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 ?
Convolutional coding essentially reduces the error probability that leads to a BER vanishing for antennas with diameter of more than 1.
A dependence of a BER on satellite transponder gain is shown in figure 7 for two noise temperatures without coding and with convolutional coding.
In comparison to our previous paper [8] we report significant increase in terrain classification capability of the convolutional neural network as the software that prepared imagery for the network has been improved.
The Viterbi algorithm (VA) is known as a maximum likelihood (ML)-decoding algorithm for convolutional codes.
Mittelholzer, 1996, Convolutional Codes Over Groups, IEEE Transactions on Information Theory, 42(6), pp.
Code symbol outputs from the convolutional encoder may be repeated based on the repetition factor.
The CEVA Deep Neural Network framework provided a quick and smooth path from offline training to real-time detection for our convolutional neural network based algorithms," said Steven Hanna, president and co-founder at Phi Algorithm Solutions.
Eyeris uses convolutional neural networks as a deep learning architecture to train and deploy its algorithm in to a number of today's commercial applications.
Altera Corporation and Baidu, China s largest online search engine, are collaborating on using FPGAs and convolutional neural network (CNN) algorithms for deep learning applications set to play a critical role in the development of more accurate and faster online search.
This deep network necessitates more than 120 million parameters utilizing locally connected layers without weight sharing, rather than the standard convolutional layers.
Algorithms 1-5 and 8 are convolutional methods, based on approximation of differential operators by finite differences.

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