
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
M.J. Corinthios, "Optimal Parallel and Pipelined Processing Through a New Class of Matrices with Application to Generalized Spectral Analysis," IEEE Transactions on Computers, vol. 43, no. 4, pp. 443459, April, 1994.  
BibTex  x  
@article{ 10.1109/12.278482, author = {M.J. Corinthios}, title = {Optimal Parallel and Pipelined Processing Through a New Class of Matrices with Application to Generalized Spectral Analysis}, journal ={IEEE Transactions on Computers}, volume = {43}, number = {4}, issn = {00189340}, year = {1994}, pages = {443459}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.278482}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Optimal Parallel and Pipelined Processing Through a New Class of Matrices with Application to Generalized Spectral Analysis IS  4 SN  00189340 SP443 EP459 EPD  443459 A1  M.J. Corinthios, PY  1994 KW  pipeline processing; parallel architectures; matrix algebra; pipelined processing; matrices; parallel processing; generalbase matrices; sampling matrices; computer architecture; Poles; zeros; pointers; spans; algorithm parameters; parallel pipelined processors; memory topology; access uniformity; shuffle complexity; algorithm factorizations; pipelined architecture; matrix theory; generalized perfect shuffle; Chrestenson generalized Walsh transform; generalized spectral analysis. VL  43 JA  IEEE Transactions on Computers ER   
A new class of generalbase matrices, named sampling matrices, which are meant to bridge the gap between algorithmic description and computer architecture is proposed. "Poles," "zeros," "pointers," and "spans" are among the terms introduced to characterize properties of this class of matrices. A formalism for the decomposition of a general matrix in terms of generalbase sampling matrices is proposed. "Span" matrices are introduced to measure the dependence of a matrix span on algorithm parameters and, among others, the interaction between this class of matrices and the generalbase perfect shuffle permutation matrix previously introduced. A classification of generalbase parallel "recirculant" and parallel pipelined processors based on memory topology, access uniformity and shuffle complexity is proposed. The matrix formalism is then used to guide the search for algorithm factorizations leading to optimal parallel and pipelined processor architecture.
[1] Y.Y. Jou and J. A. Abraham, "Fault tolerant FFT networks,"IEEE Trans. Comput., vol. 37, no. 5, May 1988, pp. 548561.
[2] H. K. Nagpal, G. A. Jullien, and W. C. Miller, "Processor architectures for twodimensional convolvers using a single multiplexed computational element with finite field arithmetic,"IEEE Trans. Comput., vol. C32, no. 11, pp. 9891001, Nov, 1983.
[3] G. F. Taylor, R. H. Steinvorth, and J. F. McDonald, "An architecture for a video rate twodimensional fast fourier transform processor,"IEEE Trans. Comput, vol. 37, no. 9, pp. 11451151, Sept. 1988.
[4] C. Moraga, "Design of a multiplevalued systolic system for the computation of the chrestenson spectrum,"IEEE Trans. Comput., vol. C35, no. 2, pp. 183188, Feb. 1986.
[5] C. F. Chen and W. K. Leung, "Algorithms for converting sequency, dyadic and Hadamard ordered Walsh functions,"Math and Comput. in Sim., vol. 27, pp. 471478, 1985.
[6] P. M. Grant and J. H. Collins, "Introduction to electronic warfare,"IEEE Proc., vol. 129, pt. F, no. 3, pp. 113132, June 1982.
[7] T. D. Roziner, M. G. Karpovsky, and L. A. Trachtenberg, "Fast Fourier transforms over finite groups by multiprocessor systems,"IEEE Trans. Accoustics, Speech&Signal Processing, vol. 38, no. 2, pp. 226240, Feb. 1990.
[8] C. Moraga and K. Seseke, "The Chrestenson transform in pattern analysis," inSpectral Techniques and Fault Detection, M. Karpovsky, Ed. New York: Academic Press, 1985.
[9] M. J. Corinthios, "3D cellular arrays for parallel/cascade image/signal processing," inSpectral Techniques and Fault Detection, M. Karpovsky, Ed. New York: Academic Press, 1985.
[10] M. J. Corinthios, "Pipeline constant geometry algorithms and processors for the generalized spectral analysis of images," presented at theProc. IMACSIFAC Symp. Parallel and Distrib. ComputingP.D. COM'91, Corfu, Greece, June 2328, 1991.
[11] H. E. Chrestenson, "A class of generalized Walsh functions,"Pacific J. of Math., vol. 5, pp. 1731, 1955.
[12] M. J. Corinthios, "The design of a class of fast Fourier transform computers,"IEEE Trans. Comput., vol. C20, pp. 617623, June 1971.
[13] H. Sloate, "Matrix representations for sorting and the fast Fourier transform,"IEEE Trans. Circuits&Syst., vol. CAS21, no. 1, pp. 109116, Jan. 1974.
[14] N. A. Alexandridis, "Relations among sequency, axis symmetry and period of Walsh functions,"IEEE Trans. Inform. Theory, pp. 495497, July 1971.
[15] Y. A. Geadah and M. J. Corinthios, "Natural, dyadic and sequency algorithms and processors for the WalshHadamard transform,"IEEE Trans. Comput., vol. C26, no. 5, pp. 435442, May 1977.
[16] M. J. Corinthios, K. C. Smith, and J. L. Yen, "A parallel radix 4 FFT computer,"IEEE Trans. Comput., vol. C24, no. 1, pp. 8092, Jan. 1975.
[17] M. J. Corinthios, Y. Geadah, and K. C. Smith, "Generalized spectral analysis algorithms and processors," inProc. Int. Conf. Inform. Sci. Syst., Patras, Greece, Aug. 1924, 1976, pp. 257262.