convolution

A twist or fold.

Noun

  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. 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.
    • 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...
    • 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...
    • 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...

    Coordinate Terms: deconvolution

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

Origin

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.

Forms

convolutions

Related

convolve convolute convoluted autocorrelation cross-correlation

Derived

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