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The transformation of a sequence a_1, a_2, ... with a_n=sum_(d|n)b_d (1) into the sequence b_1, b_2, ... via the Möbius inversion formula, b_n=sum_(d|n)mu(n/d)a_d. (2) The ...

There are three flavors of Hough transform. The first (original) was used to detect straight lines in bubble chamber images. The technique parameterizes pattern space, then ...

Let the two-dimensional cylinder function be defined by f(x,y)={1 for r<R; 0 for r>R. (1) Then the Radon transform is given by ...

The integral transform defined by g(x)=int_1^inftyt^(1/4-nu/2)(t-1)^(1/4-nu/2)P_(-1/2+ix)^(nu-1/2)(2t-1)f(t)dt (Samko et al. 1993, p. 761) or ...

Let f(t) and g(t) be arbitrary functions of time t with Fourier transforms. Take f(t) = F_nu^(-1)[F(nu)](t)=int_(-infty)^inftyF(nu)e^(2piinut)dnu (1) g(t) = ...

The structure factor S_Gamma of a discrete set Gamma is the Fourier transform of delta-scatterers of equal strengths on all points of Gamma, S_Gamma(k)=intsum_(x in ...

The even impulse pair is the Fourier transform of cos(pik), AdjustmentBox[I, BoxMargins -> {{0.13913, -0.13913}, {-0.5, 0.5}}]I(x)=1/2delta(x+1/2)+1/2delta(x-1/2). (1) It ...

Any discrete finite wavelet transform can be represented as a matrix, and such a wavelet matrix can be computed in O(n) steps, compared to O(nlgn) for the Fourier matrix, ...

For a given signal, the power spectrum gives a plot of the portion of a signal's power (energy per unit time) falling within given frequency bins. The most common way of ...

Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. The term "discrete mathematics" is therefore used in ...