Class Wiki - User contributions [en]

Signals and Systems

2008-10-11T06:38:51Z

ChrisRas:

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

===Individual Subjects===
*[[Linear Time Invariant System|Linear Time Invariant 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]]
*[[Relationship between e, sin and cos]]

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

[[2006-2007 Assignments]]

[http://people.wallawalla.edu/~Rob.Frohne/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:baldwin.britton|Baldwin Britton]]

[[User:Fonggr|Greg Fong]]

[[User:Harrde|Denver Harris]]

[[User:Pridma|Mark Priddy]]

[[User:ChrisRas|Chris Rasmussen]]

[[User:RothMi|Michael Roth]]

[[User:Rothsa|Sally Roth]]

==2008-2009 Contributors==
[[User:eric.clay|Eric Clay]]

[[User:tsung-lin.yang|Chuck Yang]]

[[User:elton.zebron|Elton Zebron]]

[[User:Luke.chilson|Luke Chilson]]

Chris' Page for HW 14 (Fixing Errors)

2007-12-14T22:52:11Z

ChrisRas:

I uploaded the pictures from my HW 8 and 12.

I fixed the spelling of my name on the main page.

Uploaded this missing picture Image 1597.jpg.

Signals and Systems

2007-12-14T22:49:38Z

ChrisRas:

== 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:baldwin.britton|Baldwin Britton]]

[[User:Fonggr|Greg Fong]]

[[User:Harrde|Denver Harris]]

[[User:Pridma|Mark Priddy]]

[[User:ChrisRas|Chris Rasmussen]]

[[User:RothMi|Michael Roth]]

[[User:Rothsa|Sally Roth]]

Chris' Page for HW 14 (Fixing Errors)

2007-12-14T22:49:24Z

ChrisRas:

I uploaded the pictures from my HW 8 and 12.

I fixed the spelling of my name on the main page.

Chris' Page for HW 14 (Fixing Errors)

2007-12-14T22:49:18Z

ChrisRas: New page: I uploaded the pictures from my HW 8 and 12. I fixed the spelling of my name on the main page.

I uploaded the pictures from my HW 8 and 12.
I fixed the spelling of my name on the main page.

User:ChrisRas

2007-12-14T22:48:49Z

ChrisRas:

'''Hi All,''' [[Image:Image_1597.jpg |thumb|]]

I'm here making my HomePage, just trying to pass Signals and Systems.

Here is a link to a digital signal processing based product that I worked on.
The largest version has 32 channels of DSP and 32 audio power amplifiers.
[http://renkus-heinz.com/loudspeakers/iconyx/index.html Renkus-Heinz Iconyx]

--[[User:ChrisRas|ChrisRas]] 18:04, 24 Sep 2007 (PDT)

----
'''Articles'''

[[Chris' Page for HW 4 (Fourier Transforms)]]

[[Chris' Page for HW 8 (sampling)]]

[[Chris' Page on Aliasing using MatLab]] -- HW11

[[Chris' Page for HW 13 (Sampling at 3Hz)]]

[[Chris' Page for HW 14 (Fixing Errors)]]

[[Chris' Page on how a SACD works]]

Chris' Page for HW 13 (Sampling at 3Hz)

2007-12-14T22:47:30Z

ChrisRas:

'''Sample <math> sin( 2 \pi nt) </math> at 3 Hz; take the DFT, explain the results.'''

<pre>
t1 = 0:1/3:3;
t2 = 0:1/1000:3;
y1 = sin(2*pi*t1);
y2 = sin(2*pi*t2);
NFFT1 = 2^nextpow2(length(y1));
NFFT2 = 2^nextpow2(length(y2));
Y1 = fft(y1,NFFT1)/length(y1);
Y2 = fft(y2,NFFT2)/length(y2);

f1 = 1/3./(2*linspace(0,1,NFFT1/2));
f2 = 10000./(2*linspace(0,1,NFFT2/2));

figure(2)
hold on
h = stem(t1(1:10),y1(1:10),'fill','--');
set(get(h,'BaseLine'),'LineStyle',':')
set(h,'MarkerFaceColor','green')
plot(t1(1:10),y1(1:10), t2(1:3000), y2(1:3000))
legend('3Hz Sample Points','Sine sampled at 3Hz','Sine sampled at 1kHz')
xlabel('Time in seconds')
ylabel('Magnitude')
title('Sin(2\pi t) Sampled at 3 Hz')
hold off
</pre>
[[Image:3Hz&1kHz.jpg]]

