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• W2603318838 abstract "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 bandpass kernel for the interval [-W, W]. We provide an analytic proof of this fact and measure the corresponding rate of convergence in L <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sup> 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." @default.
• W2603318838 created "2017-04-07" @default.
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• W2603318838 date "2017-12-01" @default.
• W2603318838 modified "2023-10-15" @default.
• W2603318838 title "MSE Estimates for Multitaper Spectral Estimation and Off-Grid Compressive Sensing" @default.
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• W2603318838 doi "https://doi.org/10.1109/tit.2017.2718963" @default.
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