Zolotarev polynomials and optimal FIR filters

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.