<Pre>
figure(3)
plot(f1,2*abs(Y1(1:NFFT1/2)))
axis([0 2 0 1])
title('3Hz Sampele Rate')
xlabel('Frequancy')
ylabel('Magnitude')

figure(4)
plot(f2,2*abs(Y2(1:NFFT2/2)))
axis([0 12000000 0 1])
title('1Khz Sample Rate')
xlabel('Frequancy')
ylabel('Magnatude')
</pre>

[[Image:3HzSample.jpg]]
[[Image:1kHzSample.jpg]]

----

With only 3 samples points per cycle the sinusoid looks like a triangle wave. Having too few sample points results in a DFT with edge effects that are large compared to the actual signal. As the number of sample points increases the accuracy of the digitized function increases and the DFT becomes a better representation of the true frequency components.

Chris' Page for HW 13 (Sampling at 3Hz)

2007-12-14T22:41:32Z

ChrisRas:

File:1kHzSample.jpg

2007-12-14T22:40:56Z

ChrisRas:

File:3HzSample.jpg

2007-12-14T22:40:47Z

ChrisRas:

Chris' Page for HW 13 (Sampling at 3Hz)

2007-12-14T22:40:27Z

ChrisRas:

Chris' Page for HW 13 (Sampling at 3Hz)

2007-12-14T22:31:56Z

ChrisRas:

Chris' Page for HW 13 (Sampling at 3Hz)

2007-12-14T22:31:11Z

ChrisRas:

Chris' Page for HW 13 (Sampling at 3Hz)

2007-12-14T22:31:00Z

ChrisRas:

File:3Hz&1kHz.jpg

2007-12-14T22:30:26Z

ChrisRas:

Chris' Page for HW 13 (Sampling at 3Hz)

2007-12-14T22:30:00Z

ChrisRas:

Chris' Page for HW 13 (Sampling at 3Hz)

2007-12-14T22:27:38Z

ChrisRas: New page: '''Sample <math> sin( 2 \pi nt) </math> at 3Hz; take the DFT, explain the results.'''

'''Sample <math> sin( 2 \pi nt) </math> at 3Hz; take the DFT, explain the results.'''

User:ChrisRas

2007-12-14T22:25:28Z

ChrisRas:

'''Hi All,''' [[Image:Image_1597.jpg |thumb|]]

I'm here making my HomePage, just trying to pass Signals and Systems.

Here is a link to a digital signal processing based product that I worked on.
The largest version has 32 channels of DSP and 32 audio power amplifiers.
[http://renkus-heinz.com/loudspeakers/iconyx/index.html Renkus-Heinz Iconyx]

--[[User:ChrisRas|ChrisRas]] 18:04, 24 Sep 2007 (PDT)

----
'''Articles'''

[[Chris' Page for HW 4 (Fourier Transforms)]]

[[Chris' Page for HW 8 (sampling)]]

[[Chris' Page on Aliasing using MatLab]] --HW11

[[Chris' Page for HW 13 (Sampling at 3Hz)]] --

[[Chris' Page on how a SACD works]]

User:ChrisRas

2007-12-14T22:25:13Z

ChrisRas:

'''Hi All,''' [[Image:Image_1597.jpg |thumb|]]

I'm here making my HomePage, just trying to pass Signals and Systems.

