Dokument
| Titel: | Statistical Analysis of Audio Signals using Time-Frequency Analysis |
| Autor: | Tafo Noutseche, Idris Pavel |
| Weitere Beteiligte: | Holzmann, Hajo (Prof. Dr.) |
| Veröffentlicht: | 2023 |
| URI: | https://archiv.ub.uni-marburg.de/diss/z2023/0666 |
| DOI: | https://doi.org/10.17192/z2023.0666 |
| URN: | urn:nbn:de:hebis:04-z2023-06660 |
| DDC: | 510 Mathematik |
| Titel (trans.): | Statistische Analyse von Audiosignalen mittels Zeit-Frequenz-Analyse |
| Publikationsdatum: | 2023-11-20 |
| Lizenz: | https://creativecommons.org/licenses/by-nc-nd/4.0/ |
| Schlagwörter: |
|---|
| Zeit-Frequenz Analyse, Minimax, Gabor Frames, Frames,, time-frequency analysis, Thresholding, minimax, short-time Fourier transform, Gabor frame, Gabor transform, thresholding, short-time Fourier Transformation, Modulationsräume, alpha-modulation Räume, modulation spaces, alpha-modulation spaces |
Summary:
In this thesis, we provide nonparametric estimation of signals corrupted by stationary noise in the white noise model. We derive adaptive and rate-optimal estimators of signals in modulation spaces by thresholding the coefficients obtained from the Gabor expansion. The rates obtained using the classical oracle inequalities of Donoho and Johnstone (1994) exhibit new features that reflect the inclusion of both time and frequency. The scope of our results is extended to alpha-modulation spaces in the one-dimensional setting, allowing a comparison with Sobolev and Besov spaces. To confirm the practical applicability of our methods, we perform extensive simulations. These simulations evaluate the performance of our methods in comparison to state-of-the-art methods over a range of scenarios.
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