convolution - meaning and definition. What is convolution
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What (who) is convolution - definition

BINARY MATHEMATICAL OPERATION ON FUNCTIONS
Convolution (music); Convolve; Convolution kernel; Convolution operator; Convolution operation; Linear convolution; Nonlinear convolution; Convolution of functions; Faltung; Convolved; Convolution integral; Continuous-time convolution; Carson's integral; Superposition integral; Convolution (mathematics); Discrete convolution; Convolutions; Cross Convolution; Auto-convolution; Self convolution
  • Discrete 2D Convolution Animation
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  • [[Gaussian blur]] can be used to obtain a smooth grayscale digital image of a [[halftone]] print.

Convolution         
·noun The act of rolling anything upon itself, or one thing upon another; a winding motion.
II. Convolution ·noun An irregular, tortuous folding of an organ or part; as, the convolutions of the intestines; the cerebral convolutions. ·see Brain.
III. Convolution ·noun The state of being rolled upon itself, or rolled or doubled together; a tortuous or sinuous winding or fold, as of something rolled or folded upon itself.
convolution         
n.
1.
Rolling together.
2.
Coil, fold, bight.
convolution         
(convolutions)
1.
Convolutions are curves on an object or design that has a lot of curves. (LITERARY)
N-COUNT: usu pl
2.
You can use convolutions to refer to a situation that is very complicated. (LITERARY)
...the thorny convolutions of love.
N-VAR: oft N of n

Wikipedia

Convolution

In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions (f and g) that produces a third function ( f g {\displaystyle f*g} ) that expresses how the shape of one is modified by the other. The term convolution refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The choice of which function is reflected and shifted before the integral does not change the integral result (see commutativity). The integral is evaluated for all values of shift, producing the convolution function.

Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution ( f g {\displaystyle f*g} ) differs from cross-correlation ( f g {\displaystyle f\star g} ) only in that either f(x) or g(x) is reflected about the y-axis in convolution; thus it is a cross-correlation of g(−x) and f(x), or f(−x) and g(x). For complex-valued functions, the cross-correlation operator is the adjoint of the convolution operator.

Convolution has applications that include probability, statistics, acoustics, spectroscopy, signal processing and image processing, geophysics, engineering, physics, computer vision and differential equations.

The convolution can be defined for functions on Euclidean space and other groups (as algebraic structures). For example, periodic functions, such as the discrete-time Fourier transform, can be defined on a circle and convolved by periodic convolution. (See row 18 at DTFT § Properties.) A discrete convolution can be defined for functions on the set of integers.

Generalizations of convolution have applications in the field of numerical analysis and numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing.

Computing the inverse of the convolution operation is known as deconvolution.

Examples of use of convolution
1. Arar added that the media and convolution of different cultures have affected the youth. «They feel they have a freedom of choice and opinion.