Class Wiki - User contributions [en]

Using the DFT

2007-11-27T18:18:28Z

Baldwin.britton:

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:.01:2;

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

Using the DFT

2007-11-27T18:18:10Z

Baldwin.britton:

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:.01:2;

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

Using the DFT

2007-11-27T18:13:56Z

Baldwin.britton:

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]]

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

Using the DFT

2007-11-27T18:11:11Z

Baldwin.britton:

sampling <math>sin(2*pi*t)</math> and taking the DFT we get this graph:

[[Image:Signals-13.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

Using the DFT

2007-11-27T18:09:19Z

Baldwin.britton:

sampling <math>sin(2*pi*t)</math> and taking the DFT we get this graph:

[[Image:Signals-13.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

Using the DFT

2007-11-12T18:44:30Z

Baldwin.britton:

sampling <math>sin(2*pi*t)</math> and taking the DFT we get this graph:

[[Image:Signals-13.jpg]]

Script for matlab:
clear all;

t=0:.01:1;

T=0.20;

ts=0:T:1;

f1=2;

f2=1/0.125;

x = sin(2*pi*3*t); %this is the function

plot(t,x); % plot the original signal

X = fft(x); % take the DFT

pause (2);

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

Using the DFT

2007-11-12T18:43:52Z

Baldwin.britton:

sampling <math>sin(2*pi*t)</math> and taking the DFT we get this graph:
[[Image:Signals-13.jpg]]

Script for matlab:
clear all;

t=0:.01:1;

T=0.20;

ts=0:T:1;

f1=2;

f2=1/0.125;

x = sin(2*pi*3*t); %this is the function

plot(t,x); % plot the original signal

X = fft(x); % take the DFT

pause (2);

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

File:Signals-13.jpg

2007-11-12T18:43:22Z

Baldwin.britton: dft

dft

Using the DFT

2007-11-12T18:42:45Z

Baldwin.britton:

sampling <math>sin(2*pi*t)</math> and taking the DFT we get this graph:

Script for matlab:
clear all;

t=0:.01:1;

T=0.20;

ts=0:T:1;

f1=2;

f2=1/0.125;

x = sin(2*pi*3*t); %this is the function

plot(t,x); % plot the original signal

X = fft(x); % take the DFT

pause (2);

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

Using the DFT

2007-11-12T18:42:24Z

Baldwin.britton:

sampling <math>sin(2*pi*t)</math> and taking the DFT we get this graf:

Script for matlab:
clear all;

t=0:.01:1;

T=0.20;

ts=0:T:1;

f1=2;

f2=1/0.125;

x = sin(2*pi*3*t); %this is the function

plot(t,x); % plot the original signal

X = fft(x); % take the DFT

pause (2);

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

Using the DFT

2007-11-12T18:40:35Z

Baldwin.britton:

Script for matlab:
clear all;

t=0:.01:1;

T=0.20;

ts=0:T:1;

f1=2;

f2=1/0.125;

x = sin(2*pi*3*t); %this is the function

plot(t,x); % plot the original signal

X = fft(x); % take the DFT

pause (2);

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

Using the DFT

2007-11-12T18:38:36Z

Baldwin.britton: New page: Script for matlab: clear all; t=0:.01:1; T=0.20; ts=0:T:1; f1=2; f2=1/0.125; x = sin(2*pi*3*t); %this is the function plot(t,x); % plot the original signal X = fft(x); % take the DFT pause...

Script for matlab:
clear all;
t=0:.01:1;
T=0.20;
ts=0:T:1;
f1=2;
f2=1/0.125;
x = sin(2*pi*3*t); %this is the function
plot(t,x); % plot the original signal
X = fft(x); % take the DFT
pause (2);
plot (t,X); %plot the DFT of the signal

More about Sampling

2007-11-12T18:37:50Z

Baldwin.britton: /* Aliasing */

===Aliasing===

Aliasing is when different continuous signals become indistinguishable when sampled, this might happen when sampling too slow. It can also refer to the distortion that occurs when a signals are sampled and reconstructed as aliases of the original signals.

Here is an example of aliasing:

[[Image:Signals 2hw-11.jpg]]
[[Image:Signals hw-11.jpg]]

Like we can see in this images, the samples that we are getting out of the yellow wave, can be also samples in the blue one.

Script for Matlab:
clear all;

t=0:.01:1;

T=0.20;

ts=0:T:1;

f1=2;

f2=1/0.125;

plot(t,cos(2*pi*f2*t),'b-',ts,cos(2*pi*f1*ts),'r*',t,cos(2*pi*f1*t),'y-');

plot(ts,cos(2*pi*f1*ts),'r*',t,cos(2*pi*f1*t),'y-');

More about Sampling

2007-11-12T18:37:29Z

Baldwin.britton: /* Aliasing */

===Aliasing===

Aliasing is when different continuous signals become indistinguishable when sampled, this might happen when sampling too slow. It can also refer to the distortion that occurs when a signals are sampled and reconstructed as aliases of the original signals.

