Fourier series - Revision history

Wilspa: /* The Fourier Series */

2008-02-13T10:21:23Z

The Fourier Series

← Older revision		Revision as of 03:21, 13 February 2008
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	==The Fourier Series==		==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.		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. One way to represent a Fourier series is
	<center>		<center>
	<math> f(t) = \sum_{k= -\infty}^ \infty \alpha_k e^ \frac{j 2 \pi k t}{T} </math>.		<math> f(t) = \sum_{k= -\infty}^ \infty \alpha_k e^ \frac{j 2 \pi k t}{T} </math>.
	</center>		</center>


	==See Also==		==See Also==

2008-02-13T10:20:08Z

Dirichlet Conditions

← Older revision		Revision as of 03:20, 13 February 2008
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	</center>		</center>
	==Dirichlet Conditions==		==Dirichlet Conditions==
	The conditions for a periodic function <math>f</math> with period 2L to have a convergent Fourier series.		The conditions for a periodic function <math>f</math> with period 2L to have a convergent Fourier series are as follows:

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

2006-10-29T23:55:07Z

See Also

← Older revision		Revision as of 16:55, 29 October 2006
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	*[[Orthogonal Functions]]		*[[Orthogonal Functions]]
	*[[Fourier Transforms]]		*[[Fourier Transforms]]

	~~<small>If anyone knows how to make the Fourier transform link into an internal, please do. I wasn't able to do so.</small>~~

	==Contributors==		==Contributors==

2006-10-08T21:50:18Z

← Older revision		Revision as of 14:50, 8 October 2006
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			*[[Signals and systems\|Signals and Systems]]
	==Introduction==		==Introduction==
	Born in Auxerre, France in 1768, Jean Baptiste Joseph Fourier was orphaned at the age of eight. Later he was instructed by Benedictine monks who taught at and ran a military college.		Born in Auxerre, France in 1768, Jean Baptiste Joseph Fourier was orphaned at the age of eight. Later he was instructed by Benedictine monks who taught at and ran a military college.

2006-09-29T18:27:45Z

See Also

← Older revision		Revision as of 11:27, 29 September 2006
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	==See Also==		==See Also==
	*[[Orthogonal Functions]]		*[[Orthogonal Functions]]
	*[[~~http://cubex.wwc.edu/~frohro/wiki/index.php/Fourier_transform~~ Fourier Transforms]]		*[[Fourier Transforms]]

	<small>If anyone knows how to make the Fourier transform link into an internal, please do. I wasn't able to do so.</small>		<small>If anyone knows how to make the Fourier transform link into an internal, please do. I wasn't able to do so.</small>

2005-10-13T05:16:07Z

''Theorem:''

← Older revision		Revision as of 22:16, 12 October 2005
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	The conditions for a periodic function <math>f</math> with period 2L to have a convergent Fourier series.		The conditions for a periodic function <math>f</math> with period 2L to have a convergent Fourier series.

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

	Let <math>f</math> be a piecewise regular real-valued function defined on some interval [-L,L], such that <math>f</math> has		Let <math>f</math> be a piecewise regular real-valued function defined on some interval [-L,L], such that <math>f</math> has

2005-10-13T04:57:30Z

See Also

← Older revision		Revision as of 21:57, 12 October 2005
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	*[[Orthogonal Functions]]		*[[Orthogonal Functions]]
	*[[http://cubex.wwc.edu/~frohro/wiki/index.php/Fourier_transform Fourier Transforms]]		*[[http://cubex.wwc.edu/~frohro/wiki/index.php/Fourier_transform Fourier Transforms]]

			<small>If anyone knows how to make the Fourier transform link into an internal, please do. I wasn't able to do so.</small>

	==Contributors==		==Contributors==

2005-10-07T15:27:38Z

See Also

← Older revision		Revision as of 08:27, 7 October 2005
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	==See Also==		==See Also==
	*[[Orthogonal Functions]]		*[[Orthogonal Functions]]
	*[[Fourier Transforms]]		*[[http://cubex.wwc.edu/~frohro/wiki/index.php/Fourier_transform Fourier Transforms]]

	==Contributors==		==Contributors==

2005-10-07T15:25:16Z

See Also

2005-10-07T15:24:22Z

See Also