Using the DFT

This is what we get when we sample the signal at 3Hz File:Hw13 1.jpg

Taking the original signal $sin(2*pi*t)$ and applying the DFT we get this graph:

Now taking the DFT of this sampled signal, we get a graph like this: File:Hw13 2.jpg

Script for matlab:

clear all;

t=0:.01:2;

T=1/3;

ts=0:T:2;

f1=2;

f2=1/0.125;

x = sin(2*pi*ts); %this is the function

plot(ts,sin(2*pi*ts),'r-',t,sin(2*pi*t)); % plot the original signal and the signal sampled at 3Hz

X = fft(x); % take the DFT

pause (2);

plot (ts,X); %plot the DFT of the signal sampled at 3Hz

pause (4);

x=sin(2*pi*t);

plot(t,x);

pause(2);

X = fft(x);

plot(t,X); %plot the DFT of the original signal