Dictionary

convolution en · NOUN

Pronunciation

• /kɑn.vəˈluːʃ(ə)n/ (General-American)
• (Southern-England) audio
• /kɒn.vəˈluːʃ(ə)n/ (Received-Pronunciation)

Etymology

Etymology tree Proto-Indo-European *ḱe? Proto-Indo-European *ḱóm Proto-Italic *kom Proto-Italic *kom- Latin con- Proto-Indo-European *welH-der. Proto-Italic *wolwō Latin volvō Latin convolvō Latin convolūtusbor. English -tion English convolution 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.

Meanings

1. (countable, uncountable) A twist or fold.
2. (countable, uncountable) Any of the folds on the surface of the brain.
3. (countable, uncountable) The shape of something rotating; a vortex.
4. (countable, uncountable) The state or condition of being convoluted.
5. (countable, qualifier:functional analysis, uncountable) 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.
   • In Chapter 11 we considered H-convolutions of generalized H-transforms. These convolutions are bilinear, commutative and associative operations[…]. 1994, Semen B. Yakubovich, Yurii F. Luchko, The Hypergeometric Approach to Integral Transforms and Convolutions, Springer, page 183:
   • 1934, Aurel Wintner, 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.
   • Linear convolution is one of the most frequent computations carried out in digital signal processing (DSP). 1997, Richard Tolimieri, Myoung An, Chao Lu, Algorithms for Discrete Fourier Transform and Convolution, 2nd edition, Springer, page 101:
6. (countable, uncountable) A function which maps a tuple of sequences into a sequence of tuples.
7. (countable, uncountable) One 360° turn in a spring or similar helix.

Forms

Coordinates

deconvolution

Deriveds

deconvolution · reconvolution · autoconvolution · convolutionless · convolution transform · Titchmarsh convolution theorem · convolutional · convolution theorem

Relateds

convolute · convoluted · autocorrelation · convolve · cross-correlation

Translations (25)

bg витка (shape of something rotating; a vortex — see also vortex) · fi laskos (twist or fold) · ca circumvolució (any of the folds on the surface of the brain) · fi kiertyminen (state or condition of being convoluted) · ckb پێچ (mathematics: mathematical operation on two functions) · bg обърканост (state or condition of being convoluted) · bg конволюция (computing: function that maps a tuple of sequences into a sequence of tuples) · bg конволюция (mathematics: mathematical operation on two functions) · fi kierros (one 360° turn in a spring or similar helix) · cs konvoluce (mathematics: mathematical operation on two functions) · bg гънка (any of the folds on the surface of the brain) · it convoluzione (mathematics: mathematical operation on two functions) · es convolución (mathematics: mathematical operation on two functions) · cmn 卷積 /卷积 (mathematics: mathematical operation on two functions) · ckb لوول (mathematics: mathematical operation on two functions) · cmn 褶積 /褶积 (mathematics: mathematical operation on two functions) · fi poimu (any of the folds on the surface of the brain) · bg витка (twist or fold) · pl splot (mathematics: mathematical operation on two functions) · bg извивка (twist or fold) · fi kierre (shape of something rotating; a vortex — see also vortex) · fr circonvolution (any of the folds on the surface of the brain) · is földun (mathematics: mathematical operation on two functions) · hu konvolúció (mathematics: mathematical operation on two functions) · fi poimu (twist or fold)