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...
محفوظ في:
| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | |
| التنسيق: | Dissertation |
| اللغة: | الإنجليزية |
| منشور في: |
Philipps-Universität Marburg
2023
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| الموضوعات: | |
| الوصول للمادة أونلاين: | PDF النص الكامل |
| الوسوم: |
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| الملخص: | 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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| وصف مادي: | 146 Seiten |
| DOI: | 10.17192/z2023.0666 |