Class Wiki - User contributions [en]

User:Goeari

2007-10-02T06:26:31Z

Goeari: /* Introduction */

[[Image:p1010006.JPG|thumb|Aric Goe]]
== Signals & Systems ==
*[[Signals and systems|Signals and Systems]]

=== Introduction ===

[http://www.myspace.com/goemaster Aric's Homepage (Updated 10.01.07)],

==== Becoming familiar with Wiki ====
Well, it all seems a little too convenient to me.

====Practicing TEX====

;Simple Transformer Equation

:<math>\frac{Ep}{Tp} = \frac{Es}{Ts}</math>

== How a CD Player Works ==

[[Image:CDplayerdiagram.jpg|Description]]

First, a digital signal <math>\ x(kt) </math> is read from the CD and then convolved with a pulse function <math>\ p(t) </math> in the D/A converter. The result in the time domain looks like this:

<center>
[[Image:DAOutput.jpg|Description]]

<math>
\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT)
</math>
</center>

Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.

<center>
[[Image:DAfreqout.jpg|Description]]

<math>\hat X(f) = \frac{1}{T} \sum_{n=-\infty}^\infty X(f - \frac{n}{T}) \cdot P(f)</math>
</center>
where
<center>
<math>P(f) = \int_{-\frac{T}{2}}^{\frac{T}{2}} e^{j2\pi ft} \, dt = T sinc(fT)
</math>
</center>

The low pass filter then knocks the high frequencies out of the signal coming from the D/A converter, which smoothes out the edges of the reproduced sine wave <math>\hat x(t)</math> in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.

Contributing Authors:

[[User:caswto|Todd Caswell]]

[[User:goeari|Aric Goe]]

User:Goeari

2007-10-02T06:09:24Z

Goeari: /* Introduction */

[[Image:p1010006.JPG|thumb|Aric Goe]]
== Signals & Systems ==
*[[Signals and systems|Signals and Systems]]

=== Introduction ===

[http://www.myspace.com/goemaster Aric's Homepage],

==== Becoming familiar with Wiki ====
Well, it all seems a little too convenient to me.

====Practicing TEX====

;Simple Transformer Equation

:<math>\frac{Ep}{Tp} = \frac{Es}{Ts}</math>

== How a CD Player Works ==

[[Image:CDplayerdiagram.jpg|Description]]

First, a digital signal <math>\ x(kt) </math> is read from the CD and then convolved with a pulse function <math>\ p(t) </math> in the D/A converter. The result in the time domain looks like this:

<center>
[[Image:DAOutput.jpg|Description]]

<math>
\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT)
</math>
</center>

Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.

<center>
[[Image:DAfreqout.jpg|Description]]

<math>\hat X(f) = \frac{1}{T} \sum_{n=-\infty}^\infty X(f - \frac{n}{T}) \cdot P(f)</math>
</center>
where
<center>
<math>P(f) = \int_{-\frac{T}{2}}^{\frac{T}{2}} e^{j2\pi ft} \, dt = T sinc(fT)
</math>
</center>

The low pass filter then knocks the high frequencies out of the signal coming from the D/A converter, which smoothes out the edges of the reproduced sine wave <math>\hat x(t)</math> in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.

Contributing Authors:

[[User:caswto|Todd Caswell]]

[[User:goeari|Aric Goe]]

User:Goeari

2004-12-07T04:37:21Z

Goeari: /* How a CD Player Works */

[[Image:p1010006.JPG|thumb|Aric Goe]]
== Signals & Systems ==
*[[Signals and systems|Signals and Systems]]

=== Introduction ===

[http://homepages.wwc.edu/student/goeari Aric's Homepage],

==== Becoming familiar with Wiki ====
Well, it all seems a little too convenient to me.

====Practicing TEX====

;Simple Transformer Equation

:<math>\frac{Ep}{Tp} = \frac{Es}{Ts}</math>

== How a CD Player Works ==

[[Image:CDplayerdiagram.jpg|Description]]

First, a digital signal <math>\ x(kt) </math> is read from the CD and then convolved with a pulse function <math>\ p(t) </math> in the D/A converter. The result in the time domain looks like this:

<center>
[[Image:DAOutput.jpg|Description]]

<math>
\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT)
</math>
</center>

Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.

