Fourier transform - Revision history

Wilspa: /* A Second Approach to Fourier Transforms */

2008-02-13T10:32:23Z

A Second Approach to Fourier Transforms

← Older revision		Revision as of 03:32, 13 February 2008
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	Some other usefull pairs can be found here: [[Fourier Transforms]]		Some other usefull pairs can be found here: [[Fourier Transforms]]

	==~~A Second Approach to~~ Fourier Transforms==		==Another look at Fourier Transforms==
	*[[Fourier Transforms]]		*[[Fourier Transforms]]

	Return to *[[Signals and systems\|Signals and Systems]]		Return to [[Signals and systems\|Signals and Systems]]

Wilspa: /* Fourier Transform */

2008-02-13T10:30:43Z

Fourier Transform

← Older revision		Revision as of 03:30, 13 February 2008
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	==Fourier Transform==		==Fourier Transform==
	What is a Fourier Transform? A Fourier Transform is a function that changes a signal or waveform from the time domain into the frequency domain. One simple way to look at it is this: Suppose you are at the beach, watching the waves. You could say that a wave hits the shore at specific times (0 second, 2 seconds, 4 seconds, etc.) that would be describing the waveform in the time domain. If, however, you were to say that the waves hit the beach every two seconds, that would be describing it in the frequency domain. So a Fourier transform would take the data given in the time domain and convert that into the frequency domain. The function that does this is: <math> X(f)=\int_{-\infty}^{\infty} x(t) e^{-j2\pi ft}\, dt		What is a Fourier Transform? A Fourier Transform is a function that changes a signal or waveform from the time domain into the frequency domain. One simple way to look at it is this: Suppose you are at the beach, watching the waves. You could say that a wave hits the shore at specific times (0 second, 2 seconds, 4 seconds, etc.) that would be describing the waveform in the time domain. If, however, you were to say that the waves hit the beach every two seconds, that would be describing it in the frequency domain. So a Fourier transform would take the data given in the time domain and convert that into the frequency domain. The function that does this is: <math> X(f)=\int_{-\infty}^{\infty} x(t) e^{-j2\pi ft}\, dt </math>.

	The reverse is also possible. You can take the information from the frequency domain, and convert it into the time domain using an Inverse Fourier Transform.		The reverse is also possible. You can take the information from the frequency domain, and convert it into the time domain using an Inverse Fourier Transform.
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	\mathcal{F}^{-1}[\Beta(f)]=\beta(t)=\int_{-\infty}^\infty \Beta(f) e^{j2\pi fkt}\,df		\mathcal{F}^{-1}[\Beta(f)]=\beta(t)=\int_{-\infty}^\infty \Beta(f) e^{j2\pi fkt}\,df
	</math>		</math>

	==Some Useful Fourier Transform Pairs==		==Some Useful Fourier Transform Pairs==
	<math>		<math>

Wilspa at 10:30, 13 February 2008

2008-02-13T10:30:06Z

← Older revision		Revision as of 03:30, 13 February 2008
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	*[[Signals and ~~systems\|Signals~~ and ~~Systems]]~~		==Fourier Transform==
			What is a Fourier Transform? A Fourier Transform is a function that changes a signal or waveform from the time domain into the frequency domain. One simple way to look at it is this: Suppose you are at the beach, watching the waves. You could say that a wave hits the shore at specific times (0 second, 2 seconds, 4 seconds, etc.) that would be describing the waveform in the time domain. If, however, you were to say that the waves hit the beach every two seconds, that would be describing it in the frequency domain. So a Fourier transform would take the data given in the time domain and convert that into the frequency domain. The function that does this is: <math> X(f)=\int_{-\infty}^{\infty} x(t) e^{-j2\pi ft}\, dt

			The reverse is also possible. You can take the information from the frequency domain, and convert it into the time domain using an Inverse Fourier Transform.

