Skip to main content
SpringerLink
Log in

Precision Analysis for an Optimal Parallel IIR Filter’s Implementation

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

Abstract

This paper addresses the precision analysis of filters in the parallel form framework. The precision analysis consists of determining suitable fractional bit-widths to set a tradeoff between resource consumption and computational accuracy. Although the stability of the parallel form is relatively better controlled than the related direct form, its bit-width optimization did not receive much consideration in the literature, despite its significant contribution to the optimization of the filter’s physical implementation. To carry out the needed bit-width optimization, we present two heuristics based on the Estimation of Distribution Algorithm, which falls within the category of probabilistic model-building genetic algorithm. The performance of the proposed approach is discussed, and compared to chosen benchmarks, the results show that our hardware implementations reduce the cost of the resulted circuits up to \(37\%\).

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Data Availability Statement

The data that support the findings of this study are the benchmarks provided in [36] which have been generated by the authors.

References

  1. A. Aggarwal, T.K. Rawat, D.K. Upadhyay, Optimal design of l 1-norm based iir digital differentiators and integrators using the bat algorithm. IET Signal Process. 11(1), 26–35 (2016)

    Article  Google Scholar 

  2. N. Agrawal, A. Kumar, V. Bajaj, A new method for designing of stable digital iir filter using hybrid method. Circuits Syst. Signal Process. 38(5), 2187–2226 (2019)

    Article  MathSciNet  Google Scholar 

  3. C.R. Babu, B.H. Kumar, S.L. Kumari Narava, A heuristic approach of designing parallel filter using an enriched pole placement technique. Order 6(4) (2018)

  4. S. Baluja, Population-based incremental learning. A method for integrating genetic search based function optimization and competitive learning. Tech. rep., Carnegie-Mellon Univ Pittsburgh Pa Dept Of Computer Science (1994)

  5. S. Baluja, R. Caruana, Removing the genetics from the standard genetic algorithm, in Machine Learning Proceedings 1995. (Elsevier, 1995), pp. 38–46

  6. S. Baluja, S. Davies, Combining multiple optimization runs with optimal dependency trees (Carnegie-mellon univ pittsburgh pa dept of computer science, Tech. rep., 1997)

  7. R. Bellal, E.S. Lamini, H. Belbachir, S. Tagzout, A. Belouchrani, Improved affine arithmetic-based precision analysis for polynomial function evaluation. IEEE Trans. Comput. 68(5), 702–712 (2018)

    Article  MathSciNet  Google Scholar 

  8. D. Boland, G.A. Constantinides, Bounding variable values and round-off effects using handelman representations. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 30(11), 1691–1704 (2011)

    Article  Google Scholar 

  9. G. Caffarena, C. Carreras, J.A. López, Á. Fernández, Sqnr estimation of fixed-point dsp algorithms. EURASIP J. Adv. Signal Process. 2010(1), 171027 (2010)

    Article  Google Scholar 

  10. A. Carini, V.J. Mathews, G.L. Sicuranza, Sufficient stability bounds for slowly varying direct-form recursive linear filters and their applications in adaptive iir filters. IEEE Trans. Signal Process. 47(9), 2561–2567 (1999)

    Article  Google Scholar 

  11. J.L.D. Comba, J. Stol, A ne arithmetic and its applications to computer graphics, in Proceedings of VI SIBGRAPI (Brazilian Symposium on Computer Graphics and Image Processing) (Citeseer, 1993), pp. 9–18

  12. G.A. Constantinides, P.Y. Cheung, W. Luk, The multiple wordlength paradigm, in The 9th Annual IEEE Symposium on Field-Programmable Custom Computing Machines (FCCM’01) (IEEE, 2001), pp. 51–60

  13. G.A. Constantinides, G.J. Woeginger, The complexity of multiple wordlength assignment. Appl. Math. Lett. 15(2), 137–140 (2002)

    Article  MathSciNet  Google Scholar 

  14. J. De Bonet, C. Isbell, P. Viola, Mimic: finding optima by estimating probability densities. Adv. Neural Inf. Process. Syst. 9, 424–430 (1996)

