Gegenbauer (ultraspherical) polynomials for Gabor-type wavelet approximation and FIR filter function generation in wavelet analysis
A. Saed, J.J. Soltis, Majid A. Ahmadi · 2002
Gegenbauer polynomials are very suitable for approximation of low-pass and bandpass finite filter functions in the time domain. The presented class of functions is characterized by a grid and an interdependence of two polynomial parameters, offering great flexibility in the choice of the filter characteristic. The provided definition of series within the class enables, that with only small optimization efforts, polynomials up to any degree can be applied in the search for the most desirable approximation.