Etymology

Borrowed from LatinCategory:English terms borrowed from Latin#CONVOLUTIONCategory:English terms derived from Latin#CONVOLUTION convolutus (“to roll together”), past participle of convolvere, from con- + volvere (“to roll”), with the suffix -tion. Equivalent to convolute +‎ -ionCategory:English terms suffixed with -ion#CONVOLUTION. The mathematical sense is a semantic calque from Faltung.

Pronunciation

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• Rhymes: -uːʃənCategory:Rhymes:English/uːʃən#CONVOLUTIONCategory:Rhymes:English/uːʃən/4 syllables#CONVOLUTION

Noun

convolution (countable and uncountable, plural convolutions)Category:English lemmas#CONVOLUTIONCategory:English nouns#CONVOLUTIONCategory:English uncountable nouns#CONVOLUTIONCategory:English countable nouns#CONVOLUTIONCategory:English countable nouns#CONVOLUTIONCategory:English entries with incorrect language header#CONVOLUTIONCategory:Pages with entries#CONVOLUTIONCategory:Pages with 2 entries#CONVOLUTION

1. A twist or fold.
2. Any of the folds on the surface of the brain.
3. The shape of something rotating; a vortex.
4. The state or condition of being convoluted.
5. (mathematicsCategory:en:Mathematics#CONVOLUTION, functional analysisCategory:en:Functional analysis#CONVOLUTION) 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 term: deconvolution

   • 1934, Aurel Wintner, (Can we date this quote by Wintner and provide title, author’s full name, and other details?)Category:Requests for date in English entries#CONVOLUTION

     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.

   • 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).

     Category:English terms with quotations#CONVOLUTION

   • 1994, Semen B. Yakubovich, Yurii F. Luchko, The Hypergeometric Approach to Integral Transforms and Convolutions, Springer, page 183:

     In Chapter 11 we considered ${\displaystyle H}$-convolutions of generalized ${\displaystyle H}$-transforms. These convolutions are bilinear, commutative and associative operations […] .

     Category:English terms with quotations#CONVOLUTION

6. (computingCategory:en:Computing#CONVOLUTION) A function which maps a tuple of sequences into a sequence of tuples.
7. One 360° turn in a spring or similar helix.

See also

• autocorrelation
• cross-correlation

References

• “convolution”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.
• William Dwight Whitney, Benjamin E[li] Smith, editors (1911), “convolution”, in The Century Dictionary […], New York, N.Y.: The Century Co., →OCLC.

Further reading

• Convolution (disambiguation) on Wikipedia.Wikipedia
• Convolution (computer science) on Wikipedia.Wikipedia
• Convolution on Wolfram MathWorld
• Convolution of functions on Encyclopedia of Mathematics

Etymology

Formed from LatinCategory:French terms derived from Latin#CONVOLUTION convolutus, with the suffix -tion.

Pronunciation

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Noun

convolution f (plural convolutions)Category:French lemmas#CONVOLUTIONCategory:French nouns#CONVOLUTIONCategory:French countable nouns#CONVOLUTIONCategory:French entries with incorrect language header#CONVOLUTIONCategory:French feminine nouns#CONVOLUTIONCategory:Pages with entries#CONVOLUTIONCategory:Pages with 2 entries#CONVOLUTION

1. convolution

Further reading

• “convolution”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012