A Characterization of MRA Based Wavelet Frames Generated by the Walsh Polynomials |
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| Authors: | Firdous A Shah Sunita Goyal |
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| Institution: | 1. Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India;2. Department of Mathematics, JJT University, Jhunjhunu-333001, Rajasthan, India |
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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 poly-nomials, 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. |
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| Keywords: | Frame wavelet frame polyphase matrix extension principles Walsh polynomial Walsh-Fourier transform |
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