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Mathematics 2015, 3(4), 1171-1191; doi:10.3390/math3041171

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
Received: 24 August 2015 / Revised: 20 November 2015 / Accepted: 20 November 2015 / Published: 3 December 2015
View Full-Text   |   Download PDF [250 KB, uploaded 3 December 2015]

Abstract

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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

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

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