Zolotarev polynomials and optimal FIR filters

  • Authors:
  • M. Vlcek;R. Unbehauen

  • Affiliations:
  • Fac. of Transp. Sci., Czech Tech. Univ., Prague;-

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 1999

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Abstract

The algebraic form of Zolotarev polynomials refraining from their parametric representation is introduced. A recursive algorithm providing the coefficients for a Zolotarev polynomial of an arbitrary order is obtained from a linear differential equation developed for this purpose. The corresponding narrowband, notch, and complementary pair FIR filters are optimal in the Chebyshev sense. A recursion giving an explicit access to the impulse response coefficients is also presented. Some design examples are included to demonstrate the efficiency of the presented approach