Non-Separable Meyer-like Wavelet Frames

Zhihua Zhang
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Zhihua Zhang: School of Mathematics, Shandong University, Jinan 250100, China

Mathematics, 2022, vol. 10, issue 13, 1-14

Abstract: In the theory of wavelet frames, the known Daubechies wavelet bases have been generalized to compactly supported (Daubechies-like) wavelet frames, while the known bandlimited Meyer wavelet bases have not been generalized to date. In this study, we will generalize known Meyer wavelet basis into non-separable Meyer-like wavelet frames. By using a characteristic function to mask the Fourier transform of the one-dimensional Meyer scaling function with a width parameter, we can produce a family of Meyer-like frame scaling functions and associated Meyer-like wavelet frames. After that, by inserting a real-valued function into the width parameter of a one-dimensional Meyer-like frame scaling function, we propose a novel approach to construct non-separable Meyer-like frame scaling functions with unique circular symmetry. Finally, we construct the corresponding non-separable Meyer-like wavelet frames.

Keywords: wavelet frame; non-separable frames; Meyer-like frames (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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