Periodic Prolate Spheroidal Wavelets

ABSTRACT

Prolate spheroidal wavelets (PS wavelets) were recently introduced by the authors. They were based on the first prolate spheroidal wave function (PSWF) and had many desirable properties lacking in other wavelets. In particular, the subspaces belonging to the associated multiresolution analysis (MRA) were shown to be closed under differentiation and translation. In this paper, we introduce periodic prolate spheroidal wavelets. These periodic wavelets are shown to possess properties inherited from PS wavelets such as differentiation and translation. They have the potential for applications in modeling periodic phenomena as an alternative to the usual periodic wavelets as well as the Fourier basis.

Keywords:

• Bandlimited signal
• Paley-Wiener space
• Periodic wavelets
• Prolate spheroidal wave functions
• PS wavelets
• Wavelets

Mathematics Subject Classification:

• Primary 42C40
• Secondary 33E10, 42C05, 94A11, 94A12

ACKNOWLEDGMENT

The second author was partially supported by Professor Naoki Saito's grant ONR YIP N00014-00-1-0469 while completing this paper.