Write a code in MATLAB for the Frequency modulation (FM) scheme where message m(t)= sin(2 π 10t) and carrier signal c(t)= 10 sin(2 π 1000t).

frequency_modulation.m

%FM modulation
Ac=10; %amplitude of carrier wave
fm=10; %frequency of message signal (Hz)
fc=1000; %carrier frequency (Hz)
F=10000; %sampling frequency (Hz)
kf=800; %frequency sensitivity
mi=kf/fm; % modulation index
T=1/F;
t=0:T:0.1;% time vector
 
%1.Message signal
m=sin(2*pi*fm*t);
figure(1);
subplot(311); % plot at 1st position in a 3-by-1 grid 
plot(t,m); xlabel('t(sec)'); ylabel('m(t)');
title('Message signal Vs Time')
 
%Spectrum of message signal
n=length(m); %length returns period of the message signal
M=fftshift(fft(m,n)); %zero-centered fast fourier transform
f=F*[-n/2:n/2-1]/n; %zero-centered frequency range
figure(2);subplot(311); 
plot(f,abs(M));xlabel('f(Hz)'); ylabel('M(f)');
title('Spectrum of Message signal');
 
%2.Carrier wave
c=Ac*sin(2*pi*fc*t);
figure(1); subplot(312);
plot(t,c); xlabel('t(sec'); ylabel('c(t)');
title('Carrier signal Vs Time');
 
%Spectrum of carrier wave
N=length(c);
C=fftshift(fft(c,N));
f=F*[-N/2:N/2-1]/N;
figure(2); subplot(312);
plot(f,abs(C)); xlabel('f(Hz)'); ylabel('C(f)');
title('Spectrum of Carrier wave');
 
%3.FM modulated signal
x_fm=Ac*sin(2*pi*fc*t-(mi*cos(2*pi*fm*t))); 
figure(1); subplot(313);
plot(t,x_fm); xlabel('t(Sec)'); ylabel('x_f_m(t)');
title('FM modulated signal Vs Time');
 
%Spectrum of fm modulated signal
l=length(x_fm);
X_fm=fftshift(fft(x_fm,l));
f=F*[-l/2:l/2-1]/l;
figure(2); subplot(313);
plot(f,abs(X_fm)); xlabel('f(Hz)'); ylabel('X_f_m(f)');
title('Spectrum of FM modulated signal');