Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A Fast Mellin and Scale Transform Antonio De Sena1 and Davide Rocchesso2 | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2007 Article ID 89170 9 pages doi 2007 89170 Research Article A Fast Mellin and Scale Transform Antonio De Sena1 and Davide Rocchesso2 1 Dipartimento di Informatica Universita di Verona Strada Le Grazie 15-37134 Verona Italy 2 Dipartimento di Arti e Disegno Industriale Universita Iuav di Venezia Dorsoduro 2206 30123 Venezia Italy Received 24 August 2006 Revised 30 December 2006 Accepted 5 March 2007 Recommended by Jar-Ferr Kevin Yang A fast algorithm for the discrete-scale and S-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 S-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. Copyright 2007 A. De Sena and D. Rocchesso. 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. 1. INTRODUCTION The Mellin transform and the particular version called scale transform can represent a signal in terms of scale. The scale can be interpreted similarly to frequency as a physical attribute of signals. The proposed fast subquadratic implementation allows this transform to be used in practical applications. The algorithm can compute the Mellin transform 00 Mf p j0 f t tp-1dt 1 in the complex variable p - jc S with S V R fixed parameter and c e R independent variable. We call this family of transforms the S-Mellin transform. It is indeed a restriction of the Mellin transform as the real
