Journal ArticleDOI
Discrete wavelets and the Vilenkin-Chrestenson transform
TLDR
In this article, the Vilenkin-Chrestenson transforms are used to construct new orthogonal wavelet bases defined by finite collections of parameters in the spaces of complex periodic sequences.Abstract:
In the spaces of complex periodic sequences, we use the Vilenkin-Chrestenson transforms to construct new orthogonal wavelet bases defined by finite collections of parameters. Earlier similar bases were defined for the Cantor and Vilenkin groups by means of generalized Walsh functions. It is noted that similar constructions can be realized for biorthogonal wavelets as well as for the space l2(ℤ+).read more
Citations
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Journal ArticleDOI
Examples of frames on the Cantor dyadic group
TL;DR: In this paper, a Parseval frame related to the generalized Walsh-Dirichlet kernel and a Daubechies-type "admissible condition" were constructed on the locally compact Cantor dyadic group.
Journal ArticleDOI
Periodic wavelets on the p -adic Vilenkin group
TL;DR: Using the Walsh-Dirichlet type kernel, periodic wavelets on the p-adic Vilenkin group are constructed, similar to the trigonometric wavelets which were introduced by C. K. Chui and H. N. Mhaskar.
Journal ArticleDOI
Periodic Wavelets in Walsh Analysis
TL;DR: In this article, a review of wavelets related to generalized Walsh functions on the p-adic Vilenkin group Gp is presented, where wavelets in the spaces of periodic complex sequences are considered.
Journal ArticleDOI
On biorthogonal discrete wavelet bases
Yu. A. Farkov,E. A. Rodionov +1 more
TL;DR: The proposed method to construct of biorthogonal N-periodic discrete MRA wavelets on the basis of generalized Walsh functions is illustrated by a numerical example.
Journal ArticleDOI
Periodic dyadic wavelets and coding of fractal functions
Yu. A. Farkov,M. E. Borisov +1 more
TL;DR: In this article, the first author has defined periodic dyadic wavelets on the positive semiaxis which are similar to the Chui-Mhaskar trigonometric wavelets.
References
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Book
A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Book
An introduction to wavelets through linear algebra
TL;DR: In this paper, the authors present the first stage of construction of Wavelet on $bZ_N$: The First Stage 3.2 The Iteration Step for Wavelets on$bZ$ 4.3 The Fast Fourier Transform 3.5 First-Stage Wavelets 4.7 Implementation and Examples 5 Wavelet-Galerkin Methods for Differential Equations 6.3 Multiresolution Analysis and Wavelets 5.5 Wavelets with Compact Support and Their Computation 6 Wavelets and Differential Eq 6.1 The Condition Number of a Matrix
Book
Walsh Series and Transforms: Theory and Applications
TL;DR: In this article, the authors define the Walsh functions on the interval [0, 1] and the Walsh Fourier series as a generalization of the Fourier-Stieltjes series.
Wavelet analysis on the cantor dyadic group
TL;DR: In this article, exactly supported orthogonal wavelets are built on the Can- tor dyadic group (the dyadic or a-series local field), and sufficient conditions are given on a trigonometric polynomial scaling filter for a mul- tiresolution analysis to result.
Book
Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing
S. Allen Broughton,Kurt Bryan +1 more
TL;DR: This work focuses on the development of discrete wavelet transforms for convolution and filtering in the time domain and frequency domain, and on the design of filter banks for these transformations.