MSE Estimates for Multitaper Spectral Estimation and Off-Grid Compressive Sensing
In: IEEE Transactions on Information Theory, Jg. 63 (2017-12-01), S. 7770-7776
Online
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Zugriff:
We obtain estimates for the Mean Squared Error (MSE) for the multitaper spectral estimator and certain compressive acquisition methods for multi-band signals. We confirm a fact discovered by Thomson [Spectrum estimation and harmonic analysis, Proc. IEEE, 1982]: assuming bandwidth $W$ and $N$ time domain observations, the average of the square of the first $K=2NW$ Slepian functions approaches, as $K$ grows, an ideal band-pass kernel for the interval $[-W,W]$. We provide an analytic proof of this fact and measure the corresponding rate of convergence in the $L^{1}$ norm. This validates a heuristic approximation used to control the MSE of the multitaper estimator. The estimates have also consequences for the method of compressive acquisition of multi-band signals introduced by Davenport and Wakin, giving MSE approximation bounds for the dictionary formed by modulation of the critical number of prolates.
Comment: 16 pages, 2 figures. (This article replaces arXiv: 1503.02991.)
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MSE Estimates for Multitaper Spectral Estimation and Off-Grid Compressive Sensing
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Autor/in / Beteiligte Person: | José Luis Romero ; Luís Daniel Abreu |
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Zeitschrift: | IEEE Transactions on Information Theory, Jg. 63 (2017-12-01), S. 7770-7776 |
Veröffentlichung: | Institute of Electrical and Electronics Engineers (IEEE), 2017 |
Medientyp: | unknown |
ISSN: | 1557-9654 (print) ; 0018-9448 (print) |
DOI: | 10.1109/tit.2017.2718963 |
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