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 - <p style="text-align: justify;">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.</p>