Question

Complete using matlab

5. A msg m(t) that is used too modulate a carrier and frequency (fc) is 1500 in a FM system. Kf is 80. Plot the FM signal in time AND frequency domain using Matlab. The signal is shown below, m(t) is zero for t>250ms and t<0 ms. m(t) (V) Half Sinusoid 3.5 t (ms) 250

Answer 1

MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% define the parameters as below
fc = 1500; t0 = 0.25;
kf =80; ts = 0.0001; fs = 1/ts;

% define time vector
t = 0:ts:t0-ts;

% define m(t)
m = abs(3.5*sin(2*pi/t0*t));

% compute integral of m(t)
int_m(1) = 0;
for k =1:length(m)-1
int_m(k+1) = int_m(k) + m(k)*ts;
end

% now plot m(t) and it's integral
figure;
plot(t,m,'linewidth',2);grid on;xlabel('time');ylabel('Amplitude');
title('m(t)');ylim([-0.5 4]);

% now define fm signal as follows
u = cos(2*pi*fc*t + 2*pi*kf*int_m);

% plotting the FM signal
figure;
plot(t,u);
grid on;xlabel('time');ylabel('Amplitude');
title('FM :u(t)');%ylim([-1.2 1.2]);

% frequency spectrum of m(t)
N = nextpow2(length(m));
X = fftshift(fft(m,2^N));
X = 2* X / length(m);
k = -(length(X)-1)/2:1:length(X)/2;
f = k/length(X) * fs;
figure;subplot(211);plot(f,abs(X));grid;
xlabel('Frequency in Hz');%xlim([-500 500]);
ylabel('Amplitude');
title('Double sided Magnitude spectrum of m(t)');

% frequency spectrum of u(t)
N = nextpow2(length(u));
X = fftshift(fft(u,2^N));
X = 2* X / length(u);
k = -(length(X)-1)/2:1:length(X)/2;
f = k/length(X) * fs;
subplot(212);plot(f,abs(X));grid;
xlabel('Frequency in Hz');%xlim([-500 500]);
ylabel('Amplitude');
title('Double sided Magnitude spectrum of u(t)');

m(t) 4 3.5 3 2.5 E 1.5 0.5 0 0.5 0.1 0.05 0.25 0 0.15 0.2 time

FM :u(t) 0.8 0.6 0.4 ” 0.2 0.2 -0.4 0.6 0.8 -1 0 0.05 0.1 0.15 0.2 0.25 time

ble sided Magnitude spectrum of Doub m(t) 4 1500 -1000 500 500 1000 500 2000 Frequency in Hz Double sided Magnitude spectrum of u(t) 0.2 0.1 1500 1000 500 500 1000 1500 2000 Frequency in Hz