Construction of Periodic Wavelet Frames Generated by the Walsh Polynomials

Mathematics

Sunita Goyal¹  Firdous A. Shah² 

[1] Department of Mathematics, Shri Jagdishprasad Jhabarmal Tibrewala University (JJTU), Jhunjhunu 333001, Rajasthan, India;Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India;

关键词: periodic wavelet frame;    extension principle;    Walsh polynomial;    Walsh–Fourier transform;   

DOI  :  10.3390/math3041171

来源: DOAJ

【 摘 要 】

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 onR+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 onR + . Then, we construct a pair of dual periodic wavelet frames generated by the Walsh polynomials onR +using the machinery of the mixed extension principle and Walsh–Fourier transforms.

【 授权许可】

Unknown