Continuous empirical wavelets systems
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914988363350016 |
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| author | Gilles, Jerome |
| author_facet | Gilles, Jerome |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Continuous empirical wavelets systems Gilles, Jerome Spectral Theory Functional Analysis 42C40 G.0 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. |
| title | Continuous empirical wavelets systems |
| topic | Spectral Theory Functional Analysis 42C40 G.0 |
| url | https://arxiv.org/abs/2410.19167 |