View source for Convolution

==English==
[[File:Keychain with text "Encryption is key".jpg|right|thumb|A [[keyring]] is a helix containing two '''convolutions''' (360° turns).]]
{{wikipedia}}

===Etymology===
Borrowed from {{bor|en|la|convolutus||to roll together}}, past participle of {{m|la|convolvere}}, from {{m|la|con-}} + {{m|la|volvere||to roll}}, with the suffix {{m|en|-tion}}. Equivalent to {{suffix|en|convolute|ion}}. The mathematical sense is a semantic calque from {{m|de|Faltung}}.

===Pronunciation===
* {{rhymes|en|uːʃən|s=4}}

===Noun===
{{en-noun|~}}

# A [[twist]] or [[fold]].
# Any of the [[fold]]s on the [[surface]] of the [[brain]].
# The shape of something [[rotating]]; a [[vortex]].
# The state or condition of being [[convoluted]].
# {{lb|en|mathematics|functional analysis}} A mathematical operation on two functions that produces a third that expresses how the shape of one is modified by the other; the [[integral]] of the product of the two functions after one is reflected about the ''y''-axis and shifted along the ''x''-axis.
#: {{coordinate terms|en|deconvolution}}
#* '''1934''', [[w:Aurel Wintner|Aurel Wintner]], {{rfdatek|en|Wintner}}<!--title?-->
#*: The proper method in dealing with distribution functions and their '''convolutions''' (“Faltungen”) is the method of Fourier transforms, first applied systematically by Levy in his book on the calculus of probability.
#* {{quote-book|en|year=1997|author=Richard Tolimieri; Myoung An; Chao Lu|title=Algorithms for Discrete Fourier Transform and '''Convolution'''|edition=2nd|pageurl=https://books.google.com.au/books?id=Na3hBwAAQBAJ&pg=PA101&dq=%22convolution%22%7C%22convolutions%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjpmf_sopn7AhU47TgGHSilCCsQ6AF6BAheEAI#v=onepage&q=%22convolution%22%7C%22convolutions%22&f=false|page=101|publisher=Springer
|passage=Linear '''convolution''' is one of the most frequent computations carried out in digital signal processing (DSP).}}
#* {{quote-book|en|year=1994|author=Semen B. Yakubovich; Yurii F. Luchko|title=The Hypergeometric Approach to Integral Transforms and '''Convolutions'''|pageurl=https://books.google.com.au/books?id=VKz9CAAAQBAJ&pg=PA183&dq=%22convolution%22%7C%22convolutions%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjpmf_sopn7AhU47TgGHSilCCsQ6AF6BAhhEAI#v=onepage&q=%22convolution%22%7C%22convolutions%22&f=false|page=183|publisher=Springer
|passage=In Chapter 11 we considered <math>H</math>-'''convolutions''' of generalized <math>H</math>-transforms. These '''convolutions''' are bilinear, commutative and associative operations{{...}}.}}
# {{lb|en|computing}} A function which maps a [[tuple]] of [[sequences]] into a sequence of tuples.
# One 360° turn in a spring or similar helix.

====Usage notes====
* {{sense|functional analysis}} The term refers to both the result function and to the process of computing it.

====Derived terms====
{{col|en|autoconvolution|convolutionless|reconvolution|deconvolution
|convolutional|convolution theorem|convolution transform|Titchmarsh convolution theorem}}

====Related terms====
* {{l|en|convolve}}
* {{l|en|convolute}}
* {{l|en|convoluted}}

====Translations====
{{trans-top|twist or fold}}
* Bulgarian: {{t+|bg|извивка|f}}, {{t|bg|витка|f}}
* Finnish: {{t+|fi|poimu}}, {{t+|fi|laskos}}
{{trans-bottom}}

{{trans-top|any of the folds on the surface of the brain}}
* Bulgarian: {{t+|bg|гънка|f}}
* Catalan: {{t+|ca|circumvolució|f}}
* Finnish: {{t+|fi|poimu}}
* French: {{t+|fr|circonvolution|f}}
{{trans-bottom}}

{{trans-top-also|shape of something rotating; a vortex|vortex}}
* Bulgarian: {{t|bg|витка|f}}
* Finnish: {{t+|fi|kierre}}
{{trans-bottom}}

{{trans-top|state or condition of being convoluted}}
* Finnish: {{t+|fi|kiertyminen}}
{{trans-bottom}}

{{trans-top|mathematics: mathematical operation on two functions}}
* Chinese:
*: Mandarin: {{t|cmn|卷積|tr=juǎnjī}}, {{t|cmn|褶積|tr=zhějī}}
* Czech: {{t|cs|konvoluce|f}}
* Hungarian: {{t+|hu|konvolúció}}
* Icelandic: {{t|is|földun|f}}
* Italian: {{t|it|convoluzione|f}}
* Kurdish:
*: Central Kurdish: {{t|ckb|لوول}}, {{t|ckb|پێچ}}
* Polish: {{t+|pl|splot|m}}
{{trans-bottom}}

{{trans-top|computing: function that maps a tuple of sequences into a sequence of tuples}}
{{trans-bottom}}

{{trans-top|one 360° turn in a spring or similar helix}}
* Finnish: {{t+|fi|kierros}}
{{trans-bottom}}

{{checktrans-top}}
* Scottish Gaelic: {{t-check|gd|comh-shnìomh|m}}
{{trans-bottom}}

===See also===
* {{l|en|autocorrelation}}
* {{l|en|cross-correlation}}

===References===
* {{R:Webster 1913}}
* {{R:Century 1911}}

===Further reading===
* {{pedia|Convolution (disambiguation)}}
* {{pedia|Convolution (computer science)}}
* [https://mathworld.wolfram.com/Convolution.html Convolution] on {{w|MathWorld|Wolfram MathWorld}}
* [https://encyclopediaofmath.org/wiki/Convolution_of_functions Convolution of functions] on {{w|Encyclopedia of Mathematics}}

==French==

===Etymology===
Formed from {{der|fr|la|convolutus}}, with the suffix {{m|fr|-tion}}.

===Pronunciation===
* {{audio|fr|LL-Q150 (fra)-WikiLucas00-convolution.wav}}

===Noun===
{{fr-noun|f}}

# [[#Noun|convolution]]

===Further reading===
* {{R:fr:TLFi}}