53. New Compactly Supported Scaling and Wavelet Functions Derived from Gegenbauer Polynomials

A new family of scaling and wavelet functions is introduced, which is derived from Gegenbauer polynomials.
The association of ordinary second order differential equations to multiresolution filters is employed
to construct these new functions. These functions, termed ultraspherical harmonic or Gegenbauer scaling and
wavelet functions, possess compact support and generalized linear phase. This is an interesting property since,
from the computational point of view, only half the number of filter coefficients is required to be computed.
By using an alpha factor that is within the orthogonality range of such polynomials, there are generated scaling
and wavelet that are frequency selective FIR filters. Potential application of such wavelets includes
fault detection in transmission lines of power systems.