Thomson’s Multitaper Method Revisited

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