Square wave frequency modulation

I am trying to modulate a square wave with a DC value. Simple stuff at least i thought. Basically as the DC value increases so should the frequency of the square wave and it should be represented on graphs. It's not working as intended as the DC value increases. It envolves the use of Fourier. The code follows:

Square wave frequency modulation

% Define parameters
t = linspace(0, 1, 1000);   % Time vector
fc = 5;                    % Fundamental frequency (Hz)
kf = 0.1;                   % Frequency deviation constant
Vc = 1;                     % Amplitude of the carrier signal
Vdc_values = [0, 5, 10];   % Values of Vdc for the DC signals

% Generate carrier signal
vc = Vc/2;
for k = 1:2:10000
    vc = vc + (2*Vc/(pi*k)) * cos(2*pi*k*fc*t - 90*pi/180);
end

% Plot carrier signal
figure;
plot(t, vc, 'LineWidth', 2);
xlabel('Time');
ylabel('Amplitude');
title('Carrier Signal for Frequency Modulation');
ylim([0, 1]);  % Adjust ylim as needed
grid on;

% Frequency domain parameters
fs = 1000;                  % Sampling frequency
f = linspace(0, fs, 1000);  % Frequency vector


% Generate and plot frequency-modulated signals separately for each Vdc
for i = 1:length(Vdc_values)
    Vdc = Vdc_values(i);

    % Generate frequency-modulated signal
    v_fm = Vc/2;
    for k = 1:2:1000
        v_fm = v_fm + (2*Vc/(pi*k)) * cos(2*pi*2*k*fc*t - 90*pi/180 + 2*pi*kf*Vdc*t);
    end

    % Compute Fourier transform of frequency-modulated signal
    V_fm = abs(fft(v_fm));

    % Plot frequency-modulated signal in the time domain
    figure;
    subplot(2, 1, 1);
    plot(t, v_fm, 'LineWidth', 2);
    xlabel('Time');
    ylabel('Amplitude');
    title(['Frequency-Modulated Signal with Vdc = ', num2str(Vdc), ' (Time Domain)']);
    ylim([0, 1]);  % Adjust ylim as needed
    grid on;

    % Plot frequency-modulated signal in the frequency domain
    subplot(2, 1, 2);
    plot(f, V_fm, 'LineWidth', 2);
    xlabel('Frequency (Hz)');
    ylabel('Magnitude');
    title(['Frequency-Modulated Signal with Vdc = ', num2str(Vdc), ' (Frequency Domain)']);
    xlim([0, 200]);  % Adjust xlim as needed
    grid on;
end

As you can see as Vdc increases the signal breaks down. I'm not used to the

Answer 1

[Manikanta Aditya]

Hi,

The issue with your code is that you are not actually modulating the frequency of the square wave correctly. The way you are implementing it, you are adding a phase shift to the cosine terms, which does not directly modulate the frequency.

To modulate the frequency of a square wave correctly using a DC value, you need to generate the square wave first, and then modulate its frequency based on the DC value.

% Define parameters
t = linspace(0, 1, 1000); % Time vector
fc = 5; % Fundamental frequency (Hz)
kf = 0.1; % Frequency deviation constant
Vc = 1; % Amplitude of the carrier signal
Vdc_values = [0, 5, 10]; % Values of Vdc for the DC signals

% Generate carrier signal (square wave)
vc = square(2*pi*fc*t);

% Plot carrier signal
figure;
plot(t, vc, 'LineWidth', 2);
xlabel('Time');
ylabel('Amplitude');
title('Carrier Signal (Square Wave)');
ylim([-1.2, 1.2]); % Adjust ylim as needed
grid on;

% Frequency domain parameters
fs = 1000; % Sampling frequency
f = linspace(0, fs, 1000); % Frequency vector

% Generate and plot frequency-modulated signals separately for each Vdc
for i = 1:length(Vdc_values)
    Vdc = Vdc_values(i);
    
    % Generate frequency-modulated signal
    fm_freq = fc + kf * Vdc; % Modulated frequency
    v_fm = square(2*pi*fm_freq*t); % Frequency-modulated square wave
    
    % Compute Fourier transform of frequency-modulated signal
    V_fm = abs(fft(v_fm));
    
    % Plot frequency-modulated signal in the time domain
    figure;
    subplot(2, 1, 1);
    plot(t, v_fm, 'LineWidth', 2);
    xlabel('Time');
    ylabel('Amplitude');
    title(['Frequency-Modulated Signal with Vdc = ', num2str(Vdc), ' (Time Domain)']);
    ylim([-1.2, 1.2]); % Adjust ylim as needed
    grid on;
    
    % Plot frequency-modulated signal in the frequency domain
    subplot(2, 1, 2);
    plot(f, V_fm, 'LineWidth', 2);
    xlabel('Frequency (Hz)');
    ylabel('Magnitude');
    title(['Frequency-Modulated Signal with Vdc = ', num2str(Vdc), ' (Frequency Domain)']);
    xlim([0, 200]); % Adjust xlim as needed
    grid on;
end

Thanks, hope this helps.

[ashanni sonny]

It did I was able to adjust what I did thanks to you. I also gained a better understanding of frequency modulation.