<center>
[[Image:DAfreqout.jpg|Description]]

<math>\hat X(f) = \frac{1}{T} \sum_{n=-\infty}^\infty X(f - \frac{n}{T}) \cdot P(f)</math>
</center>
where
<center>
<math>P(f) = \int_{-\frac{T}{2}}^{\frac{T}{2}} e^{j2\pi ft} \, dt = T sinc(fT)
</math>
</center>

The low pass filter then knocks the high frequencies out of the signal coming from the D/A converter, which smoothes out the edges of the reproduced sine wave <math>\hat x(t)</math> in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.

Contributing Authors:

[[User:caswto|Todd Caswell]]

[[User:goeari|Aric Goe]]

User:Goeari

2004-12-07T04:31:58Z

Goeari: /* How a CD Player Works */

[[Image:p1010006.JPG|thumb|Aric Goe]]
== Signals & Systems ==
*[[Signals and systems|Signals and Systems]]

=== Introduction ===

[http://homepages.wwc.edu/student/goeari Aric's Homepage],

==== Becoming familiar with Wiki ====
Well, it all seems a little too convenient to me.

====Practicing TEX====

;Simple Transformer Equation

:<math>\frac{Ep}{Tp} = \frac{Es}{Ts}</math>

== How a CD Player Works ==

[[Image:CDplayerdiagram.jpg|Description]]

First, a digital signal <math>\ x(kt) </math> is read from the CD and then convolved with a pulse function <math>\ p(t) </math> in the D/A converter. The result in the time domain looks like this:

<center>
[[Image:DAOutput.jpg|Description]]

<math>
\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT)
</math>
</center>

Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.

<center>
[[Image:DAfreqout.jpg|Description]]

<math>\hat X(f) = \frac{1}{T} \sum_{n=-\infty}^\infty X(f - \frac{n}{T}) \cdot P(f)</math>
</center>
where
<center>
<math>P(f) = \int_{-T/2}^{T/2} e^{j2\pi ft} \, dt = T sinc(fT)
</math>
</center>

The low pass filter then knocks the high frequencies out of the signal coming from the D/A converter, which smoothes out the edges of the reproduced sine wave <math>\hat x(t)</math> in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.

Contributing Authors:

[[User:caswto|Todd Caswell]]

[[User:goeari|Aric Goe]]

User:Goeari

2004-12-07T03:33:57Z

Goeari: /* Introduction */

[[Image:p1010006.JPG|thumb|Aric Goe]]
== Signals & Systems ==
*[[Signals and systems|Signals and Systems]]

=== Introduction ===

[http://homepages.wwc.edu/student/goeari Aric's Homepage],

==== Becoming familiar with Wiki ====
Well, it all seems a little too convenient to me.

====Practicing TEX====

;Simple Transformer Equation

:<math>\frac{Ep}{Tp} = \frac{Es}{Ts}</math>

== How a CD Player Works ==

[[Image:CDplayerdiagram.jpg|Description]]

First, a digital signal <math>\ x(kt) </math> is read from the CD and then convolved with a pulse function <math>\ p(t) </math> in the D/A converter. The result in the time domain looks like this:

<center>
[[Image:DAOutput.jpg|Description]]

<math>
\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT)
</math>
</center>

Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.

<center>
[[Image:DAfreqout.jpg|Description]]

<math>\hat X(f) = 1/T \sum_{n=-\infty}^\infty X(f - n/T) \cdot P(f)</math>
</center>
where
<center>
<math>P(f) = \int_{-T/2}^{T/2} e^{j2\pi ft} \, dt = T sinc(fT)
</math>
</center>

The low pass filter then knocks the high frequencies out of the signal coming from the D/A converter, which smoothes out the edges of the reproduced sine wave <math>\hat x(t)</math> in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.

Contributing Authors:

[[User:caswto|Todd Caswell]]

[[User:goeari|Aric Goe]]

User:Goeari

2004-12-07T03:31:17Z

Goeari: /* Introduction */

[[Image:p1010006.JPG|thumb|Aric Goe]]
== Signals & Systems ==
*[[Signals and systems|Signals and Systems]]

=== Introduction ===
[[http://homepages.wwc.edu/student/goeari|Aric's Homepage]]

==== Becoming familiar with Wiki ====
Well, it all seems a little too convenient to me.

