Skip to main content
Article thumbnail
Location of Repository

Optimal design of magnitude responses of rational infinite impulse response filters

By Charlotte Yuk-Fan Ho, Bingo Wing-Kuen Ling, Yan-Qun Liu, Peter Kwong-Shun Tam and Kok-Lay Teo


This correspondence considers a design of magnitude responses of optimal rational infinite impulse response (IIR) filters. The design problem is formulated as an optimization problem in which a total weighted absolute error in the passband and stopband of the filters (the error function reflects a ripple square magnitude) is minimized subject to the specification on this weighted absolute error function defined in the corresponding passband and stopband, as well as the stability condition. Since the cost function is nonsmooth and nonconvex, while the constraints are continuous, this kind of optimization problem is a nonsmooth nonconvex continuous functional constrained problem. To address this issue, our previous proposed constraint transcription method is applied to transform the continuous functional constraints to equality constraints. Then the nonsmooth problem is approximated by a sequence of smooth problems and solved via a hybrid global optimization method. The solutions obtained from these smooth problems converge to the global optimal solution of the original optimization problem. Hence, small transition bandwidth filters can be obtained

Topics: H600 Electronic and Electrical Engineering
Publisher: IEEE
Year: 2006
DOI identifier: 10.1109/TSP.2006.880317
OAI identifier:

Suggested articles


  1. (1999). A bridging method for global optimization,” doi
  2. (2003). A hybrid global optimization method: the multidimensional case,” doi
  3. (2002). A unified approach for the design of 2-D digital filters via semi-definite programming,” doi
  4. (2002). Closed-form design of maximally flat IIR half-band filters,” doi
  5. (1999). Comments on “A weighted least-squares method for the design of stable doi
  6. (1994). Design of 1-D and 2-D IIR eigenfilters,” doi
  7. (2003). Design of IIR digital all-pass filters using least pth phase error criterion,” doi
  8. (1999). Design of IIR digital allpass filters based on eigenvalues problem,” doi
  9. (1998). Design of IIR eigenfilters in the frequency domain,” doi
  10. (2004). Design of stable IIR digital filter based on least ppower error criterion,”
  11. (1999). Design of stable IIR digital filters with equiripple passbands and peak-constrained least-squares stopbands,” doi
  12. (1994). Eigenfilter design of 1-D and 2-D IIR digital all-pass filters,” doi
  13. (2001). Ewa Hermanowicz and Mirosław Rojewski, “A WISE method for designing IIR filters,” doi
  14. (2002). Hans Torp and Kjell Kristoffersen, “Clutter filter design for ultrasound color flow imaging,” doi
  15. (2000). Least-squares design of IIR filters with prescribed magnitude and phase responses and a pole radius constraint,” doi
  16. (1999). Lihua Xie, Wei-Yong Yan and Yeng Chai Soh, “Design of low-order linear-phase IIR filters via orthogonal projection,” doi
  17. (2004). Masahiro Yoshida and Masaaki Ikehara, “Design of IIR digital filters in the complex domain by transforming the desired response,” doi
  18. (2004). Multistage IIR filter design using convex stability domains defined by positive realness,” doi
  19. (1988). On constrained optimization problems with nonsmooth cost functionals,” doi
  20. (2002). On the design and implementation of FIR and IIR digital filters with variable frequency characteristics,” doi
  21. (2003). Recursive identification of acoustic echo systems using orthonormal basis functions,” doi
  22. Reply to “Comments on ‘A weighted least-squares method for the design of stable doi
  23. (1998). Soo-Chang Pei and Chien-Cheng Tseng, “A weighted least-squares method for the design of stable 1-D and 2-D IIR digital filters,” doi
  24. (2001). Stable IIR notch filter design with optimal pole placement,” doi
  25. (2003). Yao Xue and Charayaphan Charoensak, “Design of optimal and narrow-band Laguerre filters for sigma-delta demodulators,” doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.