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  1. In MATLAB, you can implement critical modulation (often referring to amplitude modulation at the critical modulation index of 1) using built-in functions like ammod or by manually generating the modulated waveform. This ensures the carrier amplitude equals the message amplitude, avoiding over-modulation.

    Steps to Implement

    1. Define Parameters Set the sampling frequency, carrier frequency, message frequency, and modulation index (critical value = 1).

    2. Generate Message and Carrier Signals Create a sinusoidal message signal and a carrier wave.

    3. Apply Amplitude Modulation Use MATLAB’s ammod function or manually compute the AM signal using the formula: [ y(t) = (1 + m \cdot x(t)) \cdot \cos(2\pi f_c t) ] where ( m = 1 ) for critical modulation.

    4. Plot and Analyze Visualize both time-domain and frequency-domain representations to verify correct modulation.

    Example MATLAB Code

    % Parameters
    fs = 1000; % Sampling frequency (Hz)
    fc = 100; % Carrier frequency (Hz)
    fm = 10; % Message frequency (Hz)
    m_index = 1; % Critical modulation index
    t = 0:1/fs:1; % Time vector

    % Message signal
    msg = cos(2*pi*fm*t);

    % AM using built-in function
    y_builtin = ammod(msg, fc, fs, 0, 1); % Carrier amplitude = 1

    % AM using manual formula
    carrier = cos(2*pi*fc*t);
    y_manual = (1 + m_index * msg) .* carrier;

    % Plot results
    figure;
    subplot(3,1,1); plot(t, msg); title('Message Signal');
    subplot(3,1,2); plot(t, carrier); title('Carrier Signal');
    subplot(3,1,3); plot(t, y_manual); title('AM Signal (Critical Modulation)');
    نقل کر لیا گیا!
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