DOI QR코드

DOI QR Code

An Analytical Approach for Design of Nth-band FIR Digital Filters with Equi-Ripple Passband

  • Published : 2009.09.01

Abstract

In FIR (Finite Impulse Response) filter applications, Nth-band FIR digital filters are known to be important due to their reduced computational requirements. The conventional methods for designing FIR 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 after Mintzer's research. However, a disadvantage of the Parks-McClellan algorithm is that it needs a large 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 equi-ripple in passband. Our proposed method produces a passband response that is equi-ripple to within a minuscule error, comparable to that of Mintzer's design method which uses the Parks-McClellan algorithm.

Keywords

References

  1. L. R. Rabiner and B. Gold, Theory and Applications of Digital Signal Processing, Englewood Cliffs NJ: Prentice-Hall, 1975
  2. Naoyuki Aikawa and Masamitsu Sato, 'Designing Linear Phase FIR Digital Filters with Flat Passband. and Equiripple Stopband Characteristics', Electronics and Communications in Japan, Part 3, vol. 86, No. 4, pp. 89-95, 2003 https://doi.org/10.1002/ecjc.1148
  3. Y. C. Jenq, 'On FIR digital filter implementations for interpolation', IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. 29, Issue 2, pp. 315-317, Apr. 1981 https://doi.org/10.1109/TASSP.1981.1163550
  4. P. P. Vaidyanathan and Truong Nguyen, 'A ‘trick’ for the design of FIR half-band filters', IEEE Trans. on Circuits and Systems, vol. 34, Issue 3, pp. 297- 300, Mar. 1987 https://doi.org/10.1109/TCS.1987.1086124
  5. R. E. Crochiere and L. R. Rabiner, Multirate Digital Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1983
  6. J. H. McClellan, T. W. Parks, and L. R. Rabiner, 'A computer program for designing optimum FIR linear phase digital filters', IEEE Trans. on Audio and Electroacoustics, vol. 21, Issue 6, pp. 506-526, Dec. 1973 https://doi.org/10.1109/TAU.1973.1162525
  7. M. Vlcek, P. Zahradnik, R. Unbehauen, 'Analytical design of FIR filters', IEEE Trans. on Signal Processing, vol. 48, Issue 9, pp. 2705-2709, Sept. 2000 https://doi.org/10.1109/78.863090
  8. F. Mintzer, 'On half-band, third-band, and Nth-band FIR filters and their design', IEEE Trans. On Acoustics, Speech, and Signal Processing, vol. 30, 5, pp. 734-738, Oct. 1982 https://doi.org/10.1109/TASSP.1982.1163950
  9. A. N.Willson and H. J. Orchard, 'A design method for half-band FIR filters', IEEE Trans. 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
  10. J. M. Nohrden and T. Q. Nguyen, 'Constraints on the cutoff frequencies of Mth-band linear-phase FIR filters', IEEE Trans. on Signal Processing, vol. 43, Issue 10, pp. 2401-2405, Oct. 1995 https://doi.org/10.1109/78.469850
  11. 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
  12. 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
  13. W. H. Press et al., Numerical Recipes, Cambridge, U.K.: Cambridge, Univ. Press, 1986, pp. 148-149