Compact functions and the Frazier-Jawerth transform

Abstract

Summary form only given. The Frazier-Jawerth transform (FJT), originally the phi-transform, is similar to the wavelet transform and is distinguished by the fact that the analyzing functions form an overcomplete basis for he signal space and may be nonorthogonal. This added flexibility makes possible the definition of optimal analyzing functions, which are the focus of this study. For continuous-time and infinite discrete-time signals, the optimally localized functions are the prolate spheroidal wave functions and their discrete versions. For finite discrete-time signals and images, generalizations of these functions that are applicable for use in the FJT have been identified by the authors.<>