====Practicing TEX====

;Simple Transformer Equation

:<math>\frac{Ep}{Tp} = \frac{Es}{Ts}</math>

== How a CD Player Works ==

[[Image:CDplayerdiagram.jpg|Description]]

First, a digital signal <math>\ x(kt) </math> is read from the CD and then convolved with a pulse function <math>\ p(t) </math> in the D/A converter. The result in the time domain looks like this:

<center>
[[Image:DAOutput.jpg|Description]]

<math>
\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT)
</math>
</center>

Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.

<center>
[[Image:DAfreqout.jpg|Description]]

<math>\hat X(f) = 1/T \sum_{n=-\infty}^\infty X(f - n/T) \cdot P(f)</math>
</center>
where
<center>
<math>P(f) = \int_{-T/2}^{T/2} e^{j2\pi ft} \, dt = T sinc(fT)
</math>
</center>

The low pass filter then knocks the high frequencies out of the signal coming from the D/A converter, which smoothes out the edges of the reproduced sine wave <math>\hat x(t)</math> in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.

Contributing Authors:

[[User:caswto|Todd Caswell]]

[[User:goeari|Aric Goe]]

User:Goeari

2004-12-07T03:29:25Z

Goeari: /* Introduction */

[[Image:p1010006.JPG|thumb|Aric Goe]]
== Signals & Systems ==
*[[Signals and systems|Signals and Systems]]

=== Introduction ===
[[http://homepages/student/goeari:Aric's Homepage]]

==== Becoming familiar with Wiki ====
Well, it all seems a little too convenient to me.

====Practicing TEX====

;Simple Transformer Equation

:<math>\frac{Ep}{Tp} = \frac{Es}{Ts}</math>

== How a CD Player Works ==

[[Image:CDplayerdiagram.jpg|Description]]

First, a digital signal <math>\ x(kt) </math> is read from the CD and then convolved with a pulse function <math>\ p(t) </math> in the D/A converter. The result in the time domain looks like this:

<center>
[[Image:DAOutput.jpg|Description]]

<math>
\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT)
</math>
</center>

Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.

<center>
[[Image:DAfreqout.jpg|Description]]

<math>\hat X(f) = 1/T \sum_{n=-\infty}^\infty X(f - n/T) \cdot P(f)</math>
</center>
where
<center>
<math>P(f) = \int_{-T/2}^{T/2} e^{j2\pi ft} \, dt = T sinc(fT)
</math>
</center>

The low pass filter then knocks the high frequencies out of the signal coming from the D/A converter, which smoothes out the edges of the reproduced sine wave <math>\hat x(t)</math> in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.

Contributing Authors:

[[User:caswto|Todd Caswell]]

[[User:goeari|Aric Goe]]

User:Goeari

2004-12-07T03:26:03Z

Goeari: /* Becoming familiar with Wiki */

[[Image:p1010006.JPG|thumb|Aric Goe]]
== Signals & Systems ==
*[[Signals and systems|Signals and Systems]]

=== Introduction ===
==== Becoming familiar with Wiki ====
Well, it all seems a little too convenient to me.

====Practicing TEX====

;Simple Transformer Equation

:<math>\frac{Ep}{Tp} = \frac{Es}{Ts}</math>

== How a CD Player Works ==

[[Image:CDplayerdiagram.jpg|Description]]

First, a digital signal <math>\ x(kt) </math> is read from the CD and then convolved with a pulse function <math>\ p(t) </math> in the D/A converter. The result in the time domain looks like this:

<center>
[[Image:DAOutput.jpg|Description]]

<math>
\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT)
</math>
</center>

Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.

<center>
[[Image:DAfreqout.jpg|Description]]

<math>\hat X(f) = 1/T \sum_{n=-\infty}^\infty X(f - n/T) \cdot P(f)</math>
</center>
where
<center>
<math>P(f) = \int_{-T/2}^{T/2} e^{j2\pi ft} \, dt = T sinc(fT)
</math>
</center>

The low pass filter then knocks the high frequencies out of the signal coming from the D/A converter, which smoothes out the edges of the reproduced sine wave <math>\hat x(t)</math> in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.