Here is a link to a digital signal processing based product that I worked on.
The largest version has 32 channels of DSP and 32 audio power amplifiers.
[http://renkus-heinz.com/loudspeakers/iconyx/index.html Renkus-Heinz Iconyx]

--[[User:ChrisRas|ChrisRas]] 18:04, 24 Sep 2007 (PDT)

----
'''Articles'''

[[Chris' Page for HW 4 (Fourier Transforms)]]

[[Chris' Page for HW 8 (sampling)]]

[[Chris' Page on Aliasing using MatLab]] --HW11

[[Chris' Page for HW13]] --

[[Chris' Page on how a SACD works]]

Talk:Homework: Sampling: A class review

2007-11-06T07:10:53Z

ChrisRas:

I'm curious about the last sentence in your article "Once these values are recorded, there is alot more processing that is required to restore it to the original signal - at least close enough to the real thing that you can't hear the difference."

Could you please expand on this as I don't understand what additional processing is needed to output a waveform once you have the sampled values. When we did our embedded project we sampled data in, then simply repeated the data back out the DAC.

Thanks Chris. As you remember, we did put the sampled data right back out on the DAC. However, that information could have been filtered to smooth out the signal by averaging two consecutive samples, like we did in class. I'm not sure how that would come out audibly, but I'm pretty sure it would be better.

Ha Ha Funny.

Here is a quote from mathworld.wolfram.com summarizing the Shannon-Nyquist Sampling Theorem.

''In order for a band-limited (i.e., one with a zero power spectrum for frequencies nu>B) baseband (nu>0) signal to be reconstructed fully, it must be sampled at a rate nu>=2B. A signal sampled at nu==2B is said to be Nyquist sampled, and nu==2B is called the Nyquist frequency. '''No information is lost if a signal is sampled at the Nyquist frequency''', and no additional information is gained by sampling faster than this rate.''

Averaging two sample points would simply act as a low-pass filter. I've applied this to a recorded song to demonstrate.

Here's the code I used.

<code>
y = wavread('\\skynet.local\StudentsHome\chris.rasmussen\My Documents\ICanSeeClearlyNow.wav')

windowSize = 10;

yy = filter(ones(1,windowSize)/windowSize,1,y);

clear y

wavwrite(yy,44100,16,'\\skynet.local\StudentsHome\chris.rasmussen\My Documents\ICanSeeClearlyNowSmooth15.wav')

clear all

</code>

Talk:Homework: Sampling: A class review

2007-11-06T07:10:24Z

ChrisRas:

I'm curious about the last sentence in your article "Once these values are recorded, there is alot more processing that is required to restore it to the original signal - at least close enough to the real thing that you can't hear the difference."

Could you please expand on this as I don't understand what additional processing is needed to output a waveform once you have the sampled values. When we did our embedded project we sampled data in, then simply repeated the data back out the DAC.

Thanks Chris. As you remember, we did put the sampled data right back out on the DAC. However, that information could have been filtered to smooth out the signal by averaging two consecutive samples, like we did in class. I'm not sure how that would come out audibly, but I'm pretty sure it would be better.

Ha Ha Funny.

Here is a quote from mathworld.wolfram.com summarizing the Shannon-Nyquist Sampling Theorem.

''In order for a band-limited (i.e., one with a zero power spectrum for frequencies nu>B) baseband (nu>0) signal to be reconstructed fully, it must be sampled at a rate nu>=2B. A signal sampled at nu==2B is said to be Nyquist sampled, and nu==2B is called the Nyquist frequency. '''No information is lost if a signal is sampled at the Nyquist frequency''', and no additional information is gained by sampling faster than this rate.''

Averaging two sample points would simply act as a low-pass filter. I've applied this to a recorded song to demonstrate.

Here's the code I used.

<code>
y = wavread('\\skynet.local\StudentsHome\chris.rasmussen\My Documents\ICanSeeClearlyNow.wav')
windowSize = 10;
yy = filter(ones(1,windowSize)/windowSize,1,y);
clear y
wavwrite(yy,44100,16,'\\skynet.local\StudentsHome\chris.rasmussen\My Documents\ICanSeeClearlyNowSmooth15.wav')
clear all
</code>

Talk:Homework: Sampling: A class review

2007-11-06T07:09:36Z

ChrisRas:

I'm curious about the last sentence in your article "Once these values are recorded, there is alot more processing that is required to restore it to the original signal - at least close enough to the real thing that you can't hear the difference."

