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The integral transform (Kf)(x)=Gamma(p)int_0^infty(x+t)^(-p)f(t)dt. Note the lower limit of 0, not -infty as implied in Samko et al. (1993, p. 23, eqn. 1.101).

The following integral transform relationship, known as the Abel transform, exists between two functions f(x) and g(t) for 0<alpha<1, f(x) = int_0^x(g(t)dt)/((x-t)^alpha) (1) ...

A two-sided (doubly infinite) Z-Transform, Z^((2))[{a_n}_(n=-infty)^infty](z)=sum_(n=-infty)^infty(a_n)/(z^n) (Zwillinger 1996; Krantz 1999, p. 214). The bilateral transform ...

The exponential transform is the transformation of a sequence a_1, a_2, ... into a sequence b_1, b_2, ... according to the equation ...

The fast Fourier transform (FFT) is a discrete Fourier transform algorithm which reduces the number of computations needed for N points from 2N^2 to 2NlgN, where lg is the ...

The Hilbert transform (and its inverse) are the integral transform g(y) = H[f(x)]=1/piPVint_(-infty)^infty(f(x)dx)/(x-y) (1) f(x) = ...

The Radon inverse transform is an integral transform that has found widespread application in the reconstruction of images from medical CT scans. The Radon and inverse Radon ...

If, after constructing a difference table, no clear pattern emerges, turn the paper through an angle of 60 degrees and compute a new table. If necessary, repeat the process. ...

The Radon transform is an integral transform whose inverse is used to reconstruct images from medical CT scans. A technique for using Radon transforms to reconstruct a map of ...

A rotation combined with an expansion or geometric contraction.