echo on
%  This script illustrates the distortion on a modulated pulse
%  transmitted down a bandpass channel.
% Hit any key to continue
pause

tint = .03;                       %  time interval over which pulse is defined
fs = 10e3;                         %  Set sampling Rate to about 10 times highest pulse freq.
t = [-tint/2:(1/fs):(tint)];      %  Define t-axis with a sampling rate fs
len = length(t)                   %  See how big time axis vector is
% Hit any key to continue
pause

tau1 = 1/50;                      %  Pulse duration case 1                         
tau2 = 1/100;                     %  Pulse duration case 2
tau3 = 1/300;                     %  Pulse duration case 3
w0 = 500*2*pi;                    %  Modulating frequency and center
                                  %   frequency of Transfer function
a = 2*pi*100;                     %  Transfer function gain parameter (a/b)
b = 2*pi*100;                     %  Transfer function bandwidth parameter
figure(1);                        %   Case 1 pulse

s1 = tau1*rectw(t,tau1).*cos(w0*t);   % create signal
plot(t,s1);
title('original signal, tau = 1/50')
xlabel('seconds')
grid

fs1 = fft(s1,2*len);           %  Take the FT to create twice the frequency samples
f = [-fs/2:(fs/(2*len)):(fs/2)-fs/(2*len)];  %  Create Frequency Axis to
                                             %   evaluate Transfer function
p = j*2*pi*f;                  %  Create jw values
h = a*p ./ ( p.^2+b*p+w0^2);   %  Evaluate transfer function
pd = fs1.*fftshift(h);   %  Must shift Frequency axis, multiply by
                               %   FT of pulse, and divide by interval
                               %   over which the pulse was defined    
figure(2)
y1 = real(ifft(pd));           %  Take inverse FT (then take real part).
plot(t,y1(1:len));
title('channel output, tau = 1/50')
xlabel('seconds')
grid

%  Hit any key to continue
pause;

figure(1);                        %   Case 2 pulse
s2 = tau2*rectw(t,tau2).*cos(w0*t);
plot(t,s2);
title('original signal, tau = 1/100')
xlabel('seconds')
grid
fs2 = fft(s2,2*len);            %  Take the FT to create twice the frequency samples


p = j*2*pi*f;                  %  Create jw values
h = a*p ./ ( p.^2+b*p+w0^2);   %  Evaluate transfer function
pd = fs2.*fftshift(h);   %  Must shift Frequency axis, multiply by
                               %   FT of pulse, and divide by interval
                               %   over which the pulse was defined    
figure(2)
y2 = real(ifft(pd));           %  Take inverse FT (then take real part).
plot(t,y2(1:len)); 
title('channel output, tau = 1/100')
xlabel('seconds')
grid

% Hit any key to continue
pause;

figure(1);                        %   Case 3 pulse
s3 = tau3*rectw(t,tau3).*cos(w0*t);
plot(t,s3);
title('original signal, tau = 1/300')
xlabel('seconds')
grid
fs3 = fft(s3,2*len);            %  Take the FT to create twice the frequency samples

p = j*2*pi*f;                  %  Create jw values
h = a*p ./ ( p.^2+b*p+w0^2);   %  Evaluate transfer function
pd = fs3.*fftshift(h);         %  Must shift Frequency axis, multiply by
                               %  FT of pulse, and divide by interval
                               %   over which the pulse was defined    
figure(2)
y3 = real(ifft(pd));           %  Take inverse FT (then take real part).
plot(t,y3(1:len));            
title('channel output, tau = 1/300')
xlabel('seconds')
grid
echo off