Could you please expand on this as I don't understand what additional processing is needed to output a waveform once you have the sampled values. When we did our embedded project we sampled data in, then simply repeated the data back out the DAC.

Thanks Chris. As you remember, we did put the sampled data right back out on the DAC. However, that information could have been filtered to smooth out the signal by averaging two consecutive samples, like we did in class. I'm not sure how that would come out audibly, but I'm pretty sure it would be better.

Ha Ha Funny.

Here is a quote from mathworld.wolfram.com summarizing the Shannon-Nyquist Sampling Theorem.

''In order for a band-limited (i.e., one with a zero power spectrum for frequencies nu>B) baseband (nu>0) signal to be reconstructed fully, it must be sampled at a rate nu>=2B. A signal sampled at nu==2B is said to be Nyquist sampled, and nu==2B is called the Nyquist frequency. No information is lost if a signal is sampled at the Nyquist frequency, and no additional information is gained by sampling faster than this rate.''

Averaging two sample points would simply act as a low-pass filter. I've applied this to a recorded song to demonstrate.

Here's the code I used.

<code>
y = wavread('\\skynet.local\StudentsHome\chris.rasmussen\My Documents\ICanSeeClearlyNow.wav')
windowSize = 10;
yy = filter(ones(1,windowSize)/windowSize,1,y);
clear y
wavwrite(yy,44100,16,'\\skynet.local\StudentsHome\chris.rasmussen\My Documents\ICanSeeClearlyNowSmooth15.wav')
clear all
</code>

Main Page

2007-11-06T07:02:25Z

ChrisRas:

== Classes ==
*[[Signals and systems|Signals and Systems]]

Talk:Homework: Sampling: A class review

2007-11-05T20:36:54Z

ChrisRas:

Chris' Page for HW 8 (sampling)

2007-11-05T08:27:33Z

ChrisRas:

Sampling is a method of discretized and quantizing the infinite amount of information stored in a continuous signal.

A standard sampling device measures a continuous signal at regular intervals. The sampled value is quantized
and fed into some type of processing device.

Talk:Homework: Sampling: A class review

2007-11-04T23:59:20Z

ChrisRas:

Chris' Page on Aliasing using MatLab

2007-11-04T23:54:57Z

ChrisRas:

== Demo of Aliasing Using Matlab ==

Frequencies above half the sample rate will produce aliasing. This should appear as a lower frequency signal.

Below is a spectrogram of a quadratic sweep from 20 Hertz to 20,000 Hertz using a 441000 Hertz sample rate.

[[Image:Chirp41000b.jpg]]

[[Media:44100hz.ogg]]

This one is the same script and parameters except the sample rate has been changed to 8000 Hertz.

[[Image:Chirp8000b.jpg]]

[[Media:8000hz.ogg]]

'''Matlab Program'''

% Chris Rasmussen

% Based on Matlab examples

% Show aliasing

clc

%****************%

% Parameters

duration = 8

fmax = 20000

fmin = 20

samplerate = 8000

%****************%

%****************%
% Setup Soundcard
% Will still work if this is removed, you just won't hear anything
% It works with my onboard soundcard with Vista.

AO = analogoutput('winsound');

chan = addchannel(AO,1);

set(AO,'SampleRate',samplerate);

set(AO,'TriggerType','Manual');

ActualRate = get(AO,'SampleRate')

%****************%

%****************%

% Setup arrays

totalsamples = ActualRate*duration;

t = 0:1./ActualRate:duration;

y= 0.2 .* chirp(t,fmin,duration, fmax,'q',[],'concave');

%****************%

%****************%

% Write data to soundcard and play

% Will still work if this is removed, you just won't hear anything

putdata(AO,y')

start(AO)

trigger(AO)

waittilstop(AO,duration+1)

