# 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 ?
Conversely, Convolve argued for a broader application of the waiver--specifically an application that covered advice received by Seagate from its in-house and trial counsel.
Convolve is the exclusive licensee of patented motion control technology called Input Shaping, originally developed at and licensed from MIT.
As it can be appreciated, it is enough to define metrics and order in the colour space to be able to convolve the image with the partial derivative in one direction, and later convolve perpendicularly the result (let's remember that they are already real numbers) with a Gaussian mask.
As a radar training device or active countermeasure, the ACT device may be used to convolve a threat radar pulse with a user-defined radar cross-section profile to simulate the return from a complex target at any aspect angle.
Even though the Fourier transform is slow, it is still the fastest way to convolve an image with a large kernel filter.
Through this kind of process of elimination, a TIA can estimate each component of jitter and convolve them to determine TJ.
Considering that a complete distribution of wavelengths was not used in the primary beam, (we use a single wavelength in the raytracing and we convolve the raytraced profile with the emission profile) the agreement between model and simulation is rather good; the low angle reflections are a bit broader than expected, whereas the opposite is true for the high angle ones (cf.
The normalized 2d form image is converted into 1D signal, and these signals are used to convolve with 1d Gabor wavelets.
To simplify the procedure one can convolve the vertical angular spread of the electron beam with the contribution from the beam size first.

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