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In the paper we obtain sufficient conditions for a trigonometric polynomial to be a refinement mask corresponding to a tight wavelet frame. The condition is formulated in terms of the roots of a mask. In particular, it is proved that any trigonometric polynomial can serve as a mask if its associated algebraic polynomial has only negative roots (at least one of them, of course, equals $-1$).
An explicit description of all Walsh polynomials generating tight wavelet frames is given. An algorithm for finding the corresponding wavelet functions is suggested, and a general form for all wavelet frames generated by an appropriate Walsh polynomi
In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be dilated by a procedure comparable to the operation of steering
We study $p$-adic multiresolution analyses (MRAs). A complete characterisation of test functions generating MRAs (scaling functions) is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions. We also suggest
The application of the continuous wavelet transform to study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies due to the admissibility condition. We propose an alternative reconstruction formu
This note outlines the steps for proving that the moments of a randomly-selected subset of a general ETF (complex, with aspect ratio $0<gamma<1$) converge to the corresponding MANOVA moments. We bring here an extension for the proof of the Kesten-Mck