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A fast Mellin transformation. (English) Zbl 0557.65085

A fast algorithm of the Mellin transform is proposed. Its process consists of two steps: (1) Discrete Fourier Transformation (DFT) based on sampling through a symmetric window, (2) Multiplication of DFT coefficients by pre-calculated Mellin transforms of the Fourier basis functions. The pre-calculation is related to the incomplete gamma function. Thus, the discrete Mellin transform is implemented by \(N^ 2\) multiplications.
Reviewer: Y.Kobayashi

MSC:

65R10 Numerical methods for integral transforms
65T40 Numerical methods for trigonometric approximation and interpolation
44A15 Special integral transforms (Legendre, Hilbert, etc.)
65Yxx Computer aspects of numerical algorithms
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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