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

Construction of shift-orthogonal wavelets using splines

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

HIGH APPROXIMATION ORDER BIORTHOGONAL MULTISCALING FUNCTIONS WITH DILATION FACTOR a

2010 ◽  
Vol 08 (06) ◽  
pp. 895-903 ◽  
Author(s):  
CHANGZHEN XIE
Keyword(s):  
Approximation Order ◽  
High Approximation ◽  
Dilation Factor ◽  
High Approximation Order ◽  
Special Case ◽  
Multiscaling Function

An algorithm is presented for constructing a pair of high approximation order biorthogonal multiscaling function with dilation factor a in terms of any given pair of biorthogonal multiscaling function. The special case that a = 2 is discussed. If the dilation factor a = 2, then a biorthogonal multiwavelet pair is constructed explicitly. Finally, examples are given.

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. .

Orthonormal basis of wavelets with customizable frequency bands

2016 ◽  
Vol 14 (06) ◽  
pp. 1650050 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang
Keyword(s):  
Frequency Domain ◽  
Infinite Number ◽  
Orthonormal Basis ◽  
The Other ◽  
Just Intonation ◽  
Frequency Bands ◽  
Orthonormal Bases ◽  
Major Scale ◽  
Dilation Factor ◽  
New Type

We already proved the existence of an orthonormal basis of wavelets having an irrational dilation factor with an infinite number of wavelet shapes, and based on its theory, we proposed an orthonormal basis of wavelets with an arbitrary real dilation factor. In this paper, with the development of these fundamentals, we propose a new type of orthonormal basis of wavelets with customizable frequency bands. Its frequency bands can be freely designed with arbitrary bounds in the frequency domain. For example, we show two types of orthonormal bases of wavelets. One of them has an irrational dilation factor, and the other is designed based on the major scale in just intonation.

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