Efficient Design of Arbitrary Complex Response Continuous-Time IIR Filter

  • Chi-Un LeiEmail author
  • Chung-Man Cheung
  • Hing-Kit Kwan
  • Ngai Wong
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 33)


A continuous-time system identification technique, Vector Fitting (VF), is extended from symmetric functions, to asymmetrical cases and is used for complex infinite-impulse-response (IIR) continuous-time filter design. VF involves a two-step pole refinement process based on a linear least-squares solve and an eigenvalue problem. The proposed algorithm has lower complexity than conventional schemes by designing complex continuous-time filters directly. Numerical examples demonstrate that VF achieves highly efficient and accurate approximation to arbitrary asymmetric complex filter responses. The promising results can be realized for high dynamic frequency range networks. Robustness stability margin has also proposed for filter implementation robustness.


Complex filter Vector fitting Rational function approximation 



This work was supported in part by the Hong Kong Research Grants Council and the University Research Committee of The University of Hong Kong.


  1. 1.
    Deschrijver, D., Haegeman, B., and Dhaene, T. (2007). Orthonormal vector fitting: A robust macromodeling tool for rational approximation of frequency domain responses. IEEE Trans. Adv. Packag., 30(2):216–225.CrossRefGoogle Scholar
  2. 2.
    Deschrijver, D., Schoeman, M., Dhaene, T., and Meyer, P. (2007). Experimental analysis on the relaxation of macromodeling methods. In Proc. IEEE Africon conference.Google Scholar
  3. 3.
    Golub, G. H. and Loan, C. F. V. (1996). Matrix Computations. London: Johns-Hopkins, third edition.zbMATHGoogle Scholar
  4. 4.
    Gustavsen, B. (2004). Wide band modeling of power transformers. IEEE Trans. Power Delivery, 19(1):414–422.CrossRefGoogle Scholar
  5. 5.
    Gustavsen, B. (2006). Improving the pole relocating properties of vector fitting. IEEE Trans. Power Delivery, 21(3):1587–1592.CrossRefGoogle Scholar
  6. 6.
    Gustavsen, B. and Semlyen, A. (1999). Rational approximation of frequency domain responses by vector fitting. IEEE Trans. Power Delivery, 14(3):1052–1061.CrossRefGoogle Scholar
  7. 7.
    Hendrickx, W. and Dhaene, T. (2006). A discussion of ”Rational approximation of frequency domain responses by vector fitting”. IEEE Trans. Power Syst., 21(1):441–443.CrossRefGoogle Scholar
  8. 8.
    Kobayashi, T. and Imai, S. (1990). Design of IIR digital filters with arbitrary log magnitude function by WLS techniques. IEEE Trans. Signal Processing, 38(2):247–252.CrossRefMathSciNetGoogle Scholar
  9. 9.
    Krukowski, A. and Kate, I. (2003). DSP system design: complexity reduced IIR filter implementation for practical application.Google Scholar
  10. 10.
    Lei, C. U. and Wong, N. (2008). Efficient linear macromodeling via discrete-time time-domain vector fitting. In Proc. Intl. Conf. on VLSI Design, pages 469–474.Google Scholar
  11. 11.
    Li, E. P., Liu, E. X., Li, L. W., and Leong, M. S. (2004). A coupled efficient and systematic full-wave time-domain macromodeling and circuit simulation method for signal integrity analysis of high-speed interconnects. IEEE Trans. Antennas Propagat., 27(1):213–223.Google Scholar
  12. 12.
    Mahattanakul, J. and Khumsat, P. (2007). Structure of complex elliptic Gm-C filters suitable for fully differential implementation. IEE Proceedings - Circuits, Devices and Systems, 1(4):275–282.Google Scholar
  13. 13.
    Martin, K. (2005). Approximation of complex IIR bandpass filters without arithmetic symmetry. IEEE Trans Circuits Syst. I, 52(4):794–803.CrossRefMathSciNetGoogle Scholar
  14. 14.
    Martin, K. W. (2004). Complex signal processing is not complex. IEEE Trans. Circuits Syst. I, 51(9):1823–1836.CrossRefMathSciNetGoogle Scholar
  15. 15.
    Mekonnen, Y. S. and Schutt-Aine, J. E. (2007). Broadband macromodeling of sampled frequency data using z-domain vector-fitting method. In Proc. IEEE workshop on sig. prop. on interconnects. to appear.Google Scholar
  16. 16.
    Pandita, B. and Martin, K. W. (2007). Designing complex delta-sigma modulators with signal-transfer functions having good stop-band attenuation. In Proc. IEEE Symp. Circuits and Systems, pages 3626–3629.Google Scholar
  17. 17.
    Sanathanan, C. and Koerner, J. (1963). Transfer function synthesis as a ratio of two complex polynomials. IEEE Trans. Automat. Contr., 8(1):56–58.CrossRefGoogle Scholar
  18. 18.
    Teplechuk, M. A. and Sewell, J. I. (2006). Approximation of arbitrary complex filter responses and their realisation in log domain. IEE Proceedings - Circuits, Devices and Systems, 153(6):583–590.Google Scholar
  19. 19.
    Wong, Ngai and Lei, Chi-Un (2008). IIR approximation of FIR filters via discrete-time vector fitting. IEEE Trans. Signal Processing, 56(3):1296–1302.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V 2009

Authors and Affiliations

  • Chi-Un Lei
    • 1
    Email author
  • Chung-Man Cheung
    • 1
  • Hing-Kit Kwan
    • 2
  • Ngai Wong
    • 1
  1. 1.Department of Electrical and Electronic EngineeringThe University of Hong KongHong Kong
  2. 2.Univ. of Hong KongHong Kong

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