Periodic orthogonal splines and wavelets
type: Item
instance of: scholarly article
title: Periodic orthogonal splines and wavelets
zbMATH Open document ID: 0845.42014
author: Yanyan Li
published in: Applied and Computational Harmonic Analysis
publication date: 1996-09-04T00:00:00Z
review text: In this interesting paper, the authors develop a general approach for non-stationary multiresolution of periodic functions. For a multiresolution \(\{V_k: k\geq 0\}\), necessary and sufficient conditions for \(\bigcup_{k\geq 0} V_k\) to be dense in \(L^2_{2\pi}\) and characterizations of a function \(\phi_k\) for which \(\phi_k(\cdot - 2\pi j2^{- k})\), \(j= 0, 1,\dots, 2^k- 1\), form a basis of \(V_k\) are given. By using so-called orthogonal splines various examples of multiresolutions are provided. The construction of corresponding periodic wavelets and Riesz stability are discussed in detail. Periodic polynomial spline wavelets and the trigonometric polynomial wavelets from Chui-Mhaskar are seen to follow as a special case. The general ``orthogonal spline bases'' give rise to algorithms in which the equations are the finite Fourier transforms of the classical wavelet decomposition and reconstruction equations. For Chui-Wang spline wavelets a comparison of frequency-based algorithms investigated in this paper with time-based algorithms shows that the frequency-based algorithms can be a useful alternative.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 850654
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: periodic wavelets
zbMATH Keywords: orthogonal splines
reviewed by: Jürgen Prestin
MaRDI profile type: Publication
full work available at URL: acha.1995.1014
OpenAlex ID: W1969109780
DOI: 10.1006/ACHA.1995.1014
description: scientific article; zbMATH DE number 850654