Skip to main content
SpringerLink
Log in

Design of IIR Filters

  • Chapter
  • First Online:
Positive Trigonometric Polynomials and Signal Processing Applications

Part of the book series: Signals and Communication Technology ((SCT))

  • 1386 Accesses

Abstract

IIR filters can give the same magnitude performance with fewer parameters than FIR filters. However, they cannot have exact linear phase. Their design is more complicated due to the difficulty in ensuring stability and to the non-convexity of the optimization problems. In this short chapter, we give few guidelines for the optimization of IIR filters, insisting on algorithms that use positive polynomials. For 1D filters, we discuss two design problems, using magnitude and approximate linear phase as design criteria; in the latter case, stability domains based on positive realness are an important tool. The method for approximate linear phase is then extended to 2D, for the case when passband and stopband are described by the positivity of some polynomials.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. C.S. Burrus, J.A. Barreto, I.W. Selesnick, Iterative reweighted least-squares design of FIR filters. IEEE Trans. Sign. Proc. 42(11), 2926–2936 (1994)

    Article  Google Scholar 

  2. Y.C. Lim, J.-H. Lee, C.K. Chen, R.H. Yang, A weighted least-squares algorithm for quasi-equiripple FIR and IIR filter design. IEEE Trans. Signal Process. 40(3), 551–558 (1992)

    Article  Google Scholar 

  3. B. Dumitrescu, R. Niemistö, Multistage IIR filter design using convex stability domains defined by positive realness. IEEE Trans. Signal Proc. 52(4), 962–974 (2004)

    Article  MathSciNet  Google Scholar 

  4. B. Dumitrescu, Optimization of 2D IIR filters with nonseparable and separable denominator. IEEE Trans. Signal Proc. 53(5), 1768–1777 (2005)

    Article  Google Scholar 

  5. B. Alkire, L. Vandenberghe, Convex optimization problems involving finite autocorrelation sequences. Math. Progr. Ser. A 93(3), 331–359 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. A.T. Chottera, G.A. Jullien, A linear programming approach to recursive digital filter design with linear phase. IEEE Trans. Circ. Syst. CAS 29(3), 139–149 (1982)

    Google Scholar 

  7. W.-S. Lu, S.-C. Pei, C.-C. Tseng, A weighted least-squares method for the design of stable 1-D and 2-D IIR digital filters. IEEE Trans. Signal Process. 46, 1–10 (1998)

    Google Scholar 

  8. M.C. Lang, Least-squares design of IIR filters with prescribed magnitude and phase response and a pole radius constraint. IEEE Trans. Signal Process. 48(11), 3109–3121 (2000)

    Article  Google Scholar 

  9. A. Tarczynski, G.D. Cain, E. Hermanowicz, M. Rojewski, A WISE method for designing IIR filters. IEEE Trans. Signal Process. 49(7), 1421–1432 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. W.-S. Lu, Design of stable minimax IIR digital filters using semidefinite programming, in IEEE International Symposium Circuit System (ISCAS), vol. 1 (Geneva, Switzerland 2000), pp. 355–358

    Google Scholar 

  11. A. Jiang, H.K. Kwan, IIR digital filter design with new stability constraint based on argument principle. IEEE Trans. Circ. Syst. I 56(3), 583–593 (2009)

    Article  MathSciNet  Google Scholar 

  12. K.E. Steiglitz, L.E. McBride, A technique for the identification of linear systems. IEEE Trans. Auto. Control AC 10, 461–464 (1965)

    Google Scholar 

  13. X. Lai, Z. Lin, Minimax design of IIR digital filters using a sequential constrained least-squares method. IEEE Trans. Signal Proc. 58(7), 3901–3906 (2010)

    Article  MathSciNet  Google Scholar 

  14. A. Jiang, H.K. Kwan, Minimax design of IIR digital filters using SDP relaxation technique. IEEE Trans. Circ. Syst. I 57(2), 378–390 (2010)

    Article  MathSciNet  Google Scholar 

  15. R.C. Nongpiur, D.J. Shpak, A. Antoniou, Improved design method for nearly linear-phase IIR filters using constrained optimization. IEEE Trans. Signal Proc. 61(4), 895–906 (2013)

    Article  MathSciNet  Google Scholar 

  16. R. Niemistö, B. Dumitrescu, Simplified procedures for Quasi-Equiripple IIR filter design. IEEE Signal Proc. Lett. 11(3), 308–311 (2004)

    Article  Google Scholar 

  17. A.T. Chottera, G.A. Jullien, Design of Two-dimensional recursive digital filters using linear programming. IEEE Trans. Circ. Syst. CAS 29(12), 817–826 (1982)

    Google Scholar 

  18. J.-H. Lee, Y.-M. Chen, A new method for the design of two-dimensional recursive digital filters. IEEE Trans. Acoust. Speech Signal Proc. 36(4), 589–598 (1988)

    Google Scholar 

  19. Z. Lin, L.T. Bruton, N.R. Bartley, Design of highly selective two-dimensional recursive fan filters by relaxing symmetry constraints. Electron. Lett. 24(22), 1361–1362 (1988)

    Article  Google Scholar 

  20. P.K. Rajan, M.N.S. Swamy, Quadrantal symmetry associated with two-dimensional digital transfer functions. IEEE Trans. Circ. Syst. CAS 25(6), 341–344 (1978)

    Google Scholar 

  21. W.S. Lu, T. Hinamoto, Optimal design of IIR digital filters with robust stability using conic-quadratic-programming updates. IEEE Trans. Signal Proc. 51(6), 1581–1592 (2003)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Automatic Control and Computers, University Politehnica of Bucharest, Bucharest, Romania

    Bogdan Dumitrescu

Authors
  1. Bogdan Dumitrescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bogdan Dumitrescu .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Dumitrescu, B. (2017). Design of IIR Filters. In: Positive Trigonometric Polynomials and Signal Processing Applications. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-53688-0_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-53688-0_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53687-3

  • Online ISBN: 978-3-319-53688-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation