Skip to main content
SpringerLink
Log in

Asymptotic behavior of block floating-point digital filters

  • Published:
Circuits, Systems and Signal Processing Aims and scope Submit manuscript

Abstract

The asymptotic behavior of block floating-point and floating-point digital filters is analyzed. As a result, mantissa wordlength conditions are derived guaranteeing the absence of limit cycles in the regular dynamic range. Explicitly, the requirements are given for block floating-point state space filters with different quantization formats. Although these conditions are only sufficient, examples are given in which they are also necessary. In most cases the conditions are easily satisfied.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Bauer, Absolute error bounds for block floating-point direct form digital filters,IEEE Trans. Signal Proc., 43(8):1994–1996, Aug. 1995.

    Article  Google Scholar 

  2. P. Bauer and K. Ralev, A limit cycle suppressing arithmetic format for digital filters,IEEE Trans. Circ. Syst. I, to appear.

  3. P. Bauer and J. Wang, Limit cycle bounds for floating-point implementation of second order recursive digital filters,IEEE Trans. Circ. Syst., 40(8):493–501, Aug. 1993.

    Article  MATH  Google Scholar 

  4. S. Boyd and J. Doyle, Comparison of peak and RMS gains for discrete-time systems,Syst. Contr. Letters, 9(1):1–5, June 1987.

    Article  MATH  MathSciNet  Google Scholar 

  5. K. Kalliojärvi and J. Astola, Roundoff errors in block-floating-point systems,IEEE Trans. Signal Proc., 44:783–790, Apr. 1996.

    Article  Google Scholar 

  6. T. Kaneko, Floating point oscillations in floating-point digital filters,IEEE Trans. Audio Electroacoust., AU-21(2):100–106, Apr. 1973.

    Article  Google Scholar 

  7. T. Laakso and B. Zeng, Limit cycles in floating-point implementations of recursive filters—A review, inProc. ISCAS, pages 1816–1819, San Diego, CA, May 1992.

  8. T. Laakso, B. Zeng, I. Hartimo, and Y. Neuvo, Elimination of limit cycles in floating-point implementations of recursive digital filters,IEEE Trans. Circ. Syst., II, 41(4):308–312, Apr. 1994.

    Article  Google Scholar 

  9. J. L. Long and T. N. Trick, An absolute bound on limit cycles due to roundoff errors in digital filters,IEEE Trans. Audio Electroacoust., AU-21:27–30, Feb. 1973.

    Google Scholar 

  10. D. Mitra and J. R. Boddie, Limit cycles in floating-point digital filters, inProc. ISCAS, pages 374–377, Tokyo, Japan, 1979.

  11. A. V. Oppenheim, Realization of digital filters using block floating-point arithmetic,IEEE Trans. Audio Electroacoust., 18(2):130–136, June 1970.

    Article  Google Scholar 

  12. K. R. Ralev and P. H. Bauer, Asymptotic error bounds for block floating-point digital filters, inProc. 39th Midwest Symposium on Circuits and Systems, vol. 3, pages 1405–1408, Ames, IA, Aug. 1996.

  13. K. R. Ralev and P. H. Bauer, Asymptotic error bounds for floating-point digital filters, inProc. 3rd International Conference on Electronics, Circuits, and Systems, pages 1239–1242, Rodos, Greece, Oct. 1996.

  14. K. R. Ralev and P. H. Bauer, Implementation options for block floating-point digital filters, inProc. ICASSP-97, vol. 3, pages 2197–2200 Munich, Germany, 1997.

Download references

Author information

Authors and Affiliations

  1. Laboratory for Image and Signal Analysis Department of Electrical Engineering, Universit of Notre Dame, 46556, Notre Dame, Indiana

    Kamen Ralev & Peter Bauer

Authors
  1. Kamen Ralev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Bauer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ralev, K., Bauer, P. Asymptotic behavior of block floating-point digital filters. Circuits Systems and Signal Process 18, 75–84 (1999). https://doi.org/10.1007/BF01206546

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01206546

Keywords

Search

Navigation