convolution of two functions

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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 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 theorem — In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution is the pointwise product of Fourier transforms. In other words, convolution in one domain (e.g., time domain) equals point wise… …   Wikipedia

• Titchmarsh convolution theorem — The Titchmarsh convolution theoremis named after Edward Charles Titchmarsh.The theorem describes the properties of the support of the convolutionof two functions. Titchmarsh convolution theorem E.C. Titchmarshproved the following theorem in 1926 …   Wikipedia

• Logarithmic convolution — The scale convolution of two functions s(t) and r(t), also known as their logarithmic convolution is defined as the function : s * l r(t) = r * l s(t) = int 0^infty sleft(frac{t}{a} ight)r(a) frac{da}{a}when this quantity exists.ResultsThe… …   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

• 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

• Plancherel theorem for spherical functions — In mathematics, the Plancherel theorem for spherical functions is an important result in the representation theory of semisimple Lie groups, due in its final form to Harish Chandra. It is a natural generalisation in non commutative harmonic… …   Wikipedia

• Stirling numbers and exponential generating functions — The use of exponential generating functions or EGFs to study the properties of Stirling numbers is a classical exercise in combinatorics and possibly the canonical example of how symbolic combinatorics, the method that encapsulates the… …   Wikipedia

• Cross-correlation — In signal processing, cross correlation is a measure of similarity of two waveforms as a function of a time lag applied to one of them. This is also known as a sliding dot product or sliding inner product. It is commonly used for searching a long …   Wikipedia