Here is an example of aliasing:

[[Image:Signals 2hw-11.jpg]]
[[Image:Signals hw-11.jpg]]

Like we can see in this images, the samples that we are getting out of the yellow wave, can be also samples in the blue one.

Script for Matlab:
clear all;
t=0:.01:1;
T=0.20;
ts=0:T:1;
f1=2;
f2=1/0.125;
plot(t,cos(2*pi*f2*t),'b-',ts,cos(2*pi*f1*ts),'r*',t,cos(2*pi*f1*t),'y-');
plot(ts,cos(2*pi*f1*ts),'r*',t,cos(2*pi*f1*t),'y-');

User:Baldwin.britton

2007-11-12T18:36:03Z

Baldwin.britton: /* Homework #11 */

'''Background:'''

I'm was born in Chile, my parents are Colombian, and I grew up in Honduras.

-Getting a degree in Electrical Engineering

==Homework #4==
- [[The Fourier Transforms|Fourier Transforms]]

==Homework #8==
- [[A little about Sampling]]

==Homework #11==
- [[More about Sampling]]

==Homework #12==
- [[Relating the DFT to the Fourier transform]]

==Homework #13==
- [[Using the DFT]]

User:Baldwin.britton

2007-11-12T18:34:36Z

Baldwin.britton:

User:Baldwin.britton

2007-11-12T18:34:24Z

Baldwin.britton:

'''Background:'''

I'm was born in Chile, my parents are Colombian, and I grew up in Honduras.
-Getting a degree in Electrical Engineering

==Homework #4==
- [[The Fourier Transforms|Fourier Transforms]]

==Homework #8==
- [[A little about Sampling]]

==Homework #11==
- [[More about Sampling]]

More about Sampling

2007-11-05T00:30:43Z

Baldwin.britton:

File:Signals hw-11.jpg

2007-11-05T00:10:15Z

Baldwin.britton: aliasing

aliasing

File:Signals 2hw-11.jpg

2007-11-05T00:08:40Z

Baldwin.britton: aliasing

aliasing

User:Baldwin.britton

2007-09-26T07:31:50Z

Baldwin.britton:

'''Background:'''

I'm was born in Chile, my Colombian parents, and I grew up in Honduras.

User:Baldwin.britton

2007-09-26T07:31:22Z

Baldwin.britton: /* Headline text */

'''Background:'''

'''Background:'''
I'm was born in Chile, my Colombian parents, and I grew up in Honduras.

User:Baldwin.britton

2007-09-26T07:30:36Z

Baldwin.britton:

'''Background:'''
== Headline text ==

I'm was born in Chile, my Colombian parents, and I grew up in Honduras.

User:Baldwin.britton

2007-09-26T07:30:19Z

Baldwin.britton:

Background:
I'm was born in Chile, my Colombian parents, and I grew up in Honduras.

Signals and Systems

2007-09-26T07:27:20Z

Baldwin.britton: /* 2007-2008 contributors */

== Topics ==
[[Fourier series - by Ray Betz|Overview of Signals and Systems]]

===Individual Subjects===
*[[Linear Time Invarient System|Linear Time Invarient Systems]]
**[[The Game|"The Game"]]
*[[Orthogonal functions|Orthogonal Functions]]
*[[Energy in a signal|Finding the Energy in a Signal]]
**[[Rayleigh's Theorem]]
*[[Fourier series|Fourier Series]]
*[[Fourier transform|Fourier Transforms]]
**[[Discrete Fourier transform]]
*[[Sampling]]
*[[FIR Filter Example]]

===Course Pages===
[[2005-2006 Assignments]]

[[2006-2007 Assignments]]

[http://www.wwc.edu/~frohro/ClassNotes/engr455index.htm Class notes for Signals & Systems]

[[User:Frohro|Instructor: Rob Frohne]]

==2004-2005 contributors==

[[User:Barnsa|Sam Barnes]]

[[User:Santsh|Shawn Santana]]

[[User:Goeari|Aric Goe]]

[[User:Caswto|Todd Caswell]]

[[User:Andeda|David Anderson]]

[[User:Guenan|Anthony Guenterberg]]

==2005-2006 contributors==

[[User:GabrielaV|Gabriela Valdivia]]

[[User:SDiver|Raymond Betz]]

[[User:chrijen|Jenni Christensen]]

[[User:wonoje|Jeffrey Wonoprabowo]]

[[User:wilspa|Paul Wilson]]

==2006-2007 contributors==

[[User:Smitry|Ryan J Smith]]

[[User:Nathan|Nathan Ferch]]

[[User:Andrew|Andrew Lopez]]

[[User:Sherna|Nathan Sherman]]

[[User:Adkich|Chris Adkins]]

==2007-2008 contributors==

[[User:Fonggr|Greg Fong]]

[[User:Pridma|Mark Priddy]]

[[User:Harrde|Denver Harris]]

[[User:baldwin.britton|Baldwin Britton]]

Signals and Systems

2007-09-26T07:27:01Z

Baldwin.britton: /* 2007-2008 contributors */