Walsh-Type Wavelet Packet Expansions |
| |
Authors: | Morten Nielsen |
| |
Institution: | Department of Mathematics, University of South Carolina, South Carolina, 29208, f1 |
| |
Abstract: | We consider a family of basic nonstationary wavelet packets generated using the Haar filters except for a finite number of scales where we allow the use of arbitrary filters. Such a system, which we call a system of Walsh-type wavelet packets, can be considered as a smooth generalization of the Walsh functions. We show that the basic Walsh-type wavelet packets share a number of metric properties with the Walsh system. We prove that the system constitutes a Schauder basis for Lp(
), 1<p<∞, and we construct an explicit function in L1(
) for which the expansion fails. Then we prove that expansions of Lp(
)-functions, 1<p<∞, in the Walsh-type wavelet packets converge pointwise a.e. Finally, we prove that the analogous results are true for periodic Walsh-type wavelet packets in Lp0,1). |
| |
Keywords: | wavelet analysis nonstationary wavelet packets Walsh functions Lp-convergence convergence a e |
本文献已被 ScienceDirect 等数据库收录! |
|