📄 ip_03_11.m
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% MATLAB script for Illustrative Problem 3.11.
% Demonstration script for frequency modulation. The message signal
% is m(t)=sinc(100t).
clear
echo on
t0=.2; % signal duration
ts=0.001; % sampling interval
fc=250; % carrier frequency
snr=20; % SNR in dB (logarithmic)
fs=1/ts; % sampling frequency
df=0.3; % required freq. resolution
t=[-t0/2:ts:t0/2]; % time vector
kf=100; % deviation constant
df=0.25; % required frequency resolution
m=sinc(100*t); % the message signal
int_m(1)=0;
for i=1:length(t)-1 % integral of m
int_m(i+1)=int_m(i)+m(i)*ts;
echo off ;
end
echo on ;
[M,m,df1]=fftseq(m,ts,df); % Fourier transform
M=M/fs; % scaling
f=[0:df1:df1*(length(m)-1)]-fs/2; % frequency vector
u=cos(2*pi*fc*t+2*pi*kf*int_m); % modulated signal
[U,u,df1]=fftseq(u,ts,df); % Fourier transform
U=U/fs; % scaling
[v,phase]=env_phas(u,ts,250); % demodulation, find phase of u
phi=unwrap(phase); % Restore original phase.
dem=(1/(2*pi*kf))*(diff(phi)/ts); % demodulator output, differentiate and scale phase
pause % Press any key to see a plot of the message and the modulated signal.
subplot(2,1,1)
plot(t,m(1:length(t)))
xlabel('Time')
title('The message signal')
subplot(2,1,2)
plot(t,u(1:length(t)))
xlabel('Time')
title('The modulated signal')
pause % Press any key to see plots of the magnitude of the message and the
% modulated signal in the frequency domain.
subplot(2,1,1)
plot(f,abs(fftshift(M)))
xlabel('Frequency')
title('Magnitude spectrum of the message signal')
subplot(2,1,2)
plot(f,abs(fftshift(U)))
title('Magnitude-spectrum of the modulated signal')
xlabel('Frequency')
pause % Press any key to see plots of the message and the demodulator output with no
% noise.
subplot(2,1,1)
plot(t,m(1:length(t)))
xlabel('Time')
title('The message signal')
subplot(2,1,2)
plot(t,dem(1:length(t)))
xlabel('Time')
title('The demodulated signal')
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