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A Fast Mellin and Scale Transform

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Abstract

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.

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Correspondence to Antonio De Sena.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://doi.org/creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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De Sena, A., Rocchesso, D. A Fast Mellin and Scale Transform. EURASIP J. Adv. Signal Process. 2007, 089170 (2007) doi:10.1155/2007/89170

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Keywords

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