Contributing Authors:

[[User:caswto|Todd Caswell]]

[[User:goeari|Aric Goe]]

User:Goeari

2004-12-07T03:25:19Z

Goeari:

[[Image:p1010006.JPG|thumb|Aric Goe]]
== Signals & Systems ==
*[[Signals and systems|Signals and Systems]]

=== Introduction ===
==== Becoming familiar with Wiki ====
Well, it all seems a little too convenitent to me.

====Practicing TEX====

;Simple Transformer Equation

:<math>\frac{Ep}{Tp} = \frac{Es}{Ts}</math>

== How a CD Player Works ==

[[Image:CDplayerdiagram.jpg|Description]]

First, a digital signal <math>\ x(kt) </math> is read from the CD and then convolved with a pulse function <math>\ p(t) </math> in the D/A converter. The result in the time domain looks like this:

<center>
[[Image:DAOutput.jpg|Description]]

<math>
\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT)
</math>
</center>

Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.

<center>
[[Image:DAfreqout.jpg|Description]]

<math>\hat X(f) = 1/T \sum_{n=-\infty}^\infty X(f - n/T) \cdot P(f)</math>
</center>
where
<center>
<math>P(f) = \int_{-T/2}^{T/2} e^{j2\pi ft} \, dt = T sinc(fT)
</math>
</center>

The low pass filter then knocks the high frequencies out of the signal coming from the D/A converter, which smoothes out the edges of the reproduced sine wave <math>\hat x(t)</math> in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.

Contributing Authors:

[[User:caswto|Todd Caswell]]

[[User:goeari|Aric Goe]]

User:Goeari

2004-12-07T03:23:54Z

Goeari: /* Signals & Systems */

[[Image:p1010006.JPG|thumb|Aric Goe]]
== Signals & Systems ==
*[[Signals and systems|Signals and Systems]]

=== Introduction ===
==== Becoming familiar with Wiki ====
Well, it all seems a little too convenitent to me.

====Practicing TEX====

;Simple Transformer Equation

:<math>\frac{Ep}{Tp} = \frac{Es}{Ts}</math>

=== How a CD Player Works ===

[[Image:CDplayerdiagram.jpg|Description]]

First, a digital signal <math>\ x(kt) </math> is read from the CD and then convolved with a pulse function <math>\ p(t) </math> in the D/A converter. The result in the time domain looks like this:

<center>
[[Image:DAOutput.jpg|Description]]

<math>
\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT)
</math>
</center>

Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.

<center>
[[Image:DAfreqout.jpg|Description]]

<math>\hat X(f) = 1/T \sum_{n=-\infty}^\infty X(f - n/T) \cdot P(f)</math>
</center>
where
<center>
<math>P(f) = \int_{-T/2}^{T/2} e^{j2\pi ft} \, dt = T sinc(fT)
</math>
</center>

The low pass filter then knocks the high frequencies out of the signal coming from the D/A converter, which smoothes out the edges of the reproduced sine wave <math>\hat x(t)</math> in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.

Contributing Authors:

[[User:caswto|Todd Caswell]]

[[User:goeari|Aric Goe]]

User:Goeari

2004-12-07T03:16:41Z

Goeari: /* Contributing Authors */

[[Image:p1010006.JPG|thumb|Aric Goe]]
== Signals & Systems ==
=== Introduction ===
==== Becoming familiar with Wiki ====
Well, it all seems a little too convenitent to me.

====Practicing TEX====

;Simple Transformer Equation

:<math>\frac{Ep}{Tp} = \frac{Es}{Ts}</math>

=== How a CD Player Works ===

[[Image:CDplayerdiagram.jpg|Description]]

First, a digital signal <math>\ x(kt) </math> is read from the CD and then convolved with a pulse function <math>\ p(t) </math> in the D/A converter. The result in the time domain looks like this:

<center>
[[Image:DAOutput.jpg|Description]]

<math>
\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT)
</math>
</center>

Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.

<center>
[[Image:DAfreqout.jpg|Description]]

<math>\hat X(f) = 1/T \sum_{n=-\infty}^\infty X(f - n/T) \cdot P(f)</math>
</center>
where
<center>
<math>P(f) = \int_{-T/2}^{T/2} e^{j2\pi ft} \, dt = T sinc(fT)
</math>
</center>

The low pass filter then knocks the high frequencies out of the signal coming from the D/A converter, which smoothes out the edges of the reproduced sine wave <math>\hat x(t)</math> in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.

