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arXiv · 2410.19167

Continuous empirical wavelets systems

Jerome Gilles
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Abstract

The recently proposed empirical wavelet transform was based on a particular type of filter. In this paper, we aim to propose a general framework for the construction of empirical wavelet systems in the continuous case. We define a well-suited formalism and then investigate some general properties of empirical wavelet systems. In particular, we provide some sufficient conditions to the existence of a reconstruction formula. In the second part of the paper, we propose the construction of empirical wavelet systems based on some classic mother wavelets.

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Jerome Gilles. 2024-10-24. Continuous empirical wavelets systems. https://doi.org/10.1142/s2424922x20500060

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