%These m files show the time and frequency domain for a 0.5nS Gaussian
%monopulse(or monocycle) including an unmodulated monocycle pulse train(polycycle)
%for UWB wireless system analysis.

%The programs have not been verified since I do not have the signal processing
%toolbox that has gmonopuls and pulstran. I have shown a Ref that shows
%the waveforms and I'm assuming they work as the examples for gmonopuls in
%the matlab documentation are alike except for the frequency domain
%presentation. The monopulse is the first derivative of the Gaussian pulse.
%What is needed is m files for the 2nd derivative of the Gaussian pulse which is a
%doublet, mexican hat, etc. showing pulse trains(unmodulated and modulated schemes)
%in the time and frequency domains preferably constructed without the
%requirement of the signal processing toolbox.

% gmonopuls.mat a new function program written in Matlab for a 2GHz gaussian monopulse both in
% the Time & Frequency domains
N=12; fc=2E9; fs=100E9; n=0:N-1;
%2GHz UWB Gaussian monopulse in the time domain sampled at a rate of 100 GHz.
tc=gmonopuls ('cutoff',fc); %width of each pulse (0.5nS)
t =-2*tc: 1/fs: 2*tc; %signal evaluation time
y= gmonopuls (t,fc);
figure(1); subplot (1,1,1); subplot (1,2,1);
plot(t,y); grid; title ('UWB Gaussian Monopulse in the time domain');
xlabel ('Time in nanoseconds'); ylabel ('Unity-Amplitude');
%spectrum of a 2GHz G.monopulse
tc=gmonopuls('cutoff',fc); %width of each pulse(0.5nS)
t=-2*tc: 1/fs: 2*tc; %signal evaluation time
y=gmonopuls(t,fc); Y=fft(y); magY=abs(Y);
fy=0:(N/2)-1; %first make a vector f=0,1,2,...(N/2)-1
fy=(fy*fs)/N; %scale frequencies in Hertz
subplot (1,2,2); plot(fy,20*log10(magY(1:N/2))); grid;
title ('UWB Gaussian monopulse in the frequency domain');
xlabel('Frequency in GHz'); ylabel('Unity-Amplitude');
%Ref
%Simulation Study of Ultra-Wideband Communication System
%Tefera Tiebe
%www.ee.ucl.ac.uk/lcs/prog01/LCS051.pdf

% gpolycycle.mat a new function program written in Matlab for a 2GHz gaussian ploycycle both in
% the Time & Frequency domains
N =12; n= 0:N-1; fc=2E9; fs=100E9;
%2GHz UWB G.polypulses trains in the time domain with pulse intervals (PRI) of 100nS.
D = [0 1 2 3 4 5 6 7 8 9 ]' * 1e-7; %Pulse delay time (100nS)
tc = gmonopuls ('cutoff',fc); %width of each pulse(0.5nS)
t = 0 : 1/fs : 800*tc; %signal evaluation time
yp = pulstran (t,D,'gmonopuls',fc);
figure(1); subplot(1,1,1); subplot (1,2,1); plot(t,yp); grid;
title ('UWB Gaussian polypulse in the time domain');
xlabel ('Time in nanoseconds'); ylabel('Unity-Amplitude');
%2GHz G.poly-pulses in Frequency domain
D = [0 1 2 3 4 5 6 7 8 9 ]' * 1e-7 %Pulse delay time (100nS)
tc = gmonopuls('cutoff',fc); %width of each pulse(0.5nS)
t = 0 : 1/fs : 800*tc; %signal evaluation time
yp = pulstran (t,D,'gmonopuls',fc); YP = fft(yp);
magYP=abs(YP); fyp=0:(N/2)-1; fyp=(fyp*fs)/N;
subplot (1,2,2); plot(fyp,20*log10(magYP(1:N/2))); grid;
title ('UWB Gaussian polypulse in the frequency domain');
xlabel('Frequency in GHz'); ylabel ('Power (dB)');