convolution


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Related to convolution: Fourier transform, Convolution theorem

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 ?
In the convolution stage, we apply the convolution suggested described in Section 4.
The purpose of convolution was to identify number of the edge intersection.
Convolution filter may be a quite linear filter, which modifies or enhances pictures by linear combination (for example addition and multiplication).
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the convolution product of [[?
The non-braided hose's convolutions are farther apart ("wide pitch"), thereby reducing flexibility and increasing stiffness.
The hidden layers of LRF-ELM consists of a convolution layer and a pooling layer.
3 Identifying CUDA GPU obstacles for high-performance convolution
In the next theorem, we characterize all finite codimensional invariant subspaces of a cyclic convolution operator on [H.
The convolution is defined as fixed point of a nonlinear contractive operator T of B (I ) where the images Tg are piecewisely defined by means of apartition of the interval and a scale function.
The inverted second order Gaussian derivate is used for the laser line extraction as a kernel for convolution to the brightness (e.
N-1]) of the same of the same length N, is called discrete circular convolution of period N the sequence z = x [cross product] y = ([z.