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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

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-32-164, author = {F. A. Shah and S. Goyal}, 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 AU - F. A. Shah & S. Goyal 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 and S. Goyal. (2016). 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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