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Review of Pseudo-Boolean Methods with Applications to Digital Filter Design

  • Suhash Chandra Dutta RoyEmail author
Chapter

Abstract

The technique of pseudo-Boolean methods which forms the basis for bivalent (0, 1) programming, has been used for many socio-economic and engineering problems in the past. In this chapter, we review these methods and discuss their applications to the quantized coefficient design of digital filters. Some other applications of these methods are also briefly described.

Keywords

Pseudo-Boolean methods Digital filters Coefficient quantization 

References

  1. 1.
    G.B. Dantzig, Linear Programming and Extensions (Princeton University Press, Princeton, New Jersey, 1963)CrossRefGoogle Scholar
  2. 2.
    P.L. Ivanescu, Pseudo-Boolean Programming and Applications (Springer, Berlin, 1965)CrossRefGoogle Scholar
  3. 3.
    P.L. Ivanescu, S. Rudeanu, Pseudo-Boolean Methods for Bivalent Programing (Springer, Berlin, 1966)CrossRefGoogle Scholar
  4. 4.
    P.L. Hammer, S. Rudeanu, Boolean Methods in Operations Research and Related Areas (Springer, New York, 1968)CrossRefGoogle Scholar
  5. 5.
    T.L. Saaty, Optimization in Integers and Related External Problems (McGraw-Hill, New York, 1970)Google Scholar
  6. 6.
    R.K. Patney, S.C. Dutta Roy, Design of IIR filters using pseudo-Boolean methods, in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (1978)Google Scholar
  7. 7.
    R.K. Patney, Roundoff Noise and Co-efficient Sensitivity in Digital Filters. PhD thesis, IIT Delhi, 1978Google Scholar
  8. 8.
    R.K. Patney, S.C. Dutta Roy, Design of linear phase FIR filters using pseudo-Boolean methods. IEEE Trans. CAS-26, 4, 55–260 (1979)Google Scholar
  9. 9.
    R.K. Patney, S.C. Dutta Roy, A modified pseudo-Boolean method for quantized coefficient design of IIR filters, in Proceedings of the ICASSP (1979)Google Scholar
  10. 10.
    A.V. Oppenheim, R.W. Schafer, Digital Signal Processing (Prentice-Hall, New Jersey, 1975)zbMATHGoogle Scholar
  11. 11.
    L.R. Rabiner, B. Gold, Theory and Applications of Digital Signal Processing (Prentice-Hall, New Jersey, 1975)Google Scholar
  12. 12.
    P. Chambon, A. Desblache, Integer co-efficient optimization of digital filters, in Proceedings of the IEEE International Symposium on Circuits and Systems (1976), pp. 461–464Google Scholar
  13. 13.
    E. Avenhaus, On the design of digital filters with co-efficients of finite word lengths. IEEE Trans. AU-20, 356–373 (1972)Google Scholar
  14. 14.
    E. Avenhaus, W. Schussler, On the approximation problem in the design of digital filters with limited world length. Arch. Elek. Ubertragung. 24, 571–572 (1970)Google Scholar
  15. 15.
    K. Steiglitz, Designing short word recursive digital filters, in Proceedings 9th Annual Allerton Conference on Circuit and System (1971), pp. 778–788Google Scholar
  16. 16.
    R.E. Crochiere, A new statistical approach to the coefficient word length problem for digital filters. IEEE Trans. CAS-22, 190–196 (1975)Google Scholar
  17. 17.
    F. Berglez, Digital filter design with co-efficients of reduced wod length, in Proceedings of the IEEE Symposium on Circuits and Systems (1977), pp. 52–55Google Scholar
  18. 18.
    C. Charalambous, M.J. Best, Optimization of recursive digital filters with finite word length. IEEE Trans. ASSP- 22, 424–431 (1974)Google Scholar
  19. 19.
    M. Suk, S.K. Mitra, Computer-aided design of digital filters with finite word length. IEEE Trans. AU-20, 356–373 (1972)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Indian Institute of Technology DelhiNew DelhiIndia

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