Analytic design of optimal FIR narrow-band filters using Zolotarev polynomials

An analytic method for designing narrow-band FIR filters using Zolotarev polynomials, which are extensions of Chebyshev polynomials, is proposed. These filters are optimal in the Chebyshev sense. Bandpass and bandstop narrow-band filters, as well as low-pass and high-pass filters, can be designed by this method. The design procedure and related formulas are presented. Design examples are included to show the properties of these filters.