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• W3136361142 abstract "Thomson's multitaper method estimates the power spectrum of a signal from $N$ equally spaced samples by averaging $K$ tapered periodograms. Discrete prolate spheroidal sequences (DPSS) are used as tapers since they provide excellent protection against spectral leakage. Thomson's multitaper method is widely used in applications, but most of the existing theory is qualitative or asymptotic. Furthermore, many practitioners use a DPSS bandwidth $W$ and number of tapers that are smaller than what the theory suggests is optimal because the computational requirements increase with the number of tapers. We revisit Thomson's multitaper method from a linear algebra perspective involving subspace projections. This provides additional insight and helps us establish nonasymptotic bounds on some statistical properties of the multitaper spectral estimate, which are similar to existing asymptotic results. We show using $K=2NW-O(log(NW))$ tapers instead of the traditional $2NW-O(1)$ tapers better protects against spectral leakage, especially when the power spectrum has a high dynamic range. Our perspective also allows us to derive an $epsilon$-approximation to the multitaper spectral estimate which can be evaluated on a grid of frequencies using $O(log(NW)logtfrac{1}{epsilon})$ FFTs instead of $K=O(NW)$ FFTs. This is useful in problems where many samples are taken, and thus, using many tapers is desirable." @default.
• W3136361142 created "2021-03-29" @default.
• W3136361142 creator A5041443633 @default.
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• W3136361142 date "2021-03-22" @default.
• W3136361142 modified "2023-09-27" @default.
• W3136361142 title "Thomson's Multitaper Method Revisited." @default.
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• W3136361142 hasPublicationYear "2021" @default.
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