling and filtering within the context of continuous time modulation

1. Comprehensive study of sampling techniques (uniform, non-uniform) and filtering methods (FIR, IIR) within the context of continuous time modulation.

2. Practical demonstrations and discussions on the application of these techniques in telecommunications, audio processing, and other relevant domains, emphasizing their importance and impact on signal integrity and system performance.

% Parameters
Ac = 1.0;   % Carrier amplitude
fc = 10.0;  % Carrier frequency (Hz)
fs = 100.0; % Sampling frequency (Hz)
T = 1.0;    % Total time duration (s)
Ts = 1/fs;  % Sampling period
t = 0:Ts:T-Ts; % Time vector

% Message signal (sinusoidal)
fm = 2.0;   % Message frequency (Hz)
m_t = sin(2*pi*fm*t);

% Continuous-time modulated signal
s_t = Ac * (1 + m_t) .* cos(2*pi*fc*t);

% Sampling
x_n = s_t(1:round(fs/fc):end); % Sampling at the carrier frequency

% Filter design
cutoff = 20.0; % Cutoff frequency for the low-pass filter
nyquist = 0.5 * fs;
order = 5;  % Filter order
[b, a] = butter(order, cutoff/nyquist, 'low');

% Filtering
filtered_signal = filter(b, a, x_n);

% Plotting
figure;

subplot(3,1,1);
plot(t, s_t);
title('Continuous-Time Modulated Signal');
xlabel('Time (s)');
ylabel('Amplitude');
grid on;

subplot(3,1,2);
stem(t(1:round(fs/fc):end), x_n, 'r', 'Marker', 'o', 'LineStyle', 'none');
title('Sampled Signal');
xlabel('Time (s)');
ylabel('Amplitude');
grid on;

subplot(3,1,3);
plot(t(1:round(fs/fc):end), filtered_signal);
title('Filtered Signal');
xlabel('Time (s)');
ylabel('Amplitude');
grid on;

sgtitle('Sampling and Filtering in Continuous-Time Modulation');% Parameters
Ac = 1.0;   % Carrier amplitude
fc = 10.0;  % Carrier frequency (Hz)
fs = 100.0; % Sampling frequency (Hz)
T = 1.0;    % Total time duration (s)
Ts = 1/fs;  % Sampling period
t = 0:Ts:T-Ts; % Time vector

% Message signal (sinusoidal)
fm = 2.0;   % Message frequency (Hz)
m_t = sin(2*pi*fm*t);

% Continuous-time modulated signal
s_t = Ac * (1 + m_t) .* cos(2*pi*fc*t);

% Sampling
x_n = s_t(1:round(fs/fc):end); % Sampling at the carrier frequency

% Filter design
cutoff = 20.0; % Cutoff frequency for the low-pass filter
nyquist = 0.5 * fs;
order = 5;  % Filter order
[b, a] = butter(order, cutoff/nyquist, 'low');

% Filtering
filtered_signal = filter(b, a, x_n);

% Plotting
figure;

subplot(3,1,1);
plot(t, s_t);
title('Continuous-Time Modulated Signal');
xlabel('Time (s)');
ylabel('Amplitude');
grid on;

subplot(3,1,2);
stem(t(1:round(fs/fc):end), x_n, 'r', 'Marker', 'o', 'LineStyle', 'none');
title('Sampled Signal');
xlabel('Time (s)');
ylabel('Amplitude');
grid on;

subplot(3,1,3);
plot(t(1:round(fs/fc):end), filtered_signal);
title('Filtered Signal');
xlabel('Time (s)');
ylabel('Amplitude');
grid on;

sgtitle('Sampling and Filtering in Continuous-Time Modulation');