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Volume 32, Issue 2
A Characterization of MRA Based Wavelet Frames Generated by the Walsh Polynomials

F. A. Shah & S. Goyal

Anal. Theory Appl., 32 (2016), pp. 164-173.

Published online: 2016-04

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  • Abstract

Extension Principles play a significant role in the construction of MRA based wavelet frames and have attracted much attention for their potential applications in various scientific fields. A novel and simple procedure for the construction of tight wavelet frames generated by the Walsh polynomials using Extension Principles was recently considered by Shah in [Tight wavelet frames generated by the Walsh polynomials, Int. J. Wavelets, Multiresolut. Inf. Process., 11(6) (2013), 1350042]. In this paper, we establish a complete characterization of tight wavelet frames generated by the Walsh polynomials in terms of the polyphase matrices formed by the polyphase components of the Walsh polynomials.

  • AMS Subject Headings

42C15, 42C40, 42A38, 41A17, 22B99

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COPYRIGHT: © Global Science Press

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@Article{ATA-32-164, author = {}, title = {A Characterization of MRA Based Wavelet Frames Generated by the Walsh Polynomials}, journal = {Analysis in Theory and Applications}, year = {2016}, volume = {32}, number = {2}, pages = {164--173}, abstract = {

Extension Principles play a significant role in the construction of MRA based wavelet frames and have attracted much attention for their potential applications in various scientific fields. A novel and simple procedure for the construction of tight wavelet frames generated by the Walsh polynomials using Extension Principles was recently considered by Shah in [Tight wavelet frames generated by the Walsh polynomials, Int. J. Wavelets, Multiresolut. Inf. Process., 11(6) (2013), 1350042]. In this paper, we establish a complete characterization of tight wavelet frames generated by the Walsh polynomials in terms of the polyphase matrices formed by the polyphase components of the Walsh polynomials.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2016.v32.n2.5}, url = {http://global-sci.org/intro/article_detail/ata/4662.html} }
TY - JOUR T1 - A Characterization of MRA Based Wavelet Frames Generated by the Walsh Polynomials JO - Analysis in Theory and Applications VL - 2 SP - 164 EP - 173 PY - 2016 DA - 2016/04 SN - 32 DO - http://doi.org/10.4208/ata.2016.v32.n2.5 UR - https://global-sci.org/intro/article_detail/ata/4662.html KW - Frame, wavelet frame, polyphase matrix, extension principles, Walsh polynomial, Walsh-Fourier transform. AB -

Extension Principles play a significant role in the construction of MRA based wavelet frames and have attracted much attention for their potential applications in various scientific fields. A novel and simple procedure for the construction of tight wavelet frames generated by the Walsh polynomials using Extension Principles was recently considered by Shah in [Tight wavelet frames generated by the Walsh polynomials, Int. J. Wavelets, Multiresolut. Inf. Process., 11(6) (2013), 1350042]. In this paper, we establish a complete characterization of tight wavelet frames generated by the Walsh polynomials in terms of the polyphase matrices formed by the polyphase components of the Walsh polynomials.

F. A. Shah & S. Goyal. (1970). A Characterization of MRA Based Wavelet Frames Generated by the Walsh Polynomials. Analysis in Theory and Applications. 32 (2). 164-173. doi:10.4208/ata.2016.v32.n2.5
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