Abstract
A new factorization for the slant matrix is developed. The structure of the proposed slant algorithm based on the new factorization is suitable for vector and parallel processing of one- and two-dimensional slant transforms. A unified approach to compute the Walsh-Hadamard, Haar, and slant transforms is presented. Multitasking with four processors is implemented to improve the speed performance of two-dimensional transforms. Simulation results on CRAY X-MP/48 using single-processor and multiprocessors are also included.
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
William K. Pratt, “Slant Transform Image Coding,”IEEE Trans. Comm., vol. Com-22, 1974.
M. El-Sharkawy, W. Tsang, and M. Aburdene, “Parallel Vector Processing of Multidimensional Orthogonal Transforms for Digital Signal Processing Applications,”Multidimensional Systems Signal Process., vol. 1, 1990, pp. 199–216.
M. El-Sharkawy, W. Tsang, and M. Aburdene, “Parallel Hadamard Transform with Transputers,”Int. J. Mini Microcomputers, vol. 12, 1990, pp. 20–24.
Harry C. Andrews,Computer Techniques in Image Processing, New York: Academic Press, 1970.
Bernard J. Fino, “A Unified Treatment of Discrete Fast Unitary Transforms,”SIAM J. Comput., vol. 6, 1977.
M. El-Sharkawy, W. Tsang, and M. Aburdene, “Vector Processing of Orthogonal Transforms for Digital Signal Processing Application,”Proc. 1989 Summer Computer Simulation Conf., 1989, pp. 203–210.
Paul N. Swarztrauber, “FFT Algorithms for Vector Computers,”Parallel Computing, 1984, pp. 45–63.
David G. Korn, “Computing the Fast Fourier Transform on a Vector Computer,”Math. Comp. vol. 33, 1979, pp. 977–992.
Ramesh C. Agarwal and James W. Cooley, “Vectorized Mixed Radix Discrete Fourier Transform Algorithms,”Proc. IEEE, vol. 75, 1987.
W.P. Petersen, “Vector FORTRAN for Numerical Problems on CRAY-1,”Comm. ACM, vol. 26, 1983.
Author information
Authors and Affiliations
Additional information
This work is supported in part by the National Science Foundation, Pittsburgh Supercomputing Center and by the PEW Science Education Program.
Rights and permissions
About this article
Cite this article
El-Sharkawy, M., Aburdene, M. & Tsang, W. Parallel vector multidimensional slant, Haar, and Walsh-Hadamard transforms. Multidim Syst Sign Process 3, 409–419 (1992). https://doi.org/10.1007/BF01940233
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01940233