Analytic wavelets based upon de-orthogonalized Gegenbauer polynomials

Three new classes of analytic functions for discrete wavelet applications based upon the de-orthogonalization of Gegenbauer polynomials are presented. The first class has an appearance similar to Lemarie wavelets which have been used in the past. The second and third classes are similar to Gaussian-sinusoid wavepackets. In each case the new functions have useful recursive-polynomial properties for a basis set and should provide greater flexibility and economy of implementation in processing than the conventional approach