On construction of periodic wavelet frames

2018 ◽  
Vol 5 (1) ◽  
pp. 241-249
Author(s):  
Pavel Andrianov ◽  
Maria Skopina
Keyword(s):  
Wavelet Frames ◽  
Periodic Wavelet ◽  
Periodic Wavelet Frames

The Study of Tight Periodic Wavelet Frames and Wavelet Frame Packets and Applications

2014 ◽  
Vol 977 ◽  
pp. 532-535
Author(s):  
Qing Jiang Chen ◽  
Yu Zhou Chai ◽  
Chuan Li Cai
Keyword(s):  
Information Science ◽  
Approximation Order ◽  
Tight Frame ◽  
Extension Principle ◽  
Wavelet Frames ◽  
Decomposition Scheme ◽  
Periodic Wavelet ◽  
Unitary Extension ◽  
Periodic Wavelet Frames ◽  
Necessary And Sufficient

Information science focuses on understanding problems from the perspective of the stake holders involved and then applying information and other technologies as needed. A necessary and sufficient condition is identified in term of refinement masks for applying the unitary extension principle for periodic functions to construct tight wavelet frames. Then a theory on the approxi-mation order of truncated tight frame series is established, which facilitates construction of tight periodic wavelet frames with desirable approximation order. The pyramid decomposition scheme is derived based on the generalized multiresolution structure.

scholarly journals Construction of Periodic Wavelet Frames Generated by the Walsh Polynomials

Mathematics ◽  
2015 ◽  
Vol 3 (4) ◽  
pp. 1171-1191
Author(s):  
Sunita Goyal ◽  
Firdous Shah
Keyword(s):  
Wavelet Frames ◽  
Periodic Wavelet ◽  
Periodic Wavelet Frames

scholarly journals Construction of nonuniform periodic wavelet frames on non-Archimedean fields

2020 ◽  
Vol 74 (2) ◽  
pp. 1
Author(s):  
Owais Ahmad
Keyword(s):  
Real Life ◽  
Discrete Subgroup ◽  
Extension Principle ◽  
Mathematical Tool ◽  
Wavelet Frames ◽  
Spectral Pair ◽  
Periodic Wavelet ◽  
Spectral Pairs ◽  
Unitary Extension ◽  
Periodic Wavelet Frames

In real life applications not all signals are obtained by uniform shifts; so there is a natural question regarding analysis and decompositions of these types of signals by a stable mathematical tool. Gabardo and Nashed, and Gabardo and Yu filled this gap by the concept of nonuniform multiresolution analysis and nonuniform wavelets based on the theory of spectral pairs for which the associated translation set \(\Lambda= \{0,r/N\}+2\mathbb{Z}\) is no longer a discrete subgroup of \(\mathbb{R}\) but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair. In this paper, we introduce a notion of nonuniform periodic wavelet frame on non-Archimedean field. Using the Fourier transform technique and the unitary extension principle, we propose an approach for the construction of nonuniform periodic wavelet frames on non-Archimedean fields.

scholarly journals Tight periodic wavelet frames and approximation orders

2011 ◽  
Vol 31 (2) ◽  
pp. 228-248 ◽  
Author(s):  
Say Song Goh ◽  
Bin Han ◽  
Zuowei Shen
Keyword(s):  
Wavelet Frames ◽  
Periodic Wavelet ◽  
Periodic Wavelet Frames
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