	==From the Fourier Transform to the Inverse Fourier Transform==		==From the Fourier Transform to the Inverse Fourier Transform==
	~~An initially identity that is useful~~:		Lets start with the basic Fourier Transform:
	<math>		<math>

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	==A Second Approach to Fourier Transforms==		==A Second Approach to Fourier Transforms==
	*[[Fourier Transforms]]		*[[Fourier Transforms]]

			Return to *[[Signals and systems\|Signals and Systems]]

10.109.3.20: /* Some Useful Fourier Transform Pairs */

2006-10-31T03:50:15Z

Some Useful Fourier Transform Pairs

← Older revision		Revision as of 20:50, 30 October 2006
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	</math>		</math>
	<br>		<br>
	Some other usefull pairs can be found here ~~under Fourier Transforms page~~: [[~~User:wilspa\|Wilspa~~]]		Some other usefull pairs can be found here: [[Fourier Transforms]]

	==A Second Approach to Fourier Transforms==		==A Second Approach to Fourier Transforms==
	*[[Fourier Transforms]]		*[[Fourier Transforms]]

10.109.3.20: /* Some Useful Fourier Transform Pairs */

2006-10-31T03:48:59Z

Some Useful Fourier Transform Pairs

← Older revision		Revision as of 20:48, 30 October 2006
Line 119:		Line 119:
	</math>		</math>
	<br>		<br>
			Some other usefull pairs can be found here under Fourier Transforms page: [[User:wilspa\|Wilspa]]

	==A Second Approach to Fourier Transforms==		==A Second Approach to Fourier Transforms==
	*[[Fourier Transforms]]		*[[Fourier Transforms]]

172.16.16.91: /* A Second Approach to Fourier Transforms */

2006-10-29T23:57:06Z

A Second Approach to Fourier Transforms

← Older revision		Revision as of 16:57, 29 October 2006
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	==A Second Approach to Fourier Transforms==		==A Second Approach to Fourier Transforms==
			*[[Fourier Transforms]]

Smitry at 21:50, 8 October 2006

2006-10-08T21:50:37Z

← Older revision		Revision as of 14:50, 8 October 2006
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			*[[Signals and systems\|Signals and Systems]]
	==From the Fourier Transform to the Inverse Fourier Transform==		==From the Fourier Transform to the Inverse Fourier Transform==
	An initially identity that is useful:		An initially identity that is useful:

Andrew: /* Some Useful Fourier Transform Pairs */

2006-10-04T05:21:11Z

Some Useful Fourier Transform Pairs

← Older revision		Revision as of 22:21, 3 October 2006
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	==Some Useful Fourier Transform Pairs==		==Some Useful Fourier Transform Pairs==
	<math>		<math>
	\mathcal{F}[\alpha(t)]=\~~Alpha~~(f)		\mathcal{F}[\alpha(t)]=\frac{1}{\mid \alpha \mid}f(\frac{\omega}{\alpha})
	</math>		</math>
	<br>		<br>

Guenan: /* Some Useful Fourier Transform Identities */

2004-12-10T18:41:07Z

Some Useful Fourier Transform Identities

@@ Line 88: / Line 88: @@
 \mathcal{F}^{-1}[\Beta(f)]=\beta(t)=\int_{-\infty}^\infty \Beta(f) e^{j2\pi fkt}\,df
 </math>
-==Some Useful Fourier Transform Identities==
+==Some Useful Fourier Transform Pairs==
 <math>
 \mathcal{F}[\alpha(t)*\beta(t)]=\Alpha(f)\Beta(f)
@@ Line 96: / Line 117: @@
 \mathcal{F}[\alpha(t)\beta(t)]=\Alpha(f)*\Beta(f)
 </math>
 ==A Second Approach to Fourier Transforms==

Guenan: /* Some Useful Fourier Transform Identities */

2004-12-10T17:04:24Z

Some Useful Fourier Transform Identities

← Older revision		Revision as of 10:04, 10 December 2004
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	</math>		</math>
	==Some Useful Fourier Transform Identities==		==Some Useful Fourier Transform Identities==
	{\~~hbox~~{\~~boldmath $~~\~~textstyle #1$}}~~		<math>
			\mathcal{F}[\alpha(t)*\beta(t)]=\Alpha(f)\Beta(f)
			</math>
			<br>
			<math>
			\mathcal{F}[\alpha(t)\beta(t)]=\Alpha(f)*\Beta(f)
			</math>

	==A Second Approach to Fourier Transforms==		==A Second Approach to Fourier Transforms==