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Taylor Series, Maximally Flat, and Zero Moment Design Criteria

Module by: C. Sidney Burrus. E-mail the author

The third major approximation criterion uses some measure of the smoothness or flatness of the frequency response. Work has been done by Herrmann [1], P. P. Vaidyanathan, and Selesnick and Burrus [3], [4], [2], [5]. This approach is related to how polynomial signals are processed and may be related to zero moments in wavelet systems.

References

  1. Herrmann, O. (1971, May). On the Approximation Problem in Nonrecursive Digital Filter Design. [Reprinted in DSP reprints, IEEE Press, 1972, page 202]. IEEE Transactions on Circuit Theory, 18, 411–413.
  2. Selesnick, Ivan W. and Burrus, C. Sidney. (1996, September). Exchange Algorithms for the Design of Linear Phase FIR Filters and Differentiators Having Flat Monotonic Passbands and Equiripple Stopbands. IEEE Transactions on Circuits and Systems II, 43(9), 671–675.
  3. Selesnick, Ivan W. and Burrus, C. Sidney. (1996, June). Generalized Digital Butterworth Filter Design. IEEE Transactions on Signal Processing, 46(6), 1688–1694.
  4. Selesnick, Ivan W. and Burrus, C. Sidney. (1996, May 7–10). Generalized Digital Butterworth Filter Design. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing. (Vol. 3, pp. III-1367–1370). IEEE ICASSP-96, Atlanta
  5. Selesnick, Ivan W. and Burrus, C. Sidney. (1998, January). Maximally Flat Lowpass FIR Filters with Reduced Delay. IEEE Transaction on Circuits and Systems: II, 45(1), 53–68.

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