Please use this identifier to cite or link to this item: https://doi.org/10.1006/acha.1995.1014
Title: Periodic Orthogonal Splines and Wavelets
Authors: Koh, Y.W.
Lee, S.L. 
Tan, H.H. 
Issue Date: Jul-1995
Source: Koh, Y.W., Lee, S.L., Tan, H.H. (1995-07). Periodic Orthogonal Splines and Wavelets. Applied and Computational Harmonic Analysis 2 (3) : 201-218. ScholarBank@NUS Repository. https://doi.org/10.1006/acha.1995.1014
Abstract: Periodic scaling functions and wavelets are constructed directly from non-stationary multiresolutions of L2([0, 2π)), the space of square-integrable 2π-periodic functions. For a multiresolution {Vk : k ≥ 0}, necessary and sufficient conditions for ∪k≥0Vk to be dense in L2([0, 2π)) and characterizations of a function φk for which φk(· - 2πj/2k), j = 0, 1, . . ., 2k - 1, form a basis of Vk are given. The construction of scaling functions and wavelets are done via orthogonal bases of functions, called orthogonal splines . Sufficient conditions are given for a sequence of scaling functions to generate a multiresolution. These conditions are also sufficient for the convergence of convolution operators with the scaling functions as kernels. Sufficient conditions are also given for the wavelets to generate a stable basis of L2([0, 2π)). The orthogonal spline bases give rise to algorithms in which the equations are the finite Fourier transforms of the classical wavelet decomposition and reconstruction equations. Each equation in the orthogonal spline algorithms involves only two terms and its complexity does not depend on the length of the filter coefficients. The general construction given here includes periodic versions of known wavelets. Examples on periodic polynomial spline wavelets and an extension of Chui and Mhaskar′s trigonometric wavelets are given to illustrate the construction. These trigonometric wavelets, in particular Chui and Mhaskar′s wavelets, form a stable basis of L2([0, 2π)). © 1995 Academic Press. All rights reserved.
Source Title: Applied and Computational Harmonic Analysis
URI: http://scholarbank.nus.edu.sg/handle/10635/103923
ISSN: 10635203
DOI: 10.1006/acha.1995.1014
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

36
checked on Feb 12, 2018

WEB OF SCIENCETM
Citations

41
checked on Nov 22, 2017

Page view(s)

19
checked on Feb 16, 2018

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.