Using the DFT: Difference between revisions

Latest revision as of 11:18, 27 November 2007

This is what we get when we sample the signal at 3Hz

Taking the original signal $s i n (2 * p i * t)$ and applying the DFT we get this graph:

Now taking the DFT of this sampled signal, we get a graph like this:

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

@@ Line 1: / Line 1: @@
-sampling <math>sin(2*pi*t)</math> and taking the DFT we get this graph:
+This is what we get when we sample the signal at 3Hz
+[[Image:hw13_1.jpg]]
+Taking the original signal <math>sin(2*pi*t)</math> and applying the DFT we get this graph:
+[[Image:Signals-13.jpg]]
+Now taking the DFT of this sampled signal, we get a graph like this:
+[[Image:hw13_2.jpg]]
 Script for matlab:
 clear all;
-t=0:.01:1;
+t=0:.01:2;
-T=0.20;
+T=1/3;
-ts=0:T:1;
+ts=0:T:2;
 f1=2;
@@ Line 15: / Line 31: @@
 f2=1/0.125;
-x = sin(2*pi*3*t); %this is the function
+x = sin(2*pi*ts); %this is the function
-plot(t,x); % plot the original signal
+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
@@ Line 23: / Line 39: @@
 pause (2);
-plot (t,X); %plot the DFT of the signal
+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