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General formulation of shift and delta operator based 2-D VLSI filter structures without global broadcast and incorporation of the symmetry

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Abstract

Having local data communication (without global broadcast of signals) among the elements is important in very large scale integration (VLSI) designs. Recently, 2-D systolic digital filter architectures were presented which eliminated the global broadcast of the input and output signals. In this paper a generalized formulation is presented that allows the derivation of various new 2-D VLSI filter structures, without global broadcast, using different 1-D filter sub-blocks and different interconnecting frameworks. The 1-D sub-blocks in z-domain are represented by general digital two-pair networks which consist of direct-form or lattice-type FIR filters in one of the frequency variables. Then, by applying the sub-blocks in various frameworks, 2-D structures realizing different transfer functions are easily obtained. As delta discrete-time operator based 1-D and 2-D digital filters (in \(\gamma \)-domain) were shown to offer better numerical accuracy and lower coefficient sensitivity in narrow-band filter designs when compared to the traditional shift-operator formulation we have covered both the conventional z-domain filters as well as delta discrete-time operator based filters. Structures realizing general 2-D IIR (both z- and \(\gamma \)-domains) and FIR transfer functions (z-domain only) are presented. As symmetry in the frequency response reduces the complexity of the design, IIR transfer functions with separable denominators, and transfer functions with quadrantal magnitude symmetry are also presented. The separable denominator frameworks are needed for quadrantal symmetry structures to guarantee BIBO stability and thus presented for both the operators. Some limitations of having exact symmetry with separable 1-D denominator factors are also discussed.

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Acknowledgments

The authors would like to express their sincere thanks to the EIC and his Editorial board members for their kind suggestions to improve the quality of this paper.

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Authors and Affiliations

  1. Department of Electrical Engineering, California State University Long Beach, Long Beach, CA, USA

    I.-Hung Khoo & Hari C. Reddy

  2. College of Computer Science, National Chiao-Tung University, HsinChu City, Taiwan

    Hari C. Reddy

  3. Department of Computer Science, National Chiao-Tung University, HsinChu City, Taiwan

    Lan-Da Van & Chin-Teng Lin

Authors
  1. I.-Hung Khoo
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  2. Hari C. Reddy
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  3. Lan-Da Van
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  4. Chin-Teng Lin
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Corresponding author

Correspondence to I.-Hung Khoo.

Additional information

This paper is dedicated to Professor Eli Jury on the occasion of his 90th birthday this year (2013). Professor Jury has been a pioneer in modern digital control and multidimensional systems. It was Professor Jury who has encouraged the second author (Hari C. Reddy) to use delta discrete time operator in the study of 1-D and M-D systems and filters. This was followed by the doctoral dissertation of the first author (I-Hung Khoo) on the topic at the University of California, Irvine in 2002. This is a simple token of appreciation to Professor Jury for his mentoring, friendship and guidance.

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Khoo, IH., Reddy, H.C., Van, LD. et al. General formulation of shift and delta operator based 2-D VLSI filter structures without global broadcast and incorporation of the symmetry. Multidim Syst Sign Process 25, 795–828 (2014). https://doi.org/10.1007/s11045-013-0232-9

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  • DOI: https://doi.org/10.1007/s11045-013-0232-9

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