Convolution - Revision history

Karl Jones at 22:10, 24 August 2016

2016-08-24T22:10:55Z

Karl Jones: /* External links */

2016-08-24T22:06:49Z

‎External links

Karl Jones: /* See also */

2016-04-28T15:46:27Z

‎See also

Karl Jones at 15:40, 28 April 2016

2016-04-28T15:40:26Z

Karl Jones: Created page with "In mathematics and, in particular, functional analysis, '''convolution''' is a mathematical operation on two functions (f and g) It produces a third function, that..."

2016-04-28T15:39:32Z

Created page with "In mathematics and, in particular, functional analysis, '''convolution''' is a mathematical operation on two functions (f and g) It produces a third function, that..."

New page

In [[mathematics]] and, in particular, [[functional analysis]], '''convolution''' is a [[mathematical operation on two functions (f and g)

It produces a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.

== Description ==

Convolution is similar to [[cross-correlation]].

It has applications that include probability, statistics, computer vision, natural language processing, image and signal processing, engineering, and differential equations.

The convolution can be defined for functions on groups other than Euclidean space. For example, periodic functions, such as the discrete-time Fourier transform, can be defined on a circle and convolved by periodic convolution.

A discrete convolution can be defined for functions on the set of integers.

Generalizations of convolution have applications in the field of [[numerical analysis]] and [[numerical linear algebra]], and in the design and implementation of [[finite impulse response filters]] in [[signal processing]].

== Other usage ==

For the usage in [[formal language theory]], see [[Convolution (computer science)]].

For other uses, see [[Convolute]].

== See also ==

* [[Analog signal processing]]
* [[Circulant matrix]]
* [[Convolution for optical broad-beam responses in scattering media]]
* [[Convolution power]]
* [[Cross-correlation]]
* [[Deconvolution]]
* [[Dirichlet convolution]]
* [[Functional analysis]]
* [[Jan Mikusinski]]
* [[List of convolutions of probability distributions]]
* [[LTI system theory#Impulse response and convolution]]
* [[Multidimensional discrete convolution]]
* [[Scaled correlation]]
* [[Sketch Simplification]]
* [[Titchmarsh convolution theorem]]
* [[Toeplitz matrix (convolutions can be considered a Toeplitz matrix operation where each row is a shifted copy of the convolution kernel)]]

== External links ==

* [https://en.wikipedia.org/wiki/Convolution Convolution] @ Wikipedia

[[Category:Functional analysis]]
[[Category:Mathematics]]

← Older revision		Revision as of 22:10, 24 August 2016
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−	In [[mathematics]] and, in particular, [[functional analysis]], '''convolution''' is a [[mathematical operation]] on two [[Function (mathematics)\|functions]] (f and g)	+	In [[mathematics]] and, in particular, [[functional analysis]], '''convolution''' is a [[mathematical operation]] on two [[Function (mathematics)\|functions]] ('''f''' and '''g''').

	It produces a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.		It produces a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.

← Older revision		Revision as of 22:06, 24 August 2016
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−	~~[[Category:Functional analysis]]~~	+
	[[Category:Mathematics]]		[[Category:Mathematics]]

@@ Line 33: / Line 33: @@
 * [[Functional analysis]]
 * [[Jan Mikusinski]]
 * [[List of convolutions of probability distributions]]
 * [[LTI system theory#Impulse response and convolution]]
 * [[Multidimensional discrete convolution]]
 * [[Scaled correlation]]
 * [[Titchmarsh convolution theorem]]
 * [[Toeplitz matrix (convolutions can be considered a Toeplitz matrix operation where each row is a shifted copy of the convolution kernel)]]

@@ Line 1: / Line 1: @@
-In [[mathematics]] and, in particular, [[functional analysis]], '''convolution''' is a [[mathematical operation on two functions (f and g)
+In [[mathematics]] and, in particular, [[functional analysis]], '''convolution''' is a [[mathematical operation]] on two [[Function (mathematics)|functions]] (f and g)
 It produces a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.
@@ Line 30: / Line 30: @@
 * [[Deconvolution]]
 * [[Dirichlet convolution]]
 * [[Functional analysis]]
 * [[Jan Mikusinski]]