The Transactions of the Korean Institute of Electrical Engineers D (대한전기학회논문지:시스템및제어부문D)

The Korean Institute of Electrical Engineers (대한전기학회)
권호 표지

Analysis and Design of Nth-band FIR Filters with Equi-Ripple Passband Response

Nth 밴드 FIR 필터의 균일 리플 통과 대역 응답을 위한 해석과 설계

  • Published : 2005.10.01
Download PDF
⟨ Previous Next ⟩

Abstract

In FIR (Finite Impulse Response) filter applications, Nth-band F]U digital filters are known to be important due to their reduced computational requirements. The conventional methods for designing F]U filters use iterative approaches such as the well-known Parks-Mcclellan algorithm. The Parks-Mcclellan algorithm is also used to design Nth-band FIR digital filters. But a disadvantage of the Parks-Mcclellan algorithm is that it needs a good amount of design time. This paper describes a direct design method for Nth-band FIR Filters using Chebyshev polynomials, which provides a reduced design time over indirect methods such as the Parks-Mcclellan algorithm. The response of the resulting filter is equiripple in passband. Our proposed method produces a passband response that is equripple to within a minuscule error, comparable to that of the Parks-Mcclellan algorithm.

Keywords

References

  1. Y. C. Jenq, 'On FIR digital filter implementations for interpolation', IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 29, Issue 2, pp.315-317, Apr. 1981 https://doi.org/10.1109/TASSP.1981.1163550
  2. P. P. Vaidyanathan and Truong Nguyen, 'A 'trick' for the design of FIR half-band filters', IEEE Transactions on Circuits and Systems, vol. 34, Issue 3, pp.297- 300, Mar. 1987 https://doi.org/10.1109/TCS.1987.1086124
  3. R. E. Crochiere and L. R. Rabiner, 'Multirate Digital Signal Processing', Englewood Cliffs, NJ: Prentice- Hall, 1983
  4. J. H. McClellan, T. W. Parks, and L. R. Rabiner, 'A computer program for designing optimum FIR linear phase digital filters', IEEE Transactions on Audio and Electroacoustics, vol. 21, Issue 6, pp.506-526, Dec. 1973 https://doi.org/10.1109/TAU.1973.1162525
  5. M. Vlcek, P. Zahradnik, R. Unbehauen, 'Analytical design of FIR filters', IEEE Transactions on Signal Processing, vol. 48, Issue 9, pp. 2705-2709, Sept. 2000 https://doi.org/10.1109/78.863090
  6. F. Mintzer, 'On half-band, third-band, and Nth-band FIR filters and their design', IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 30, Issue 5, pp.734-738, Oct. 1982 https://doi.org/10.1109/TASSP.1982.1163950
  7. A. N. Willson and H. J. Orchard, 'A design method for half-band FIR filters', IEEE Transactions on Circuits and Systems - I: Fundamental Theory and Applications, vol. 46, Issue 1, pp.95-101, Jan. 1999 https://doi.org/10.1109/81.739257
  8. J, M. Nohrden and T. Q. Nguyen, 'Constraints on the cutoff frequencies of Mth-band linear-phase FIR filters', IEEE Transactions on Signal Processing, vol. 43, Issue 10, pp.2401-2405, Oct. 1995 https://doi.org/10.1109/78.469850
  9. S. Oraintara, T. Q. Nguyen, 'M-th band filter design based on cosine modulation', Circuits and Systems, 1998. ISCAS '98. Proceedings of the 1998 IEEE International Symposium, vol. 5, pp.37-40 https://doi.org/10.1109/ISCAS.1998.694402
  10. S. Oraintara, T. Q. Nguyen, 'A simple mapping between Mth-band FIR filters using cosine modulation', IEEE Signal Processing Letters, vol. 10, Issue 5, pp.125-128, May. 2003 https://doi.org/10.1109/LSP.2003.810021
  11. W. H. Press et al., Numerical Recipes. Cambridge, U.K.: Cambridge, Univ. Press, 1986, pp.148-149