Construction of periodic wavelet frames generated by the Walsh polynomials
type: Item
instance of: scholarly article
title: Construction of periodic wavelet frames generated by the Walsh polynomials
zbMATH Open document ID: 1332.42030
author: Sunita Goyal
author: Firdous Ahmad Shah
published in: Mathematics
publication date: 2016-01-12T00:00:00Z
review text: Recently, \textit{F. A. Shah} [Int. J. Wavelets Multiresolut. Inf. Process. 11, No. 6, Article ID 1350042, 15 p. (2013; Zbl 1288.42013)] established a unitary extension principle for constructing normalized tight wavelet frames generated by the Walsh polynomials on \(\mathbb{R}^+\). Using this result, the authors prove that under some mild conditions the periodization of any wavelet frame constructed by the unitary extension principle is a periodic wavelet frame on a positive half-line \(\mathbb{R}^+\). Furthermore, based on the mixed extension principle and Walsh-Fourier transforms of the wavelet frames, an explicitly constructed method for a pair of dual periodic wavelet frames generated by the Walsh polynomials is also given.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 42A38
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 22B99
zbMATH DE Number: 6528866
zbMATH Keywords: periodic wavelet frame
zbMATH Keywords: extension principle
zbMATH Keywords: Walsh polynomial
zbMATH Keywords: Walsh-Fourier transform
reviewed by: Richard A. Zalik
MaRDI profile type: Publication
full work available at URL: math3041171
OpenAlex ID: W2181748088
cites work: Affine systems in \(L_ 2(\mathbb{R}^d)\): The analysis of the analysis operator
cites work: Framelets: MRA-based constructions of wavelet frames
cites work: Periodic wavelet frames
cites work: Constructions of periodic wavelet frames using extension principles
cites work: Wavelet frame based blind image inpainting
cites work: Wavelet frames on Vilenkin groups and their approximation properties
cites work: Extension principles for tight wavelet frames of periodic functions
cites work: The construction of multivariate periodic wavelet bi-frames
cites work: Orthogonal Wavelets on the Cantor Dyadic Group
cites work: On wavelets related to the Walsh series
cites work: Dyadic wavelet frames on a half-line using the Walsh–Fourier transform
cites work: CONSTRUCTION OF WAVELET PACKETS ON p-ADIC FIELD
cites work: p-Wavelet frame packets on a half-line using the Walsh–Fourier transform
cites work: Q4598654
cites work: Tight wavelet frames generated by the Walsh polynomials
DOI: 10.3390/MATH3041171
description: scientific article; zbMATH DE number 6528866