%
% This M-file is created for the first couple weeks of lectures of 
% EE321-Linear system I 
% 
% sigvisual.m -- Generate and visualize typical signals
% @ Kefu Xue, Ph.D., Mar 27, 2001
%
% signal I: f(t)= t^2[u(t)-u(t-10)]
%
% Creat an independent time variable
deltaT=0.02;
ts=-5;
te=15;
t=ts:deltaT:te; % -5<=t<=15 with 0.2 as deltaT, or simply t=-5:0.2:15;
%
%Generate the function
indx01=find(t<0); %find indices for vector t such that t<0
z1=length(indx01);%find length of zeros in the first segment
indx02=find(t>10);%find indices for vector t such that t>10
z2=length(indx02);%find length of zeros in the second segment
indx1=find((t>=0) & (t<=10)); %find indices for vector t such that 0<=t<=10
f=[zeros(1,z1) t(indx1).^2 zeros(1,z2)]; 
plot(t,f); title('f(t)');
xlabel('time in second');ylabel('Unit');
pause
stem(t,f); title('f(t) in stems');
xlabel('time in second');ylabel('Unit');
echo on
Ef=sum(f.^2)*deltaT % check total energy
echo off
pause
%
% signal II: x(t)=2f(t-10)
% 
tnew=t+10;% move the time index to the right by 10 units
figure;subplot(2,1,1);plot(t,f,'g');title('original signal f(t)');
subplot(2,1,2);plot(tnew,2*f,'r');title('delayed signal');
%
pause
%
% signal III: x(t)=f(-t)
%
tnew=-t;
subplot(2,1,1);plot(t,f,'g');title('original signal f(t)');
subplot(2,1,2);plot(tnew,f,'r-.');title('flipped signal');
%
pause
%
% signalIV: x(t)=-2f(-t+3)
%
tnew=-t+3;
subplot(2,1,1);plot(t,f,'g');title('original signal f(t)');
subplot(2,1,2);plot(tnew,-2*f,'b--');title('flipped, reversed and shifted signal');
%
pause
%
% signal V: x(t)=f(4t)
%
%Regenerate the function
indx01=find(t<0); %find indices for vector t such that t<0
z1=length(indx01);%find length of zeros in the first segment
indx02=find(t>10/4);%find indices for vector t such that t>10
z2=length(indx02);%find length of zeros in the second segment
indx1=find((t>=0) & (t<=10/4)); %find indices for vector t such that 0<=t<=10/4
f4t=[zeros(1,z1) (4*t(indx1)).^2 zeros(1,z2)]; % (4t)^2
plot(t,f4t); title('f(4t)');
xlabel('time in second');ylabel('Unit');
%
pause
% signal VI: y(t)=3cos(20pit-pi/4)
%
w0=20*pi;% angular frequency of cos() function
T0=2*pi/w0;% period of the signal
% sample 20 samples for each period and plot 4 periods
deltaT=T0/20;
t=0:deltaT:4*T0;
y=3*cos(20*pi*t-pi/4);
% compared with cos() function without phase delay
ynd=3*cos(20*pi*t);
figure;plot(t,y,'g',t,ynd,'b--');title('cosine functions');
%
echo on
delayT=pi/4/w0 %check time delay
pause
Pav=sum(y.^2)/length(t) %check the average power, it should be 3^2/2=4.5
RMS=sqrt(Pav)
%
% Well what do you see? 4.5!! Mean Square Value!! 
echo off
%
pause
%
% if only 2 samples per period are used
%
deltaT=T0/2;
t=0:deltaT:4*T0;
y=3*cos(20*pi*t-pi/4);
% compared with cos() function without phase delay
ynd=3*cos(20*pi*t);
plot(t,y,'g',t,ynd,'b--');
title('cosine functions with only 2 samples per period');
%
pause
close all %close all the open windows