clc; clear; close all;

% 1. Time and Sampling Setup
fs = 20000;                     % Sampling frequency (20 kHz)
t = 0 : 1/fs : 0.05;            % Time duration (0.05 s)

% 2. Signal & Deviation Parameters
Am = 2;                         % Message amplitude (V)
Ac = 5;                         % Carrier amplitude (V)
fm = 50;                        % Message frequency (50 Hz)
fc = 600;                       % Carrier frequency (600 Hz)
kf = 150;                       % Frequency sensitivity (Hz/V)

delta_f = kf * Am;              % Peak Frequency Deviation (300 Hz)
beta = delta_f / fm;            % Modulation Index (beta = 6)
BW_carson = 2 * (delta_f + fm); % Carson's Rule Bandwidth (700 Hz)

fprintf('Delta f = %.2f Hz | Beta = %.2f | Carson BW = %.2f Hz\n', delta_f, beta, BW_carson);

% 3. Generate Signals
m_t = Am * cos(2 * pi * fm * t);
c_t = Ac * cos(2 * pi * fc * t);
s_fm = Ac * cos(2 * pi * fc * t + beta * sin(2 * pi * fm * t));

% 4. Plotting
figure('Name', '2. Frequency Modulation (FM)');
subplot(3, 1, 1); plot(t, m_t, 'b', 'LineWidth', 1.5);
title(['Message Signal m(t) (f_m = ', num2str(fm), ' Hz)']); ylabel('Amplitude (V)'); grid on;

subplot(3, 1, 2); plot(t, c_t, 'k', 'LineWidth', 1);
title(['Carrier Signal c(t) (f_c = ', num2str(fc), ' Hz)']); ylabel('Amplitude (V)'); grid on;

subplot(3, 1, 3); plot(t, s_fm, 'g', 'LineWidth', 1.2);
title(['FM Signal (\beta = ', num2str(beta), ', BW = ', num2str(BW_carson), ' Hz)']);
xlabel('Time (s)'); ylabel('Amplitude (V)'); grid on;