    Google Scholar 

  15. A. Fernandez-Vazquez, G.J. Dolecek, Generalized chebyshev filters for the design of iir filters and filter banks. Circuits Syst. Signal Process. 33(7), 2237–2250 (2014)

    Article  Google Scholar 

  16. G. Harik, et al., Linkage learning via probabilistic modeling in the ecga. IlliGAL report 99010 (1999)

  17. K. Horváth, B. Bank, Optimizing the numerical noise of parallel second-order filters in fixed-point arithmetic. J. Audio Eng. Soc. 67(10), 763–771 (2019)

    Article  Google Scholar 

  18. K.I. Kum, W. Sung, Combined word-length optimization and high-level synthesis of digital signal processing systems. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 20(8), 921–930 (2001)

    Article  Google Scholar 

  19. Lamini, E.s., Bellal, R., Tagzout, S., Belbachir, H., Belouchrani, A.: Enhanced bit-width optimization for linear circuits with feedbacks. In: 2014 9th International Design and Test Symposium (IDT), pp. 168–173. IEEE (2014)

  20. E.S. Lamini, S. Tagzout, H. Belbachir, A. Belouchrani, Precision analysis with analytical bit-width optimisation process for linear circuits with feedbacks. IET Circuits Dev. Syst. 12(5), 563–570 (2018)

    Article  Google Scholar 

  21. P. Larrañaga, J.A. Lozano, Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation, vol. 2 (Springer, 2001)

  22. D.U. Lee, A.A. Gaffar, R.C. Cheung, O. Mencer, W. Luk, G.A. Constantinides, Accuracy-guaranteed bit-width optimization. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 25(10), 1990–2000 (2006)

    Article  Google Scholar 

  23. K. Long, H. Chen, X. Li, Analysis and optimization for hardware implementation of sine/cosine with faithful rounding and monotonicity through piecewise quadratic polynomial. IEICE Electron. Exp. 18, 20210158 (2021)

    Article  Google Scholar 

  24. B. Lopez, Implémentation optimale de filtres linéaires en arithmétique virgule fixe. Ph.D. thesis (2014)

  25. V. Magron, Interval enclosures of upper bounds of roundoff errors using semidefinite programming. ACM Trans. Math. Softw. (TOMS) 44(4), 1–18 (2018)

    Article  MathSciNet  Google Scholar 

  26. V. Magron, G. Constantinides, A. Donaldson, Certified roundoff error bounds using semidefinite programming. ACM Trans. Math. Softw. (TOMS) 43(4), 1–31 (2017)

    Article  MathSciNet  Google Scholar 

  27. D. Menard, G. Caffarena, J.A. Lopez, D. Novo, O. Sentieys, Fixed-point refinement of digital signal processing systems (2019)

  28. H. Mühlenbein, The equation for response to selection and its use for prediction. Evol. Comput. 5(3), 303–346 (1997)

    Article  Google Scholar 

  29. H. Mühlenbein, G. Paass, From recombination of genes to the estimation of distributions i. binary parameters, in International Conference on Parallel Problem Solving from Nature (Springer, 1996), pp. 178–187

  30. A.V. Oppenheim, J.R. Buck, R.W. Schafer, Discrete-Time Signal Processing, vol. 2 (Prentice Hall, Upper Saddle River, 2001)

    Google Scholar 

  31. G. Ott, E.A. Costa, S.J. Almeida, M.B. Fonseca, Iir filter architectures with truncation error feedback for ecg signal processing. Circuits Syst. Signal Process. 38(1), 329–355 (2019)

    Article  Google Scholar 

  32. Y. Pang, K. Radecka, Z. Zilic, An efficient hybrid engine to perform range analysis and allocate integer bit-widths for arithmetic circuits, in 16th Asia and South Pacific Design Automation Conference (ASP-DAC 2011) (IEEE, 2011), pp. 455–460

  33. M. Pelikan, D.E. Goldberg, E. Cantu-Paz, Linkage problem, distribution estimation, and bayesian networks. Evol. Comput. 8(3), 311–340 (2000)

    Article  Google Scholar 

  34. J. Potsangbam, M. Kumar, Design and implementation of combined pipelining and parallel processing architecture for fir and iir filters using vhdl. Int. J. VLSI Des. Commun. Syst. 10(4) (2019)

