research-article

Minimum Complexity FIR Filters and Sparse Systolic Arrays

Authors:

Leonard A. Ferrari,

P. V. SankarAuthors Info & Claims

IEEE Transactions on Computers, Volume 37, Issue 6

Pages 760 - 764

https://doi.org/10.1109/12.2219

Published: 01 June 1988 Publication History

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Abstract

The properties of B-spline approximation and the integral/derivative properties of convolution lead to efficient algorithms for the implementation of multidimensional FIR filters. The implementations are of minimum time complexity under the Nyquist criterion. The algorithm can easily be implemented using a sparse systolic array architecture. The resulting B-spline convolvers have much lower circuit complexity than systolic architectures based on conventional convolution algorithms. A two-dimensional hardware implementation based on simplifications of current architectures is presented.

References

[1]

{1} J. Seidman, "Some practical applications of digital filtering in image processing," Proc. Comput. Image Proc. Recognition, vol. 2, Aug. 1971.

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[2]

{2} L. A. Ferrari, "Recursive binary valued image filters," Ph.D. dissertation, Dep. Elec. Eng., Univ. California, Irvine, 1980.

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[3]

{3} L. A. Ferrari and J. Sklansky, "A fast recursive algorithm for binary valued two dimensional filters," Comput. Vision, Graphics, Image Processing, vol. 26, pp. 292-302, 1984.

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[4]

{4} L. A. Ferrari and J. Sklansky, "A note of Duhamel's theorem and the principle of inclusion and exclusion," Comput. Vision, Graphics, Image Processing, vol. 29, pp. 358-360, 1985.

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[5]

{5} L. A. Ferrari, P. V. Sankar, S. Shinnaka, and J. Sklansky, "Recursive algorithms for implementing digital image filters," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, pp. 461-466, May 1987.

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[6]

{6} L. Ferrari, P. V. Sankar, J. Sklansky, and S. Leeman, "Efficient digital filters using B-spline approximations," Comput. Vision, Graphics, Image Processing, vol. 35, pp. 152-165, 1986.

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{7} H. T. Kung, "Why systolic architectures?," Computer, vol. 15, pp. 37-46, Jan. 1982.

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{8} L. R. Rabiner and R. W. Schafer, Digital Processing of Speech Signals. Englewood Cliffs, NJ: Prentice-Hall, 1978.

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{9} H. T. Kung and R. L. Picard, "One-dimensional systolic arrays for multidimensional convolution and resampling," in VLSI for Pattern Recognition and Image Processing, K. S. Fu, Ed. Berlin, Germany: Springer-Verlag, 1984.

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Index Terms

Minimum Complexity FIR Filters and Sparse Systolic Arrays
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
  2. Computer graphics
    1. Image manipulation
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis

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cover image IEEE Transactions on Computers

IEEE Transactions on Computers Volume 37, Issue 6

June 1988

136 pages

ISSN:0018-9340

Editor:
Bruce D. Shriver

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IEEE Computer Society

United States

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Published: 01 June 1988

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Design of two-channel linear phase IIR PRQMF banks based on the approximation of FIR filters

Hybrid structures for low-complexity variable fractional-delay FIR filters

Low power realization of FIR filters using multirate architectures

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