Contributing Authors:

[[User:caswto|Todd Caswell]]

[[User:goeari|Aric Goe]]

User:Goeari

2004-12-07T03:13:58Z

Goeari: /* How a CD Player Works */

File:DAfreqout.jpg

2004-12-07T02:55:23Z

Goeari: DA Frequency Output Graph

DA Frequency Output Graph

User:Goeari

2004-12-07T02:54:17Z

Goeari:

[[Image:p1010006.JPG|thumb|Aric Goe]]
== Signals & Systems ==
=== Introduction ===
==== Becoming familiar with Wiki ====
Well, it all seems a little too convenitent to me.

====Practicing TEX====

;Simple Transformer Equation

:<math>\frac{Ep}{Tp} = \frac{Es}{Ts}</math>

=== How a CD Player Works ===

[[Image:CDplayerdiagram.jpg|Description]]

First, a digital signal <math>x(kt)</math> is read from the CD adn then convolved with a pulse function <math>p(t)</math>. The result in the time domain looks like this:

<center>
[[Image:DAOutput.jpg|Description]]

<math>
\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT)
</math>
</center>

Let's look at this is frequency space. Note that convolution in time means multiplication in frequency.

<center>
<math>\hat X(f) = 1/T \sum_{n=-\infty}^\infty X(f - n/T) \cdot P(f)</math>
</center>
where
<center>
<math>P(f) = \int_{-T/2}^{T/2} e^{j2\pi ft} \, dt = T sinc(fT)
</math>
</center>

The low pass filter then knocks the high frequencies out of the signal to be sent to the speaker.

User:Goeari

2004-12-07T01:55:45Z

Goeari: /* How a CD Player Works */

File:DAOutput.jpg

2004-12-07T01:52:37Z

Goeari: DA Output Graph

DA Output Graph

User:Goeari

2004-12-07T01:51:15Z

Goeari:

File:CDplayerdiagram.jpg

2004-12-07T01:32:05Z

Goeari: CD Player Diagram

CD Player Diagram

User:Goeari

2004-12-07T01:31:22Z

Goeari:

Signals and Systems

2004-12-07T00:58:19Z

Goeari: /* Topics */

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

== Topics ==
*[[Orthogonal functions]]
*[[Fourier series]]
*[[Fourier transform]]
*[[Sampling]]
*[[Discrete Fourier transform]]

I couldn't figure out how to get to others Users pages easily so I decided to start posting them here, please add yours:

[[User:Frohro|Rob Frohne]]

[[User:Barnsa|Sam Barnes]]

[[User:Santsh|Shawn Santana]]

[[User:Goeari|Aric Goe]]

[[User:Caswto|Todd Caswell]]

Fourier series

2004-12-07T00:56:08Z

Goeari:

==Periodic Functions==
A continuous time signal <math>x(t)</math> is said to be periodic if there is a positive nonzero value of T such that
<center>
<math> s(t + T) = s(t)</math> for all <math>t</math>
</center>
==Dirichlet Conditions==
The conditions for a periodic function <math>f</math> with period 2L to have a convergent Fourier series.

=====''Theorem:''=====

Let <math>f</math> be a piecewise regular real-valued function defined on some interval [-L,L], such that <math>f</math> has
''only a finite number of discontinuities and extrema'' in [-L,L]. Then the Fourier series of this function converges to <math>f</math> when <math>f</math> is continuous and to the arithmetic mean of the left-handed and right-handed limit of <math>f</math> at a point where it is discontinuous.

==The Fourier Series==
A Fourier series is an expansion of a periodic function <math>f</math> in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions.
<center>
<math> f(t) = \sum_{k= -\infty}^ \infty \alpha_k e^ \frac{j 2 \pi k t}{T} </math>.
</center>

see also:[[Orthogonal Functions]]

Principle author of this page: [[User:Goeari|Aric Goe]]

User:Goeari

2004-12-07T00:39:55Z

Goeari: /* Practicing TEX */

User:Goeari

2004-12-07T00:34:41Z

Goeari: /* Becoming familiar with Wiki */

User:Goeari

2004-12-07T00:34:19Z

Goeari: /* Becoming familiar with Wiki */

[[Image:p1010006.JPG|thumb|Aric Goe]]
== Signals & Systems ==
=== Introduction ===
==== Becoming familiar with Wiki ====
Well, it all seems a little to convenitent to me.

