- Research Article
- Open Access
A Fast Mellin and Scale Transform
EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 089170 (2007)
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.
Casasent D, Psaltis D: Position, rotation, and scale invariant optical correlation. Applied Optics 1976,15(7):1795-1799. 10.1364/AO.15.001795
Casasent D, Psaltis D: New optical transforms for pattern recognition. Proceedings of the IEEE 1977,65(1):77-84.
Derrode S, Ghorbel F: Robust and efficient Fourier-Mellin transform approximations for gray-level image reconstruction and complete invariant description. Computer Vision and Image Understanding 2001,83(1):57-78. 10.1006/cviu.2001.0922
Derrode S, Ghorbel F: Shape analysis and symmetry detection in gray-level objects using the analytical Fourier-Mellin representation. Signal Processing 2004,84(1):25-39. 10.1016/j.sigpro.2003.07.006
Bertand J, Bertrand P, Ovarlez JP: The Mellin transform. In The Transforms and Applications Handbook, The Electrical Engineering Handbook. Edited by: Poularikas AD. CRC Press LLC, Boca Raton, Fla, USA; 1995:11-1-11-68.
Bertrand J, Bertrand P, Ovarlez JP: Discrete Mellin transform for signal analysis. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '90), April 1990, Albuquerque, NM, USA 3: 1603–1606.
Ovarlez JP, Bertrand J, Bertrand P: Computation of affine time-frequency distributions using the fast Mellin transform. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '92), March 1992, San Francisco, Calif, USA 5: 117–120.
Cohen L: The scale representation. IEEE Transactions on Signal Processing 1993,41(12):3275-3292. 10.1109/78.258073
De Sena A, Rocchesso D: A fast Mellin transform with applications in DAFx. Proceedings of the 7th International Conference on Digital Audio Effects (DAFx '04), October 2004, Napoli, Italy 65–69.
Irino T, Patterson RD: Segregating information about the size and shape of the vocal tract using a time-domain auditory model: the stabilised wavelet-Mellin transform. Speech Communication 2002,36(3-4):181-203. 10.1016/S0167-6393(00)00085-6
Sundaram H, Joshi SD, Bhatt RKP: Scale periodicity and its sampling theorem. IEEE Transactions on Signal Processing 1997,45(7):1862-1865. 10.1109/78.599961
Gerardi F: Application of Mellin and Hankel transforms to networks with time-varying parameters. IRE Transactions on Circuit Theory 1959,6(2):197-208.
Zalubas EJ, Williams WJ: Discrete scale transform for signal analysis. Proceedings of the 20th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '95), May 1995, Detroit, Mich, USA 3: 1557–1560.
Biner E, Akay O: Digital computation of the fractional Mellin transform. Proceedings of the 13th European Signal Processing Conference (EUSIPCO '05), September 2005, Antalya, Turkey
Smith JODigital Audio Resampling Home Page, January 2002
Schanze T: Sinc interpolation of discrete periodic signals. IEEE Transactions on Signal Processing 1995,43(6):1502-1503. 10.1109/78.388863
Candocia F, Principe JC: Comments on "sine interpolation of discrete periodic signals". IEEE Transactions on Signal Processing 1998,46(7):2044-2047. 10.1109/78.700979
Dooley SR, Nandi AK: Notes on the interpolation of discrete periodic signals using sinc function related approaches. IEEE Transactions on Signal Processing 2000,48(4):1201-1203. 10.1109/78.827555
Unser M: Splines: a perfect fit for signal and image processing. IEEE Signal Processing Magazine 1999,16(6):22-38. 10.1109/79.799930