Frequency modulation without fmmode?

I was able to solve it manually but I couldn't do it in python. I found Phi(t)= 200* PI* Triangle(t-2/2), Y(f)= sinc^2 but I couldn't define them manually in python, can you help me?

[Hassaan]

@cagri esen This is a MATLAB forum for QnA.

Answer 1

[Hassaan]

@cagri esen Assumming MATLAB environment.

% Parameters
k_f = 50; % Frequency sensitivity
f_c = 500; % Carrier frequency in Hz
t = linspace(-1, 1, 1000); % Time vector

% Message signal m(t)
m_t = tripuls(t-1/2, 2); % Triangular pulse

% Phase signal phi(t)
phi_t = 2 * k_f * cumtrapz(t, m_t); % Integral of m(t) with k_f

% FM signal y(t)
y_t = 5 * cos(2 * pi * f_c * t + phi_t);

% Plot the message signal m(t)
figure;
plot(t, m_t);
title('Message Signal m(t)');
xlabel('Time [s]');
ylabel('Amplitude');

% Magnitude spectrum of the message signal
M_f = abs(fft(m_t));
frequencies = linspace(-500, 500, length(M_f)); % Frequency vector for plotting

figure;
plot(frequencies, fftshift(M_f));
title('Magnitude Spectrum of m(t)');
xlabel('Frequency [Hz]');
ylabel('Magnitude');

% Plot the phase signal phi(t)
figure;
plot(t, phi_t);
title('Phase Signal \phi(t)');
xlabel('Time [s]');
ylabel('Phase');

% Magnitude spectrum of the phase signal
P_f = abs(fft(phi_t));

figure;
plot(frequencies, fftshift(P_f));
title('Magnitude Spectrum of \phi(t)');
xlabel('Frequency [Hz]');
ylabel('Magnitude');

% Plot the FM signal y(t)
figure;
plot(t, y_t);
title('FM Signal y(t)');
xlabel('Time [s]');
ylabel('Amplitude');

% Magnitude spectrum of the FM signal
Y_f = abs(fft(y_t));

figure;
plot(frequencies, fftshift(Y_f));
title('Magnitude Spectrum of y(t)');
xlabel('Frequency [Hz]');
ylabel('Magnitude');

% Demodulation (simplified representation)
% Differentiation
diff_phi_t = [diff(phi_t) 0]; % Differentiate phi(t)

% Diode (rectification)
rectified_phi_t = abs(diff_phi_t); % Model diode as absolute value

% Low-pass filter
LPF_phi_t = lowpass(rectified_phi_t, 1, 1/(t(2)-t(1))); % Using built-in lowpass

% DC blocking (high-pass filter)
HPF_phi_t = highpass(LPF_phi_t, 0.1, 1/(t(2)-t(1))); % Using built-in highpass

% Plot the demodulated signal
figure;
plot(t, HPF_phi_t);
title('Demodulated Signal');
xlabel('Time [s]');
ylabel('Amplitude');

1. Defines the message signal as a triangular pulse.
2. Computes the phase signal by integrating the message signal, scaled by kf​.
3. Generates the FM signal by modulating the cosine wave with the phase signal.
4. Plots the message signal and its magnitude spectrum.
5. Plots the phase signal and its magnitude spectrum.
6. Plots the FM signal and its magnitude spectrum.
7. Performs a simplified demodulation of the FM signal, including differentiation, rectification (diode), low-pass filtering, and DC blocking (high-pass filtering).
8. Plots the demodulated signal.

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