A fast Mellin and scale transform

Authors:
Antonio De Sena;Davide Rocchesso
Affiliations:
Dipartimento di Informatica, Università di Verona, Strada Le Grazie, Verona, Italy;Dipartimento di Arti e Disegno Industriale, Università Iuav di Venezia, Dorsoduro, Venezia, Italy
Venue:
EURASIP Journal on Applied Signal Processing
Year:
2007

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Abstract

A fast algorithm for the discrete-scale (and β-Mellin) transform is proposed. It performs a discrete-time discrete-scale approximation of the continuous-time transform, with subquadratic asymptotic complexity. The algorithm is based on a well-known relation between the Mellin and Fourier transforms, and it is practical and accurate. The paper gives some theoretical background on the Mellin, β-Mellin, and scale transforms. Then the algorithm is presented and analyzed in terms of computational complexity and precision. The effects of different interpolation procedures used in the algorithm are discussed.