A characterization of dimension functions of a class of semi-orthogonal Parseval frame wavelets

2014 ◽  
Vol 38 (4) ◽  
pp. 751-764 ◽  
Author(s):  
Yun-Zhang Li ◽  
Nan Lan
Keyword(s):  
Parseval Frame ◽  
Dimension Functions ◽  
Frame Wavelets

scholarly journals Characterizations of Tight Frame Wavelets with Special Dilation Matrices

2010 ◽  
Vol 2010 ◽  
pp. 1-26 ◽  
Author(s):  
Huang Yongdong ◽  
Zhu Fengjuan
Keyword(s):  
Linear Space ◽  
Multiresolution Analysis ◽  
Nonnegative Integer ◽  
Tight Frame ◽  
Dilation Matrix ◽  
Low Pass ◽  
Dimension Functions ◽  
Frame Wavelets ◽  
Low Pass Filters

We study all generalized low-pass filters and tight frame wavelets with special dilation matrixM(M-TFW), whereMsatisfiesMd=2Idand generates the checkerboard lattice. Firstly, we study the pseudoscaling function, generalized low-pass filters and multiresolution analysis tight frame wavelets with dilation matrixM(MRA M-TFW), and also give some important characterizations about them. Then, we characterize all M-TFW by showing precisely their corresponding dimension functions which are nonnegative integer valued. Finally, we also show that an M-TFW arises from our MRA construction if and only if the dimension of a particular linear space is either zero or one.

Semi-orthogonal wavelet frames on local fields

Analysis ◽  
2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Firdous A. Shah ◽  
M. Younus Bhat
Keyword(s):  
Finite Number ◽  
Positive Characteristic ◽  
Local Fields ◽  
Wavelet Frames ◽  
Orthogonal Wavelet ◽  
Basic Equations ◽  
Frame Multiresolution Analysis ◽  
Frame Wavelets ◽  
Equivalent Conditions

AbstractWe investigate semi-orthogonal wavelet frames on local fields of positive characteristic and provide a characterization of frame wavelets by means of some basic equations in the frequency domain. The theory of frame multiresolution analysis recently proposed by Shah [J. Operators (2015), Article ID 216060] on local fields is used to establish equivalent conditions for a finite number of functions

Semi-Orthogonal Parseval Wavelets Frames on Local Fields and Applications in Manufacturing Science

2013 ◽  
Vol 712-715 ◽  
pp. 2464-2468
Author(s):  
Shi Heng Wang
Keyword(s):  
Local Fields ◽  
Affine Subspace ◽  
Parseval Frame ◽  
Direct Sum ◽  
Reducing Subspaces ◽  
Dilation Factor ◽  
Definition Of ◽  
Frame Wavelets ◽  
Manufacturing Science ◽  
Orthogonal Frame

Manufacturing science focuses on understanding problems from the perspective of the stakeholders involved and then applying manufacturing science as needed. We investigate semi-orthogonal frame wavelets and Parseval frame wavelets in with a dilation factor. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces. This result is obtained through considering the basicquestion as to when the orthogonal complement of an afffine subspace in another one is still affine subspace.The definition of multiple pseudofames for subspaces with integer translation is proposed. The notion of a generalized multiresolution structure of is also introduced. The construction of a generalized multireso-lution structure of Paley-Wiener subspaces of is investigated.

scholarly journals MRA Parseval Frame Wavelets and Their Multipliers inL2(Rn)

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Wu Guochang ◽  
Yang Xiaohui ◽  
Liu Zhanwei
Keyword(s):  
Multiresolution Analysis ◽  
Scaling Functions ◽  
Parseval Frame ◽  
Integer Coefficients ◽  
Frame Wavelets

We characterize all generalized lowpass filters and multiresolution analysis(MRA) Parseval frame wavelets inL2(Rn)with matrix dilations of the form(Df)(x)=2f(Ax), where A is an arbitrary expandingn×nmatrix with integer coefficients, such that|det⁡A|=2. At first, we study the pseudo-scaling functions, generalized lowpass filters, and multiresolution analysis (MRA) Parseval frame wavelets and give some important characterizations about them. Then, we describe the multiplier classes associated with Parseval frame wavelets inL2(Rn)and give an example to prove our theory.

scholarly journals Further results on the connectivity of Parseval frame wavelets

2006 ◽  
Vol 134 (11) ◽  
pp. 3211-3221 ◽  
Author(s):  
G. Garrigós ◽  
E. Hernández ◽  
H. Šikić ◽  
F. Soria
Keyword(s):  
Parseval Frame ◽  
Frame Wavelets

The Description and Characterization of Symmetric Frames and Gabor Frames and Applications in Material Engineering

2013 ◽  
Vol 712-715 ◽  
pp. 2458-2463
Author(s):  
Qing Jiang Chen ◽  
Xiao Ting Lei ◽  
Jian Feng Zhou
Keyword(s):  
Legendre Polynomials ◽  
Materials Science ◽  
Tight Frame ◽  
Simple Approach ◽  
Gabor Frames ◽  
Wavelet Frames ◽  
Science And Engineering ◽  
Interdisciplinary Field ◽  
Frame Wavelets

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this paper, we discuss a new set of symmetric tight frame wave-lets with the associated filterbanks outputs downsampled by several generators. The frames consist of several generators obtained from the lowpass filter using spectral factorization, with lowpass fil-ter via a simple approach using Legendre polynomials. The filters are feasible to be designed and offer smooth scaling functions and frame wavelets. We shall give an example to demonstrste that so -me examples of symmetric tight wavelet frames with three compactly supported real-valued sym- metric generators will be presented to illustrate the results.

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