%****************%

%****************%

% Plot raw data

figure(1)

plot(y)

title('Waveform')

%****************%

%****************%

% Plot spectragram (uses FFT)

figure(3), specgram(y, 256, samplerate);

title('Quadratic Sine Sweep')

set(gcf,'Color',[1 1 1]);

%****************%

wavwrite(y,samplerate,16,'File.wav')

%****************%

% Picking up the messes

delete(AO)

clear AO

clear all

Chris' Page on Aliasing using MatLab

2007-11-04T23:54:44Z

ChrisRas:

User:ChrisRas

2007-11-04T09:19:44Z

ChrisRas:

Chris' Page for HW 4 (Fourier Transforms)

2007-11-04T08:52:07Z

ChrisRas:

The Fourier Transform is a process or formula that converts a signal from one domain to another. Often it is used to go between the time domain and the frequency domain.

Developed by Frenchman, Jean Baptiste Joseph Fourier (1768 - 1830), the Fourier Transform stems from the more general Fourier Analysis, which is the representation of a function with sine and cosine terms. Unlike the Fourier Series the Fourier Transform is capable of representing aperiodic signals.

== Mathematical Description ==

The Fourier Transform is detonated by;

:<math>X(f) = \int_{-\infty}^{\infty} x(t)\ e^{-j \omega t}\,dt, </math>

The Inverse Fourier Transform is;
:<math>x(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} X(\omega)\ e^{ j\omega t}\,d\omega, </math>

== Relation to Laplace Transform ==

Unless otherwise noted, a Laplace Transform is defined by the unilateral or one-sided integral

:<math>\mathcal{L} \left\{f(t)\right\}=\int_{0^-}^\infty e^{-st} f(t) \,dt. </math>

The Laplace Transform can be applied from <math>-\infty</math> to <math>\infty</math>, this is known as the Bilateral Laplace Transform and is denoted by

: <math>\mathcal{L}\left\{f(t)\right\} =\int_{-\infty}^{\infty} e^{-st} f(t)\,dt.</math>

Setting <math> s=j\omega</math> (<math>\sigma=0</math>) gives the equation

: <math>\mathcal{L}\left\{f(t)\right\} =\int_{-\infty}^{\infty} e^{-j\omega t} f(t)\,dt.</math>

which is identical to the Fourier Transform. The same relationship exists between the Inverse Laplace and the Inverse Fourier transforms.

== Examples ==

Below is a very basic example based on a Matlab help file.

The time domain signal is produced by

<code>
t = 0:0.001:.1;

y = sin(2*pi*50*t)+sin(2*pi*120*t) +sin(2*pi*150*t) +sin(2*pi*310*t) +sin(2*pi*340*t);

y = 0.2 .* y;
</code>

The t matrix represents time vectors and y is the summation of sine functions of various frequencies, then y is redefined as 1/5 the original power.

Plotted with

<code>
figure(1)

plot(1000*t(1:100),y(1:100))

title('Time Domain')

xlabel('t (ms)')
</code>

yields

[[Image:Example1time.jpg]]

Then taking the Fourier Transform via the FFT and plotting

<code>
Y = fft(y,512);

Power = Y .* conj(Y) / 512;

f = 1000*(0:256)/512;

figure(2)

plot(f,Power(1:257))

title('Frequancy Domain')

xlabel('f (Hz)')
</code>

[[Image:Example1freq.jpg]]

And if you want to hear it

<code>
wavwrite(y,1000,16,'test2.wav')
</code>

then

<code>
clear all
</code>

I believe that windowing needs to be added. Suggestions?

