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 procedur...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.展开更多
This paper proves the inexistence of symmetric,orthonormal and commpactly supported three-band wavelet system with the length（6,m,n） in terms of the method of polyphase matrix representation.
基金Supported by National Science Foundation of China(11171103)Science Foundation of Hunan Education Office(13C624+1 种基金13C621)Science Foundation of Hunan University of Arts and Science(13ZD01)
文摘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.
基金Supported by the National Natural Science Foundation of China (Grant Nos.1072606410901018)
文摘This paper proves the inexistence of symmetric,orthonormal and commpactly supported three-band wavelet system with the length（6,m,n） in terms of the method of polyphase matrix representation.
