On designing FIR filters using windows based on Gegenbauer polynomials

A new class of adjustable window functions for designing FIR filters based on Gegenbauer polynomials is introduced. In addition to the usual parameters controlling the mainlobe width and, correspondingly, the minimum attenuation of the resulting filter, these windows provide an additional parameter which can by used to combine the two window design methods: to minimize the peak sidelobe ripple of the frequency response and to minimize the energy in the sidelobes, i.e. the Dolph-Chebyshev and the Saramaki windows are shown to be special cases of the proposed window function. The new window possesses analytic expressions in both the time and frequency domains: the expressions are more straightforward than in the case of Kaiser or Saramaki windows.