Oversampling in wavelet subspaces
ReferenceProc. of IEEE International Symposium on Time-Frequency and Time-Scale Analysis (TFTS), Pittsburgh (PA), pp. 489-492, Oct. 1998
AbstractRecently, several extensions of classical Shannon sampling theory to wavelet subspaces have been reported. This paper is devoted to uniform and periodic nonuniform oversampling in wavelet subspaces. Specifically, we provide a stability analysis and we introduce a technique for calculating the condition number of wavelet subspace sampling operators. It is shown that oversampling results in improved numerical stability. We consider the reconstruction from noisy samples and we characterize compactly supported scaling functions having compactly supported synthesis functions. Finally, it is shown that in the oversampled case the synthesis functions are not uniquely determined.
KeywordsSampling, wavelet subspaces, nonuniform sampling, condition number, oversampling, numerical stability
Download this document:
Copyright Notice: © 1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.