Wandering vectors for unitary systems and orthogonal wavelets

1998 ◽  
Vol 134 (640) ◽  
pp. 0-0 ◽  
Author(s):  
Xingde Dai ◽  
David R. Larson
Keyword(s):  
Orthogonal Wavelets ◽  
Wandering Vectors

Construction of shift-orthogonal wavelets using splines

1996 ◽  
Author(s):  
Michael A. Unser ◽  
Philippe Thevenaz ◽  
Akram Aldroubi
Keyword(s):  
Orthogonal Wavelets

scholarly journals Multiresolution analysis and wavelets on Vilenkin groups

2008 ◽  
Vol 21 (3) ◽  
pp. 309-325 ◽  
Author(s):  
Yury Farkov
Keyword(s):  
Multiresolution Analysis ◽  
Linear Independence ◽  
Sufficient Conditions ◽  
Partition Of Unity ◽  
Necessary And Sufficient Conditions ◽  
Refinable Functions ◽  
Vilenkin Groups ◽  
Orthogonal Wavelets ◽  
The Stability ◽  
Necessary And Sufficient

This paper gives a review of multiresolution analysis and compactly sup- ported orthogonal wavelets on Vilenkin groups. The Strang-Fix condition, the partition of unity property, the linear independence, the stability, and the orthonormality of 'integer shifts' of the corresponding refinable functions are considered. Necessary and sufficient conditions are given for refinable functions to generate a multiresolution analysis in the L2-spaces on Vilenkin groups. Several examples are provided to illustrate these results. .

Symmetric orthogonal wavelets with dilation factor M = 3

2013 ◽  
Vol 194 (6) ◽  
pp. 667-677 ◽  
Author(s):  
A. V. Krivoshein ◽  
M. A. Ogneva
Keyword(s):  
Orthogonal Wavelets ◽  
Dilation Factor

K-L Expansion of a Random Process in Wavelet Bases

1998 ◽  
Author(s):  
Om P. Agrawal ◽  
Shantaram S. Pai
Keyword(s):  
Eigenvalue Problem ◽  
Wavelet Transforms ◽  
Series Representation ◽  
Numerical Algorithms ◽  
Analytical Techniques ◽  
Random Processes ◽  
Random Coefficients ◽  
Engineering Systems ◽  
Wavelet Bases ◽  
Orthogonal Wavelets

Abstract Random processes play a significant role in stochastic analysis of mechanical systems, structures, fluid mechanics, and other engineering systems. In this paper, a numerical method for series representation of random processes, with specified mean and correlation functions, in wavelet bases is presented. In this method, the Karhunen-Loeve expansion approach is used to represent a process as a linear sum of orthonormal eigenfunctions with uncorrelated random coefficients. The correlation and the eigenfunctions are approximated as truncated linear sums of compactly supported orthogonal wavelets. The eigenfunctions satisfy an integral eigenvalue problem. Using the above approximations, the integral eigenvalue problem is converted to a matrix (finite dimensional) eigenvalue problem. Numerical algorithms are discussed to compute one- and two-dimensional wavelet transforms of certain functions, and the resulting equations are solved to obtain the eigenvalues and the eigenfunctions. The scheme provides an improvement over other existing schemes. Two examples are considered to show the feasibility and effectiveness of this method. Numerical studies show that the results obtained using this method compare well with analytical techniques.

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