Next Article in Journal
HIV vs. the Immune System: A Differential Game
Previous Article in Journal
Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function
Open AccessArticle

Construction of Periodic Wavelet Frames Generated by the Walsh Polynomials

1
Department of Mathematics, Shri Jagdishprasad Jhabarmal Tibrewala University (JJTU), Jhunjhunu 333001, Rajasthan, India
2
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
*
Author to whom correspondence should be addressed.
Academic Editor: Palle E. T. Jorgensen
Mathematics 2015, 3(4), 1171-1191; https://doi.org/10.3390/math3041171
Received: 24 August 2015 / Revised: 20 November 2015 / Accepted: 20 November 2015 / Published: 3 December 2015
An explicit method for the construction of a tight wavelet frame generated by the Walsh polynomials with the help of extension principles was presented by Shah (Shah, 2013). In this article, we extend the notion of wavelet frames to periodic wavelet frames generated by the Walsh polynomials on R+ by using extension principles. We first show that under some mild conditions, the periodization of any wavelet frame constructed by the unitary extension principle is still a periodic wavelet frame on R + . Then, we construct a pair of dual periodic wavelet frames generated by the Walsh polynomials on R + using the machinery of the mixed extension principle and Walsh–Fourier transforms. View Full-Text
Keywords: periodic wavelet frame; extension principle; Walsh polynomial; Walsh–Fourier transform periodic wavelet frame; extension principle; Walsh polynomial; Walsh–Fourier transform
MDPI and ACS Style

Goyal, S.; Shah, F.A. Construction of Periodic Wavelet Frames Generated by the Walsh Polynomials. Mathematics 2015, 3, 1171-1191.

Show more citation formats Show less citations formats

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop