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  • Research Article
  • Open Access

A Fast Mellin and Scale Transform

EURASIP Journal on Advances in Signal Processing20072007:089170

  • Received: 24 August 2006
  • Accepted: 5 March 2007
  • Published:


A fast algorithm for the discrete-scale (and -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, -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.


  • Fourier
  • Fourier Transform
  • Information Technology
  • Computational Complexity
  • Quantum Information

Authors’ Affiliations

Dipartimento di Informatica, Università di Verona, Strada Le Grazie, Verona, 15-37134, Italy
Dipartimento di Arti e Disegno Industriale, Università Iuav di Venezia, Dorsoduro 2206, Venezia, 30123, Italy


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© A. De Sena and D. Rocchesso. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.