% MATLAB script for Illustrative Problem 3.9.
% Demonstration script for envelope detection. The message signal
% is +1 for 0 < t < t0/3, -2 for t0/3 < t < 2t0/3, and zero otherwise.
clear
echo on
t0=.15;                                	% signal duration
ts=0.001;                              	% sampling interval
fc=250;                                	% carrier frequency
a=0.85;                                	% modulation index
fs=1/ts;                               	% sampling frequency
t=[0:ts:t0];                           	% time vector
df=0.25;                               	% required frequency resolution
% message signal
m=[ones(1,t0/(3*ts)),-2*ones(1,t0/(3*ts)),zeros(1,t0/(3*ts)+1)];
c=cos(2*pi*fc.*t);                     	% carrier signal
m_n=m/max(abs(m));                     	% normalized message signal
[M,m,df1]=fftseq(m,ts,df);             	% Fourier transform 
f=[0:df1:df1*(length(m)-1)]-fs/2;      	% frequency vector
u=(1+a*m_n).*c;                        	% modulated signal
[U,u,df1]=fftseq(u,ts,df);             	% Fourier transform 
env=env_phas(u);                       	% Find the envelope. 
dem1=2*(env-1)/a;                      	% Remove dc and rescale.
signal_power=spower(u(1:length(t)));   	% power in modulated signal
noise_power=signal_power/100;          	% noise power
noise_std=sqrt(noise_power);           	% noise standard deviation
noise=noise_std*randn(1,length(u));    	% Generate noise.
r=u+noise;                             	% Add noise to the modulated signal.
[R,r,df1]=fftseq(r,ts,df);             	% Fourier transform 
env_r=env_phas(r);                     	% envelope, when noise is present
dem2=2*(env_r-1)/a;                    	% Demodulate in the presence of noise.
pause  % Press any key to see a plot of the message.
subplot(2,1,1)
plot(t,m(1:length(t)))
axis([0 0.15 -2.1 2.1])
xlabel('Time')
title('The message signal')
pause  % Press any key to see a plot of the modulated signal.
subplot(2,1,2)
plot(t,u(1:length(t)))
axis([0 0.15 -2.1 2.1])
xlabel('Time')
title('The modulated signal')
pause  % Press a key to see the envelope of the modulated signal.
clf
subplot(2,1,1)
plot(t,u(1:length(t)))
axis([0 0.15 -2.1 2.1])
xlabel('Time')
title('The modulated signal')
subplot(2,1,2)
plot(t,env(1:length(t)))
xlabel('Time')
title('Envelope of the modulated signal')
pause  % Press a key to compare the message and the demodulated signal.
clf
subplot(2,1,1)
plot(t,m(1:length(t)))
axis([0 0.15 -2.1 2.1])
xlabel('Time')
title('The message signal')
subplot(2,1,2)
plot(t,dem1(1:length(t)))
xlabel('Time')
title('The demodulated signal')
pause  % Press a key to compare in the presence of noise. 
clf
subplot(2,1,1)
plot(t,m(1:length(t)))
axis([0 0.15 -2.1 2.1])
xlabel('Time')
title('The message signal')
subplot(2,1,2)
plot(t,dem2(1:length(t)))
xlabel('Time')
title('The demodulated signal in the presence of noise')