Optimal Bandwidth for Multitaper Spectrum Estimation

Journal Article · 03 July 2017 · IEEE Signal Processing Letters

DOI: https://doi.org/10.1109/LSP.2017.2719943 · OSTI ID:1402465

Haley, Charlotte L. ^[1]; Anitescu, Mihai ^[2]

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1. Argonne National Lab. (ANL), Lemont, IL (United States)
2. Univ. of Chicago, Lemont, Chicago, IL (United States)

A systematic method for bandwidth parameter selection is desired for Thomson multitaper spectrum estimation. We give a method for determining the optimal bandwidth based on a mean squared error (MSE) criterion. When the true spectrum has a second-order Taylor series expansion, one can express quadratic local bias as a function of the curvature of the spectrum, which can be estimated by using a simple spline approximation. This is combined with a variance estimate, obtained by jackknifing over individual spectrum estimates, to produce an estimated MSE for the log spectrum estimate for each choice of time-bandwidth product. The bandwidth that minimizes the estimated MSE then gives the desired spectrum estimate. Additionally, the bandwidth obtained using our method is also optimal for cepstrum estimates. We give an example of a damped oscillatory (Lorentzian) process in which the approximate optimal bandwidth can be written as a function of the damping parameter. Furthermore, the true optimal bandwidth agrees well with that given by minimizing estimated the MSE in these examples.

• Research Organization: Argonne National Lab. (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 1402465
• Journal Information: IEEE Signal Processing Letters, Journal Name: IEEE Signal Processing Letters Journal Issue: 11 Vol. 24; ISSN 1070-9908
• Publisher: IEEE Signal Processing SocietyCopyright Statement
• Country of Publication: United States
• Language: English