Using the DFT

sampling $sin(2*pi*t)$ and taking the DFT we get this graph:

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