Algorithms for the Fast Computation of PWL and PHL Transforms
In this paper, the construction of fast algorithms for the computation of Periodic Walsh Piecewise-Linear PWL transform and the Periodic Haar Piecewise-Linear PHL transform will be presented. Algorithms for the computation of the inverse transforms are also proposed. The matrix equation of the PWL and PHL transforms are introduced. Comparison of the computational requirements for the periodic piecewise-linear transforms and other orthogonal transforms shows that the periodic piecewise-linear transforms require less number of operations than some orthogonal transforms such as the Fourier, Walsh and the Discrete Cosine transforms.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082785Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1355
 Brigham E. O. , The Fast Fourier Transform, Prentice-Hall, Englewood Cliffs, NJ, 1974.
 Elliot D., Rao K. R. , Fast Transforms : Algoritms, Analysis, Applications, Academic Press, 1982
 Dziech A, Kwater M "Fast Transforms Based on Piecewise-Linear Functions" IEEE Workshop on ASSP, Beijing 1986.
 A. Dziech, F. Belgassem, S. Aboukres, A. Nabout "Periodic Haar Piecewise Linear Transform" Proceedings of the CESA'96 IMACS/IEEE-SMC Multiconference, Lile-France, July 1996, pp.157-160.
 Dziech A, Pardyka I "Shape Approximation using Fast Piecewise Linear Transforms" AMSE Review, vol. 8, No.1,1988, pp.19-30.
 Dziech A, Belgassem F, Ammar K, B. Bushofa " One-dimensional Haar Piecewise Linear Series and Transform" Proceedings of the 32nd. Science Week, University of Damascus, Damascus, Syria, Nov. 1992, pp.515-522.
 Dziech A , Pardyka I "Shape descriptors based on Fast Piecewise Linear Transforms" AMSE Int conference on Modelling and Simulation, Karlsrhe,1987.
 Paul C R, Koch R W "On Piecewise-Linear Basis Functions and Piecewise-Linear Signal Expansion" IEEE Trans. Acoust. Speech Signal Process.,ASSP-22, No.4 , Aug.1974, pp.263-268.
 Lee. P, Huang F "Restructured Recursive DCT and DST Algorithms" IEEE Trans. on Signal Processing, vol. 42, No.7, July 1994, pp 1600- 1609.