convolution
nounUK /kɒn.vəˈluːʃ(ə)n/ · US /kɑn.vəˈluːʃ(ə)n/
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.
7 senses
- 1A twist or fold.
- 2Any of the folds on the surface of the brain.
- 3The shape of something rotating; a vortex.
- 4The state or condition of being convoluted.
- 5A mathematical operation on two functions that produces…
- 6A function which maps a tuple of sequences into a…
- 7One 360° turn in a spring or similar helix.
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, Sciences 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.
Functional analysis
- 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:
1 more example
- 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:
Computing, Engineering, Mathematics, Natural sciences, Physical sciences, Sciences A function which maps a tuple of sequences into a sequence of tuples.
One 360° turn in a spring or similar helix.
- Derived terms
- autoconvolution, convolutional, convolutionless, convolution theorem, convolution transform, deconvolution, reconvolution, Titchmarsh convolution theorem
- Related terms
- convolve, convolute, convoluted, autocorrelation, cross-correlation