New classes of frame wavelets for applications

For many applications, general frame wavelets are more attractive than orthonormal wavelets owing to the extent to which the former may be tailored to suit the application. The mother wavelet may be chosen to cause, during wavelet transform, congealing of selected features into localized regions in the wavelet domain or separation of chosen features from one another during transform. Thus choice of mother wavelet impacts feature dimensionality as well as separability among features. Owing to the special importance of frames, there is a need to identify and characterize new frame wavelets in order to make available a rich variety of mothers which run the gamut of the diverse applications. This paper discusses three classes of frame wavelet mothers, to include new mothers as well as a few familiar ones, approached from the viewpoints of residues, sigmoid, and Hermitivity.