====Practicing TEX====

<math>\frac{Ep}{Tp} = \frac{Es}{Ts}</math>

Signals and Systems

2004-12-07T00:31:55Z

Goeari: /* Topics */

User:Goeari

2004-11-19T02:19:44Z

Goeari: /* Becoming familiar with Wiki */

[[Image:p1010006.JPG|thumb|Aric Goe]]
== Signals & Systems ==
=== Introduction ===
==== Becoming familiar with Wiki ====
I am currently working on deleting one of the image files I uploaded, I don't think I need it.

====Practicing TEX====

<math>\frac{Ep}{Tp} = \frac{Es}{Ts}</math>

Fourier series

2004-10-28T05:10:21Z

Goeari: /* The Fourier Series */

==Diriclet Conditions==
The conditions for a periodic function <math>f</math> with period 2L to have a convergent Fourier series.

=====''Theorem:''=====

Let <math>f</math> be a piecewise regular real-valued function defined on some interval [-L,L], such that <math>f</math> has
''only a finite number of discontinuities and extrema'' in [-L,L]. Then the Fourier series of this function converges to <math>f</math> when <math>f</math> is continuous and to the arithmetic mean of the left-handed and right-handed limit of <math>f</math> at a point where it is discontinuous.

==The Fourier Series==
A Fourier series is an expansion of a periodic function <math>f</math> in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions.

<math> f(t) = \sum_{k= \infty}^ \infty \alpha_k e^ \frac{j 2 \pi k}{T} </math>.

see also:[[Orthogonal Functions]]

Principle author of this page: [[User:Goeari|Aric Goe]]

Fourier series

2004-10-28T04:51:06Z

Goeari:

==Diriclet Conditions==
The conditions for a periodic function <math>f</math> with period 2L to have a convergent Fourier series.

=====''Theorem:''=====

Let <math>f</math> be a piecewise regular real-valued function defined on some interval [-L,L], such that <math>f</math> has
''only a finite number of discontinuities and extrema'' in [-L,L]. Then the Fourier series of this function converges to <math>f</math> when <math>f</math> is continuous and to the arithmetic mean of the left-handed and right-handed limit of <math>f</math> at a point where it is discontinuous.

==The Fourier Series==
A Fourier series is an expansion of a periodic function <math>f</math> in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions.

[[Orthogonal Functions]]

Principle author of this page: [[User:Goeari|Aric Goe]]

Fourier series

2004-10-28T04:49:17Z

Goeari:

==Diriclet Conditions==
The conditions for a periodic function <math>f</math> with period 2L to have a convergent Fourier series.

=====''Theorem:''=====

Let <math>f</math> be a piecewise regular real-valued function defined on some interval [-L,L], such that <math>f</math> has
''only a finite number of discontinuities and extrema'' in [-L,L]. Then the Fourier series of this function converges to <math>f</math> when <math>f</math> is continuous and to the arithmetic mean of the left-handed and right-handed limit of <math>f</math> at a point where it is discontinuous.

==The Fourier Series==
A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions.

[[Orthogonal Functions]])

Principle author of this page: [[User:Goeari|Aric Goe]]

Fourier series

2004-10-28T04:46:00Z

Goeari:

==Diriclet Conditions==
----

The conditions for a periodic function <math>f</math> with period 2L to have a convergent Fourier series.

=====''Theorem:''=====

Let <math>f</math> be a piecewise regular real-valued function defined on some interval [-L,L], such that <math>f</math> has
''only a finite number of discontinuities and extrema'' in [-L,L]. Then the Fourier series of this function converges to <math>f</math> when <math>f</math> is continuous and to the arithmetic mean of the left-handed and right-handed limit of <math>f</math> at a point where it is discontinuous.

==The Fourier Series==
----
A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality (see [[Orthogonal Functions]]) relationships of the sine and cosine functions.

Principle author of this page: [[User:Goeari|Aric Goe]]

Fourier series

2004-10-28T04:45:17Z

Goeari:

==Diriclet Conditions==
----

The conditions for a periodic function <math>f</math> with period 2L to have a convergent Fourier series.

