convolution function

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• Convolution — For the usage in formal language theory, see Convolution (computer science). Convolution of two square pulses: the resulting waveform is a triangular pulse. One of the functions (in this case g) is first reflected about τ = 0 and then offset by t …   Wikipedia

• Convolution for optical broad-beam responses in scattering media — Photon transport theories, such as the Monte Carlo method, are commonly used to model light propagation in tissue. The responses to a pencil beam incident on a scattering medium are referred to as Green’s functions or impulse responses. Photon… …   Wikipedia

• Convolution power — In mathematics, the convolution power is the n fold iteration of the convolution with itself. Thus if x is a function on Euclidean space Rd and n is a natural number, then the convolution power is defined by where * denotes the convolution… …   Wikipedia

• Convolution of probability distributions — The convolution of probability distributions arises in probability theory and statistics as the operation in terms of probability distributions that corresponds to the addition of independent random variables and, by extension, to forming linear… …   Wikipedia

• Convolution (computer science) — In computer science, specifically formal languages, convolution (sometimes referred to as zip) is a function which maps a tuple of sequences into a sequence of tuples. Example The convolution of and, fish, be is Definition Let Σ be an alphabet, # …   Wikipedia

• Function representation — In computer graphics the function representation (FRep [Shape Modeling and Computer Graphics with Real Functions, [http://www.hyperfun.org/F rep.html FRep Home Page] ] or F Rep) is used in solid modeling. FRep was introduced in Function… …   Wikipedia

• Dirac delta function — Schematic representation of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is usually used to specify the value of any multiplicative constant, which will give the area under the function. The other convention… …   Wikipedia

• Arithmetic function — In number theory, an arithmetic (or arithmetical) function is a real or complex valued function ƒ(n) defined on the set of natural numbers (i.e. positive integers) that expresses some arithmetical property of n. [1] An example of an arithmetic… …   Wikipedia

• Dirichlet convolution — In mathematics, the Dirichlet convolution is a binary operation defined for arithmetic functions; it is important in number theory. It was developed by Johann Peter Gustav Lejeune Dirichlet, a German mathematician. Contents 1 Definition 2… …   Wikipedia

• Circular convolution — The circular convolution, also known as cyclic convolution, of two aperiodic functions occurs when one of them is convolved in the normal way with a periodic summation of the other function.  That situation arises in the context of the… …   Wikipedia

• Multiplicative function — Outside number theory, the term multiplicative function is usually used for completely multiplicative functions. This article discusses number theoretic multiplicative functions. In number theory, a multiplicative function is an arithmetic… …   Wikipedia