**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.

** **