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| © 2006 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. |
Abstract: Wavelet transforms for discrete-time periodic signals are developed. In this finite-dimensional context, key ideas from the continuous-time papers of Daubechies and of Cohen, Daubechies, and Feauveau are isolated to give a concise, rigorous derivation of the discrete-time periodic analogs of orthonormal and symmetric biorthogonal bases of compactly supported wavelets. These discrete-time periodic wavelets are expressed in terms of circular FIR filters, and thus lead to fast wavelet transforms whose complexity is order N.
Click here for a postscript file on wavelet transforms for 2-dimensional (image) signals. This file contains a section that was not a part of the published paper.