Chris' Page for HW 4 (Fourier Transforms)

2007-11-04T08:50:16Z

ChrisRas:

File:Example1freq.jpg

2007-11-04T08:47:30Z

ChrisRas: FFT Example 1, Frequency domain y = sin(2*pi*50*t)+sin(2*pi*120*t) +sin(2*pi*150*t) +sin(2*pi*310*t) +sin(2*pi*340*t);

FFT Example 1, Frequency domain

y = sin(2*pi*50*t)+sin(2*pi*120*t) +sin(2*pi*150*t) +sin(2*pi*310*t) +sin(2*pi*340*t);

File:Example1time.jpg

2007-11-04T08:43:34Z

ChrisRas:

FFT Example 1, Time domain

t = 0:0.001:.1;

y = sin(2*pi*50*t)+sin(2*pi*120*t) +sin(2*pi*150*t) +sin(2*pi*310*t) +sin(2*pi*340*t);

y= 0.2 .* y;

Chris' Page for HW 4 (Fourier Transforms)

2007-11-04T08:42:51Z

ChrisRas:

File:Example1time.jpg

2007-11-04T08:40:40Z

ChrisRas: FFT Example 1, Time domain t = 0:0.001:.1; y = sin(2*pi*50*t)+sin(2*pi*120*t) +sin(2*pi*150*t) +sin(2*pi*310*t) +sin(2*pi*340*t); y= 0.2 .* y;

FFT Example 1, Time domain

t = 0:0.001:.1;
y = sin(2*pi*50*t)+sin(2*pi*120*t) +sin(2*pi*150*t) +sin(2*pi*310*t) +sin(2*pi*340*t);
y= 0.2 .* y;

Chris' Page for HW 4 (Fourier Transforms)

2007-11-04T06:45:15Z

ChrisRas:

Chris' Page for HW 4 (Fourier Transforms)

2007-11-03T08:29:01Z

ChrisRas:

Chris' Page for HW 4 (Fourier Transforms)

2007-11-03T08:03:42Z

ChrisRas:

Chris' Page for HW 4 (Fourier Transforms)

2007-11-03T07:27:06Z

ChrisRas:

Chris' Page for HW 4 (Fourier Transforms)

2007-11-03T02:08:02Z

ChrisRas:

User:ChrisRas

2007-11-03T02:07:40Z

ChrisRas:

User:ChrisRas

2007-11-02T14:56:23Z

ChrisRas:

'''Hi All,''' [[Image:Image_1597.jpg |thumb|]]

I'm here making my HomePage, just trying to pass Signals and Systems.

Here is a link to a digital signal processing based product that I worked on.
The largest version has 32 channels of DSP and 32 audio power amplifiers.
[http://renkus-heinz.com/loudspeakers/iconyx/index.html Renkus-Heinz Iconyx]

--[[User:ChrisRas|ChrisRas]] 18:04, 24 Sep 2007 (PDT)

----
'''Articles'''

[[Chris' Page for HW #4 (Fourier Transforms)]]

[[Chris' Page for HW #8 (sampling)]]

[[Chris' Page on Aliasing using MatLab]]

Chris' Page on Nyquist using MatLab

2007-11-02T14:55:43Z

ChrisRas: Chris' Page on Nyquist using MatLab moved to Chris' Page on Aliasing using MatLab

#REDIRECT [[Chris' Page on Aliasing using MatLab]]

Chris' Page on Aliasing using MatLab

2007-11-02T06:05:04Z

ChrisRas:

== Demo of Aliasing Using Matlab ==

Frequencies above half the sample rate will produce aliasing. This should appear as a lower frequency signal.

Below is a spectrogram of a quadratic sweep from 20 Hertz to 20,000 Hertz using a 441000 Hertz sample rate.

[[Image:Chirp41000b.jpg]]

[[Media:44100hz.ogg]]

This one is the same script and parameters except the sample rate has been changed to 8000 Hertz.

[[Image:Chirp8000b.jpg]]

[[Media:8000hz.ogg]]

'''Matlab Program'''

% Chris Rasmussen

% Matlab assignment

% Show Nyquist stuff

clc

%****************%

% Parameters

duration = 8

fmax = 20000

fmin = 20

samplerate = 8000

%****************%

%****************%
% Setup Soundcard
% Will still work if this is removed, you just won't hear anything
% It works with my onboard soundcard with Vista.