  35. N. Revol, Introduction à l’arithmétique par intervalles (2001)

  36. O. Sarbishei, Y. Pang, K. Radecka, Analysis of range and precision for fixed-point linear arithmetic circuits with feedbacks, in 2010 IEEE International High Level Design Validation and Test Workshop (HLDVT) (IEEE, 2010), pp. 25–32

  37. O. Sarbishei, K. Radecka, Z. Zilic, Analytical optimization of bit-widths in fixed-point lti systems. IEEE Trans. Comput. -Aided Des. Integr. Circuits Syst. 31(3), 343–355 (2012)

    Article  Google Scholar 

  38. C. Shi, R.W. Brodersen, Automated fixed-point data-type optimization tool for signal processing and communication systems, in Proceedings of the 41st Annual Design Automation Conference (2004), pp. 478–483

  39. J.J. Shynk, Adaptive iir filtering using parallel-form realizations. IEEE Trans. Acoust. Speech Signal Process. 37(4), 519–533 (1989)

    Article  Google Scholar 

  40. D. Sidhu, J. Dhillon, Design of digital iir filter with conflicting objectives using hybrid predator-prey optimization. Circuits Syst. Signal Process. 37(5), 2117–2141 (2018)

    Article  MathSciNet  Google Scholar 

  41. R. Singh, S.K. Arya, Genetic algorithm for the design of optimal iir digital filters (2012)

  42. K.S. Tang, K.F. Man, S. Kwong, Z.F. Liu, Design and optimization of iir filter structure using hierarchical genetic algorithms. IEEE Trans. Ind. Electron. 45(3), 481–487 (1998)

    Article  Google Scholar 

  43. T. Technologies, Clocks for the synchronized network: Common generic criteria. GR-1244-CORE. Issue 3. 2005 (2005). http://www.telcordia.com

  44. H.L.N. Thi, S. Van Gerven, C. Jutten, D. Van Compernolle, Stability study for source separation in convolutive mixtures of two sources. Signal Process. 62(2), 163–171 (1997)

    Article  Google Scholar 

  45. J.T. Tsai, J.H. Chou, T.K. Liu, Optimal design of digital iir filters by using hybrid taguchi genetic algorithm. IEEE Trans. Ind. Electron. 53(3), 867–879 (2006)

    Article  Google Scholar 

  46. S. Vakili, J.P. Langlois, G. Bois, Enhanced precision analysis for accuracy-aware bit-width optimization using affine arithmetic. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 32(12), 1853–1865 (2013)

    Article  Google Scholar 

  47. Y. Yuan, C. Chen, X. Hu, S. Peng, Unlabeled data driven channel-wise bit-width allocation and quantization refinement. Aust. J. Intell. Inf. Process. Syst. 16(4), 9–16 (2019)

    Google Scholar 

Download references

Funding

The authors did not receive support from any organization for the submitted work.

Author information

Authors and Affiliations

  1. RECITS Laboratory, Department of Operational Research, Faculty of Mathematics, USTHB, Algiers, Algeria

    Mohammed Zelmat, El-Sedik Lamini & Hacène Belbachir

  2. Research Center in Applied Economics for Development, Algiers, Algeria

    Mohammed Zelmat

  3. EPE PROXYLAN SPA, Lot N0 1, Route de Fouka, Kolea, Tipaza, Algeria

    Samir Tagzout

  4. Research Centre for Scientific and Technical Information, CERIST, Algiers, Algeria

    Hacène Belbachir

  5. LDCCP Laboratory, Department of Electrical Engineering, Ecole Nationale Polytechnique, El Harrach, Algiers, Algeria

    Adel Belouchrani

Authors
  1. Mohammed Zelmat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. El-Sedik Lamini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Samir Tagzout
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hacène Belbachir
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Adel Belouchrani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammed Zelmat.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zelmat, M., Lamini, ES., Tagzout, S. et al. Precision Analysis for an Optimal Parallel IIR Filter’s Implementation. Circuits Syst Signal Process 41, 4512–4546 (2022). https://doi.org/10.1007/s00034-022-01988-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-022-01988-7

Keywords

Search

Navigation