On construction of multidimensional periodic wavelet frames
https://doi.org/10.22405/2226-8383-2022-23-1-21-32
Abstract
Multidimensional periodic wavelet systems with matrix dilation in the framework of periodic multiresolution analyses are studied. In this work we use notion of a periodic multiresolution analysis, the most general definition of which was given by Maksimenko and M. Skopina in [25].
An algorithmic method of constructing multidimensional periodic dual wavelet frames from a suitable set of Fourier coefficients of one function is provided. This function is used as the first function in a scaling sequence that forms two periodic multiresolution analyses, which are used to construct wavelet systems. Conditions that the initial function has to satisfy are presented in terms of a certain rate of decay of its Fourier coefficients, and also mutual arrangement of zero and non-zero coefficients.
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Review
For citations:
Andreevich A.P. On construction of multidimensional periodic wavelet frames. Chebyshevskii Sbornik. 2022;23(1):21-32. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-1-21-32
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