AO = analogoutput('winsound');

chan = addchannel(AO,1);

set(AO,'SampleRate',samplerate);

set(AO,'TriggerType','Manual');

ActualRate = get(AO,'SampleRate')

%****************%

%****************%

% Setup arrays

totalsamples = ActualRate*duration;

t = 0:1./ActualRate:duration;

y= 0.2 .* chirp(t,fmin,duration, fmax,'q',[],'concave');

%****************%

%****************%

% Write data to soundcard and play

% Will still work if this is removed, you just won't hear anything

putdata(AO,y')

start(AO)

trigger(AO)

waittilstop(AO,duration+1)

%****************%

%****************%

% Plot raw data

figure(1)

plot(y)

title('Waveform')

%****************%

%****************%

% Plot spectragram (uses FFT)

figure(3), specgram(y, 256, samplerate);

title('Quadratic Sine Sweep')

set(gcf,'Color',[1 1 1]);

%****************%

wavwrite(y,samplerate,16,'File.wav')

%****************%

% Picking up the messes

delete(AO)

clear AO

clear all

Chris' Page on Aliasing using MatLab

2007-11-02T06:04:07Z

ChrisRas: Added sound files

== Demo of Aliasing Using Matlab ==

Frequencies above half the sample rate will produce aliasing. This should appear as a lower frequency signal.

Below is a spectrogram of a quadratic sweep from 20 Hertz to 20,000 Hertz using a 441000 Hertz sample rate.

[[Image:Chirp41000b.jpg]]

[[Media:44100hz.ogg]]

This one is the same script and parameters except the sample rate has been changed to 8000 Hertz.
[[Image:Chirp8000b.jpg]]

[[Media:8000hz.ogg]]

'''Matlab Program'''

% Chris Rasmussen

% Matlab assignment

% Show Nyquist stuff

clc

%****************%

% Parameters

duration = 8

fmax = 20000

fmin = 20

samplerate = 8000

%****************%

%****************%
% Setup Soundcard
% Will still work if this is removed, you just won't hear anything
% It works with my onboard soundcard with Vista.

AO = analogoutput('winsound');

chan = addchannel(AO,1);

set(AO,'SampleRate',samplerate);

set(AO,'TriggerType','Manual');

ActualRate = get(AO,'SampleRate')

%****************%

%****************%

% Setup arrays

totalsamples = ActualRate*duration;

t = 0:1./ActualRate:duration;

y= 0.2 .* chirp(t,fmin,duration, fmax,'q',[],'concave');

%****************%

%****************%

% Write data to soundcard and play

% Will still work if this is removed, you just won't hear anything

putdata(AO,y')

start(AO)

trigger(AO)

waittilstop(AO,duration+1)

%****************%

%****************%

% Plot raw data

figure(1)

plot(y)

title('Waveform')

%****************%

%****************%

% Plot spectragram (uses FFT)

figure(3), specgram(y, 256, samplerate);

title('Quadratic Sine Sweep')

set(gcf,'Color',[1 1 1]);

%****************%

wavwrite(y,samplerate,16,'File.wav')

%****************%

% Picking up the messes

delete(AO)

clear AO

clear all

File:44100hz.ogg

2007-11-02T05:59:08Z

ChrisRas: 441000 Hz sample rate

441000 Hz sample rate

File:8000hz.ogg

2007-11-02T05:58:33Z

ChrisRas: 8000Hz sample rate

8000Hz sample rate

Chris' Page on Aliasing using MatLab

2007-11-01T18:52:11Z

ChrisRas:

== Demo of Aliasing Using Matlab ==

Frequencies above half the sample rate will produce aliasing. This should appear as a lower frequency signal.

Below is a spectrogram of a quadratic sweep from 20 Hertz to 20,000 Hertz using a 441000 Hertz sample rate.

[[Image:Chirp41000b.jpg]]

This one is the same script and parameters except the sample rate has been changed to 8000 Hertz.
[[Image:Chirp8000b.jpg]]

'''Matlab Program'''

% Chris Rasmussen

% Matlab assignment

% Show Nyquist stuff

clc

%****************%

% Parameters

duration = 8

fmax = 20000

fmin = 20

samplerate = 8000

%****************%

%****************%
% Setup Soundcard
% Will still work if this is removed, you just won't hear anything
% It works with my onboard soundcard with Vista.

