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 ?
ANKARA, May 16, 2011 (TUR) -- A leading Turkish scientist has discovered a single gene that determines the formation of brain convolutions.
Unification of the parameters included in (15) is made with relation to the sum of the discrete values, which describe their change by taking into account the direction of the extremisation of criteria (13) and the requirement to minimise those, included in convolution (14) according to these expressions:
Wang and Keer [10] used a similar approach, implementing the Discrete Convolution Fast Fourier Transform (DCFFT) technique [11] in layers of constant depth.
Duchovny spends the entire episode in a catatonic stupor, looking as though a particularly rabid fan had just explained all of the series' plot convolutions to him in one sitting.
With Stasi City, 1997, the operative convolutions and reflective chicanery the Wilsons formerly conjured through cinematic reference are embodied in the chill of the institution itself.
CNAPS parallel processing technology, capable of up to seven billion operations per second, accelerates up to 100-fold image processing and recognition functions such as character recognition, filtering and convolutions and image manipulation functions such as rotation and resizing.
Instead, his work has acquired the spaciousness of a LeWitt or a Ryman or, said another way, retained the organic convolutions of the congested drawing on Rockburne's wall but opened up to and annexed the white vastness that once surrounded it.
Adaptive's CNAPS accelerates up to 100-fold image processing and recognition functions such as character recognition, filtering and convolutions and image manipulation functions such as rotation and resizing.
CNAPS accelerates up to 100-fold image processing and recognition functions such as filtering and convolutions, and image manipulation functions such as rotation and color transformation.
Morphing between a sort of sci-fi behemoth and fantastic hot rod, the work comprised everything from sections of surrounding hillside to a river, with the baroque convolutions of an elegant water-circulation system begging for scrupulous examination.
He has created a pretty compelling antagonist for Bobby and his crew in Heald's Judge Cooper, but it would take some questionable plot convolutions to reunite them for future clashes.
According to the artist, LA was a place where Bush "felt at home" and "knew what his work was"--comments whose rhetorical convolutions give some indication of the ambiguities at play here, since we all know whose home LA really is.