=====''Theorem:''=====

Let <math>f</math> be a piecewise regular real-valued function defined on some interval [-L,L], such that <math>f</math> has
''only a finite number of discontinuities and extrema'' in [-L,L]. Then the Fourier series of this function converges to <math>f</math> when <math>f</math> is continuous and to the arithmetic mean of the left-handed and right-handed limit of <math>f</math> at a point where it is discontinuous.

==The Fourier Series==
----
A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality (see *[[Orthogonal Functions]])relationships of the sine and cosine functions.

Principle author of this page: [[User:Goeari|Aric Goe]]

Fourier series

2004-10-28T04:38:49Z

Goeari:

===Diriclet Conditions===
----

The conditions for a periodic function <math>f</math> with period 2L to have a convergent Fourier series.

=====''Theorem:''=====

Let <math>f</math> be a piecewise regular real-valued function defined on some interval [-L,L], such that <math>f</math> has
''only a finite number of discontinuities and extrema'' in [-L,L]. Then the Fourier series of this function converges to <math>f</math> when <math>f</math> is continuous and to the arithmetic mean of the left-handed and right-handed limit of <math>f</math> at a point where it is discontinuous.

===The Fourier Series===
----
A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions.

Fourier series

2004-10-28T04:35:48Z

Goeari:

Fourier series

2004-10-28T04:31:53Z

Goeari: /* Diriclet Conditions */

===Diriclet Conditions===

The conditions for a periodic function <math>f</math> with period 2L to have a convergent Fourier series.

=====''Theorem:''=====

Let <math>f</math> be a piecewise regular real-valued function defined on some interval [-L,L], such that <math>f</math> has
''only a finite number of discontinuities and extrema'' in [-L,L]. Then the Fourier series of this function converges to <math>f</math> when <math>f</math> is continuous and to the arithmetic mean of the left-handed and right-handed limit of <math>f</math> at a point where it is discontinuous.

===Orthogonal Functions===

=====Orthonormal Functions=====
=====Weighing function=====
=====Kronecker delta function=====

===The Fourier Series===

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions.

----

Fourier series

2004-10-28T04:08:03Z

Goeari: /* Diriclet Conditions */

===Diriclet Conditions===

The conditions for a periodic function <math>f</math> with period 2L to have a convergent Fourier series.

''Theorem:''

Let <math>f</math> be a piecewise regular real-valued function defined on some interval [-L,L], such that <math>f</math> has only a finite number of discontinuities and extrema in [-L,L]. Then the Fourier series of this function converges to <math>f</math> when <math>f</math> is continuous and to the arithmetic mean of the left-handed and right-handed limit of <math>f</math> at a point where it is discontinuous.

Fourier series

2004-10-26T04:40:03Z

Goeari:

==Diriclet Conditions==

'''Theorem:'''

Suppose that

(1) <math>f(x)</math> is defined and single-valued except possibly at a finite number of points in <math>(-L, L)</math>

(2) <math>f(x)</math> is periodic outside <math>(-L, L)</math> with period <math>P = 2L</math>

(3) <math>f(x)</math> and <math>f'(x)</math> are piecewise continuous in <math>(-L, L)</math>.

User:Goeari

2004-09-28T06:06:12Z

Goeari:

User:Goeari

2004-09-28T06:05:05Z

Goeari:

== Signals & Systems == [[Image:p1010006.JPG|thumb|Aric Goe]]
=== Introduction ===
==== Becoming familiar with Wiki ====
I am currently working on deleting one of the image files I uploaded, I don't think I need it.

User:Goeari

2004-09-28T05:51:49Z

Goeari:

[[Image:p1010006.JPG|thumb|Aric Goe]]

User:Goeari

2004-09-28T05:50:49Z

Goeari:

[[Image:Arics.JPG|thumb|Aric Goe]]

File:Arics.JPG

2004-09-28T05:50:16Z

Goeari:

Aric Goe

User:Goeari

2004-09-28T05:49:14Z

Goeari:

[[Image:Arics.JPG|thumb|Description]]

File:Arics.JPG

2004-09-28T05:48:10Z

Goeari:

File:P1010006.JPG

2004-09-28T05:28:50Z

Goeari:

Aric

File:P1010006.JPG

2004-09-28T05:28:31Z

Goeari:

ric

File:P1010006.JPG

2004-09-28T05:21:17Z

Goeari: My Pic

My Pic