AO = analogoutput('winsound');

chan = addchannel(AO,1);

set(AO,'SampleRate',samplerate);

set(AO,'TriggerType','Manual');

ActualRate = get(AO,'SampleRate')

%****************%

%****************%

% Setup arrays

totalsamples = ActualRate*duration;

t = 0:1./ActualRate:duration;

y= 0.2 .* chirp(t,fmin,duration, fmax,'q',[],'concave');

%****************%

%****************%

% Write data to soundcard and play

% Will still work if this is removed, you just won't hear anything

putdata(AO,y')

start(AO)

trigger(AO)

waittilstop(AO,duration+1)

%****************%

%****************%

% Plot raw data

figure(1)

plot(y)

title('Waveform')

%****************%

%****************%

% Plot spectragram (uses FFT)

figure(3), specgram(y, 256, samplerate);

title('Quadratic Sine Sweep')

set(gcf,'Color',[1 1 1]);

%****************%

wavwrite(y,samplerate,16,'File.wav')

%****************%

% Picking up the messes

delete(AO)

clear AO

clear all

Chris' Page on Aliasing using MatLab

2007-11-01T18:51:49Z

ChrisRas:

== Demo of Aliasing Using Matlab ==

Frequencies above half the sample rate will produce aliasing. This should appear as a lower frequency signal.

Below is a spectrogram of a quadratic sweep from 20 Hertz to 20,000 Hertz using a 441000 Hertz sample rate.

[[Image:Chirp41000b.jpg]]

This one is the same script and parameters except the sample rate has been changed to 8000 Hertz.

'''Matlab Program'''

% Chris Rasmussen

% Matlab assignment

% Show Nyquist stuff

clc

%****************%

% Parameters

duration = 8

fmax = 20000

fmin = 20

samplerate = 8000

%****************%

%****************%
% Setup Soundcard
% Will still work if this is removed, you just won't hear anything
% It works with my onboard soundcard with Vista.

AO = analogoutput('winsound');

chan = addchannel(AO,1);

set(AO,'SampleRate',samplerate);

set(AO,'TriggerType','Manual');

ActualRate = get(AO,'SampleRate')

%****************%

%****************%

% Setup arrays

totalsamples = ActualRate*duration;

t = 0:1./ActualRate:duration;

y= 0.2 .* chirp(t,fmin,duration, fmax,'q',[],'concave');

%****************%

%****************%

% Write data to soundcard and play

% Will still work if this is removed, you just won't hear anything

putdata(AO,y')

start(AO)

trigger(AO)

waittilstop(AO,duration+1)

%****************%

%****************%

% Plot raw data

figure(1)

plot(y)

title('Waveform')

%****************%

%****************%

% Plot spectragram (uses FFT)

figure(3), specgram(y, 256, samplerate);

title('Quadratic Sine Sweep')

set(gcf,'Color',[1 1 1]);

%****************%

wavwrite(y,samplerate,16,'File.wav')

%****************%

% Picking up the messes

delete(AO)

clear AO

clear all

User:ChrisRas

2007-11-01T18:48:46Z

ChrisRas:

'''Hi All,''' [[Image:Image_1597.jpg |thumb|]]

I'm here making my HomePage, just trying to pass Signals and Systems.

Here is a link to a digital signal processing based product that I worked on.
The largest version has 32 channels of DSP and 32 audio power amplifiers.
[http://renkus-heinz.com/loudspeakers/iconyx/index.html Renkus-Heinz Iconyx]

--[[User:ChrisRas|ChrisRas]] 18:04, 24 Sep 2007 (PDT)

----
'''Articles'''

[[Chris' Page for HW #4 (Fourier Transforms)]]

[[Chris' Page for HW #8 (sampling)]]

[[Chris' Page on Nyquist using MatLab]]