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Design of optimum recursive digital filters with zeros on the unit circle

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1 Author(s)
Saramaki, T. ; Tampere University of Technology, Tampere, Finland

This paper presents an efficient algorithm for the design of low-pass recursive digital filters with Chebyshev passband and stopband, all zeros on the unit circle, and different order numerator and denominator. The procedure takes advantage of the possibility of generating analytically magnitude squared functions with Chebyshev passband and adjustable zeros or Chebyshev stopband and adjustable poles. The resulting algorithm requires only one approximation interval making it more efficient than other existing design procedures. The number of multiplications per sample required in realizing the resulting filters is discussed and the optimal denominator and numerator orders are considered in narrow-band, wide-band, and intermediate applications. It turns out that the classical elliptic filters are seldom the best representatives of the filter class discussed in the paper. Simple explanations of some properties of the filters with denominator order lower than numerator order are given, such as the existence of an extra ripple in the passband and the minimum attainable passband ripple.

Published in:

Acoustics, Speech and Signal Processing, IEEE Transactions on  (Volume:31 ,  Issue: 2 )

Date of Publication:

Apr 1983

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