A class of non linear adaptive time-frequency transforms
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929388399886336 |
|---|---|
| author | Warion, Pierre Torrésani, Bruno |
| author_facet | Warion, Pierre Torrésani, Bruno |
| contents | This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as a function of the time variable, or the frequency variable. In this respect, these transforms are non-linear, which makes the analysis more complex than usual.Under appropriate assumptions, some norm control can be obtained for both transforms in L^2(R) spaces, which extend the classical continuous frame norm control and guarantees well-definedness on L^2. Given the non-linearity of the transforms, the existence of inverse transforms is not guaranteed anymore, and is an open question. However, the results of this paper represent a first step towards a more general theory.Besides mathematical results, some elementary examples of time and frequency focus functions are provided, which can serve as staring point for concrete applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14550 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A class of non linear adaptive time-frequency transforms Warion, Pierre Torrésani, Bruno Classical Analysis and ODEs Signal Processing This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as a function of the time variable, or the frequency variable. In this respect, these transforms are non-linear, which makes the analysis more complex than usual.Under appropriate assumptions, some norm control can be obtained for both transforms in L^2(R) spaces, which extend the classical continuous frame norm control and guarantees well-definedness on L^2. Given the non-linearity of the transforms, the existence of inverse transforms is not guaranteed anymore, and is an open question. However, the results of this paper represent a first step towards a more general theory.Besides mathematical results, some elementary examples of time and frequency focus functions are provided, which can serve as staring point for concrete applications. |
| title | A class of non linear adaptive time-frequency transforms |
| topic | Classical Analysis and ODEs Signal Processing |
| url | https://arxiv.org/abs/2306.14550 |