Regularity of generalized Daubechies wavelets reproducing exponential polynomials
N. Dyn, O. Kounchev, D. Levin, H. Render
TL;DR
This paper studies non-stationary orthogonal wavelets that reproduce exponential polynomials, demonstrating their smoothness and extending Daubechies wavelet theory to a broader class of functions.
Contribution
It introduces a new class of Daubechies-type wavelets based on non-stationary subdivision schemes that reproduce exponential polynomials.
Findings
Wavelets are shown to be smooth.
Construction parallels Deslauriers-Dubuc subdivision.
Reproduction of exponential polynomials achieved.
Abstract
We investigate non-stationary orthogonal wavelets based on a non-stationary interpolatory subdivision scheme reproducing a given set of exponentials. The construction is analogous to the construction of Daubechies wavelets using the subdivision scheme of Deslauriers-Dubuc. The main result is the smoothness of these Daubechies type wavelets.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Image and Signal Denoising Methods · Digital Filter Design and Implementation