Statistical Analysis of Audio Signals using Time-Frequency Analysis
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 class...
Gespeichert in:
主要作者: | |
---|---|
其他作者: | |
格式: | Dissertation |
語言: | 英语 |
出版: |
Philipps-Universität Marburg
2023
|
主題: | |
在線閱讀: | PDF-Volltext |
標簽: |
添加標簽
沒有標簽, 成為第一個標記此記錄!
|
總結: | 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. |
---|---|
DOI: | 10.17192/z2023.0666 |