convolution

English

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convolution

Wikipedia

Etymology

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

• Rhymes: -uːʃən

Noun

convolution (countable and uncountable, plural convolutions)

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. (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 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 ${\displaystyle H}$-convolutions of generalized ${\displaystyle H}$-transforms. These convolutions are bilinear, commutative and associative operations […] .

6. (computing) A function which maps a tuple of sequences into a sequence of tuples.
7. One 360° turn in a spring or similar helix.

Usage notes

• (functional analysis): The term refers to both the result function and to the process of computing it.

Derived terms

• convolutional
• convolution theorem
• convolution transform
• Titchmarsh convolution theorem

Related terms

• convolve
• convolute
• convoluted

Translations

See also

• autocorrelation
• cross-correlation

References

• “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

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

French

Etymology

Formed from Latin convolutus, with the suffix -tion.

Pronunciation

• Audio

  (file)

Noun

convolution f (plural convolutions)

1. convolution

Further reading

• “convolution”, in Trésor de la langue française informatisé , 2012.