Question

In frequency Modulation (FM), the instantaneous frequency of a sinusoidal carrier wave will be modified proportionally to the variation of amplitude of the message signal. Use Matlab to build an FM modulation and demodulation process. The FM coefficient is Kf=80, and the carrier frequency is 300Hz.

1. Generate a baseband signal as show below. Plot the baseband signal in time domain and frequency domain. 2. Create an FM process and plot the modulated signal in time and frequency domain.

-1 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 t (sec)

Answer 1

MATLAB code is given below in bold letters with comments for explanation.

clc;
close all;
clear all;

% define sample time
ts = 1e-5;
fs = 1/ts;

% define time vector
t = -0.04:ts:0.04;

% now define the signal x(t)
x = (t>-0.02).*(t<=-0.01).*(100*t+2) + (t>-0.01).*(t<=0.01).*(-100*t)+...
(t>0.01).*(t<=0.02).*(100*t-2);

% plotting the baseband signal in time domain
figure;subplot(211);
plot(t,x,'linewidth',2);grid on;
xlabel('t(sec)');ylabel('m(t)');

% plotting the baseband signal in frequency domain
N = nextpow2(length(x));
X = fftshift(fft(x,2^N));
X = 2* X / length(x);
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');
ylabel('Amplitude');xlim([-400 400]);
title('Double sided Magnitude spectrum');

% modulation of FM
kf = 80;fc = 300;
y = fmmod(x,fc,fs,kf);

% now define the signal x(t)
figure;subplot(211);
plot(t,y,'linewidth',2);grid on;
xlabel('t(sec)');ylabel('modulated signal y(t)');

% plotting the modulated signal in frequency domain
N = nextpow2(length(y));
X = fftshift(fft(y,2^N));
X = 2* X / length(y);
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');
ylabel('Amplitude');xlim([-1000 1000]);
title('Double sided Magnitude spectrum of fm signal');

% demodulate the FM signal
z = fmdemod(y,fc,fs,kf);
figure;
plot(t,z,'linewidth',2);grid on;
xlabel('t(sec)');title('Demodulated signal z(t)');

0.5 0.5 0.04 0.03 0.02 0.01 0 0.01 0.02 0.03 0.04 t(sec) Double sided Magnitude spectrunm 0.8 0.6 400 300 -200 100 0 100 200 300 400 Frequency in Hz

0.5 -0.5 0.04 0.03 0.02 -0.01 0 0.01 0.02 0.03 0.04 t(sec) Double sided Magnitude spectrum of fm signal 0.8 0.6 0.4 0.2 1000 800 -600 400 -200 0 200 400 600 800 1000 Frequency in Hz

Demodulated signal z(t) 0.6 0.2 0.6. 0.8 0.04 0.03 0.02 0.01 0 0.01 0.02 0.03 0.04 t(sec)