A Fast Mellin and Scale Transform. (30th April 2007) - De Sena De Sena, Antonio Antonio; Rocchesso Rocchesso, Davide Davide
Abstract : A fast algorithm for the discrete-scale (andβ -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.