Skip to main content
Log in

Mapping 3-D IIR digital filter onto systolic arrays

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

We present here an efficient systolic implementation for 3-D IIR digital filters. The systolic implementation is obtained by using an algebraic mapping technique. This new mapping technique gives us the choice to mix pipelined variables and broadcast variables. We also determine, through the mapping method, the buffer sizes, the direction of variables propagations and the data feeding and extracting points. The resultant systolic array implementation is a modular structure composed of 2-D filter modules connected by simple buffers. This new systolic implementation is regular, modular and amenable to VLSI Implementation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. A. Sid-Ahmed “A Systolic Realization of 2-D,”IEEE Trans. Acoust. Speech, Signal Processing, vol. ASSP-37, 1989, pp. 560–565.

    Google Scholar 

  2. N. R. Shanbhag, “An Improved Systolic Architecture for 2-D Digital Filters,”IEEE Trans. Signal Processing, vol. 39, 1991, pp. 1195–1202.

    Article  Google Scholar 

  3. S. Sunder,VLSI Implementation of Digital Filters, Ph.D Dissertation, University of Victoria, B.C., Canada, 1992.

    Google Scholar 

  4. R. A. Derbin, L. Carpenter, and P. Hanrahan, “Volume Rendering,”Computer Graphics (Proc. Siggraph 88), vol. 22, 1988, pp. 65–74.

    Google Scholar 

  5. S. Y. Kung,VLSI Array Processors, Prentice Hall, 1988.

  6. H. T. Kung, “Why Systolic Architectures,”IEEE Computer mag., vol. 15, 1982, pp. 37–46.

    Google Scholar 

  7. S. Sunder, F. El-Guibaly, and A. Antoniou, “Systolic Implementation of Digital Filters,”Multidimensional Systems and Signal Processing, 1992, pp. 63–78.

  8. P. R. Capello and K. Steiglitz, “Digital Signal Processing Applications of Systolic Algorithms,” inVLSI systems and computations, H. T. Kung, B. Sproull and G. Steel editors, Computer Science Press, 1981, pp. 245–254.

  9. C. E. Leirseron and J. B. Saxe, “Optimizing Synchronous Systems,”Proc. IEEE 22nd Annual Symp. on Foundations of Computer Science, 1981, pp. 23–36.

  10. J. P. Charlier, M. Vanbegin, and P. van Dooren, “Systolic Algorithms for Digital Signal Processing,”Philips J. Res., vol. 43, 1988, pp. 268–290.

    Google Scholar 

  11. P. Quinton, “Automatic Synthesis of Systolic Arrays from Uniform Recurrent Equations,” inProc. 11-th Intl. Symp. on Computer Architecture, Ann Arbor, MI, 1984, pp. 208–214.

  12. P. Quinton, “The Systematic Design of Systolic Arrays,”Tech. Rep. 216, Institute National de Recherche en Informatique et en Automatique INRIA, July 1983.

  13. D. Moldovan, “On the Design of Algorithms for VLSI Systolic Arrays,”Proc. IEEE, vol. 71, 1983, pp. 113–120.

    Google Scholar 

  14. W. M. Miranker and A. Winkler, “Space-time Representation of Computational Structures,”Computing, vol. 32, 1984, pp. 93–114.

    Google Scholar 

  15. S. K. Rao,Regular Iterative Algorithms and Their Implementation on Processor Arrays, Ph.D. Thesis, Stanford, 1985.

  16. M. S. Lam and J. A. Mostow, “A Transformational Model of VLSI Systolic Design,”IEEE Computer mag., vol. 18, 1985, pp. 42–52.

    Google Scholar 

  17. J. M. Delosme and I. C. F. Ipsen, “Efficient Systolic Arrays for the Solution of Toeplitz Systems: An Illustration of a Methodology for the Construction of Systolic Architectures for VLSI,” inInternational Workshop on Systolic Arrays, W. Moore, A. McCabe, and R. Urquhart, editors, Adam Hilger, University of Oxford, UK., 1986.

    Google Scholar 

  18. H. V. Jagadish, S. K. Rao, and T. Kailath, “Array Architectures for Iterative Algorithms,”Proc. IEEE, vol. 75, 1987, pp. 1304–1321.

    Google Scholar 

  19. P. Quinton and V. Van Dongen, “The Mapping of Linear Recurrence Equations on Regular Arrays,”Technical report 485, Publication Interne IRISA, pp. 37, July, 1989.

  20. Yoav Yaacoby and P.R. Cappello, “Scheduling a System of Nonsingular Affine Recurrence Equations onto a Processor Array,”J. VLSI Signal Processing, vol. 1, 1989, pp. 115–125.

    Google Scholar 

  21. S. V. Rajopadhye, “Synthesizing Systolic Arrays with Control Signals from Recurrence Equations,”Distributed Computing, vol. 3, 1989, pp. 88–105.

    Article  Google Scholar 

  22. F. El-Guibaly, A. Tawfik, W.-S. Lu, and E. Abdel-Raheem, “Synthesizing Systolic Arrays: Basic Tools,”Technical Report VMC 92–2, ECE Dept., University of Victoria, 1992.

  23. R. M. Karp, R. E. Miller, and S. Winograd, “The Organization of Computations for Uniform Recurrence Equations,”J. Assoc. Computing Machinery, vol. 14, 1967, pp. 563–590.

    Google Scholar 

  24. G. L. Nemhause and L. A. Wolsey,Integer and Combinatorial Programming, John Wiley, 1988.

  25. F. P. Preparata and M. I. Shamos,Computational Geometry, New York: Springer-Verlag, 1985.

    Google Scholar 

  26. A. Schrijver,Theory of Linear and Integer Programming, New York: John Wiley, 1986.

    Google Scholar 

  27. Convex Analysis, Princeton University Press, 1970.

  28. D. S. Watkins,Fundamentals of Matrix Computations, New York: John Wiley, 1991.

    Google Scholar 

  29. L. L. Scharf,Statistical Signal Processing, Reading, MA: Addison-Wesley, 1991.

    Google Scholar 

  30. G. H. Golub and C. F. Van Loan,Matrix Computations, Baltimore, Maryland: Johns Hopkins University Press, 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to F. El-Guibaly.

Rights and permissions

Reprints and permissions

About this article

Cite this article

El-Guibaly, F., Tawfik, A. Mapping 3-D IIR digital filter onto systolic arrays. Multidim Syst Sign Process 7, 7–26 (1996). https://doi.org/10.1007/BF02106104

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02106104

Key Words

Navigation