# convolution

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## convolution

Anatomy any of the numerous convex folds or ridges of the surface of the brain

## convolution

(kon-vŏ-loo -shŏn) A mathematical operation that is performed on two functions and expresses how the shape of one is ‘smeared’ by the other. Mathematically, the convolution of the functions f(x) and g(x) is given by
(u )g(x u )du

It finds wide application in physics; it describes, for example, how the transfer function of an instrument affects the response to an input signal. See also autocorrelation function; radio-source structure.

## Convolution

The convolution of the two functions f1(x) and f2(x) is the function

The convolution of f1(x) and f2(x) is sometimes denoted by f1 * f2

If f1 and f2 are the probability density functions of two independent random variables X and Y, then f1 * f2 is the probability density function of the random variable X + Y. If Fk(x) is the Fourier transform of the function fk(x), that is,

then F1(x) F2(x) is the Fourier transform of the function f1 * f2. This property of convolutions has important applications in probability theory. The convolution of two functions exhibits an analogous property with respect to the Laplace transform; this fact underlies broad applications of convolutions in operational calculus.

The operation of convolution of functions is commutative and associative—that is, f1 * f2 = f2 * f1 and f1 * (f2 * f3) = (f1 * f2) * f3. For this reason, the convolution of two functions can be regarded as a type of multiplication. Consequently, the theory of normed rings can be applied to the study of convolutions of functions.

## convolution

[‚kän·və′lü·shən]
(anatomy)
A fold, twist, or coil of any organ, especially any one of the prominent convex parts of the brain, separated from each other by depressions or sulci.
(geology)
The process of developing convolute bedding.
A structure resulting from a convolution process, such as a small-scale but intricate fold.
(mathematics)
The convolution of the functions ƒ and g is the function F, defined by
(statistics)
A method for finding the distribution of the sum of two or more random variables; computed by direct integration or summation as contrasted with, for example, the method of characteristic functions.
References in periodicals archive ?
Tuan, Generalized convolutions for the Fourier integral transforms and applications, Journal of Siberian Federal Univ.
Chapter 3 of the book [5], where the corresponding complex convolutions were studied).
Now, the question is for which convolutions FFT must be used, time or spatial or both.
Using the convolution we can write for f [member of] H[a, n]
where the * denotes convolution and [bar.P](r) is the dyadic point spread function defined as
According to convolution (6), taking into account the introduced signs (7) during standardising we will have the optimisation model of optimal limited resource allocation of suppliers for one group of importance of customers:
A genetic analysis of the Turkish patient whose brain lacks the characteristic convolutions in part of his cerebral cortex revealed that the deformity was caused by the deletion of two genetic letters from 3 billion in the human genetic alphabet.
** The relation of the source function [s.sub.i](t) to the acquired signals can be described by linear differential equation and can, therefore, be described by convolution with transfer functions ([u.sub.ij](t)*[e.sub.j](t)).
Following Hirschman [10] and Haimo [9], we can study convolution for a Hankel type transformation, which is closely connected with, [h.sub.[alpha],[beta]] and one can deduce analogous results for the Hankel type transformation [h.sub.[alpha],[beta]].
According to Laws, the best mask is R5R5, from all the 25 convolutions. A 60% of the samples have been used for the training and the other 40% for the test.
* In optics, many kinds of "blur" are described by convolutions. A shadow (e.g., the shadow on the table when you hold your hand between the table and a light source) is the convolution of the shape of the light source that is casting the shadow and the object whose shadow is being cast.
[17] Yu, Fisher, and VladlenKoltun, "Multi-scale context aggregation by dilated convolutions," arXiv preprint arXiv:1511.07122, 2015.

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