convolution
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English
[edit]Etymology
[edit]Borrowed from Latin convolutus (“to roll together”), past participle of convolvere, from con + volvere (“to roll”), with the suffix tion. Equivalent to convolute + ion. The mathematical sense is a semantic calque from Faltung.
Pronunciation
[edit] Rhymes: uːʃən
Noun
[edit]convolution (countable and uncountable, plural convolutions)
 A twist or fold.
 Any of the folds on the surface of the brain.
 The shape of something rotating; a vortex.
 The state or condition of being convoluted.
 (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 yaxis and shifted along the xaxis.
 Coordinate term: deconvolution
 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.
 Aurel Wintner, 1934
 1997, Richard Tolimieri, Myoung An, Chao Lu, Algorithms for Discrete Fourier Transform and Convolution, 2nd edition, Springer, page 101:
 Linear convolution is one of the most frequent computations carried out in digital signal processing (DSP).
 1994, Semen B. Yakubovich, Yurii F. Luchko, The Hypergeometric Approach to Integral Transforms and Convolutions, Springer, page 183:
 In Chapter 11 we considered convolutions of generalized transforms. These convolutions are bilinear, commutative and associative operations […] .
 (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
[edit] (functional analysis): The term refers to both the result function and to the process of computing it.
Derived terms
[edit]Related terms
[edit]Translations
[edit]any of the folds on the surface of the brain

shape of something rotating; a vortex — see also vortex
state or condition of being convoluted

mathematics: mathematical operation on two functions
computing: function that maps a tuple of sequences into a sequence of tuples
 The translations below need to be checked and inserted above into the appropriate translation tables. See instructions at Wiktionary:Entry layout § Translations.
Translations to be checked

See also
[edit]References
[edit] “convolution”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.
 “convolution”, in The Century Dictionary […], New York, N.Y.: The Century Co., 1911, →OCLC.
Further reading
[edit] Convolution (disambiguation) on Wikipedia.Wikipedia
 Convolution (computer science) on Wikipedia.Wikipedia
 Convolution on Wolfram MathWorld
 Convolution of functions on Encyclopedia of Mathematics
French
[edit]Etymology
[edit]Formed from Latin convolutus, with the suffix tion.
Pronunciation
[edit]Audio: (file)
Noun
[edit]convolution f (plural convolutions)
Further reading
[edit] “convolution”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012.
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 English terms suffixed with ion
 Rhymes:English/uːʃən
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 English uncountable nouns
 English countable nouns
 en:Mathematics
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