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Title: Optimal Bandwidth for Multitaper Spectrum Estimation

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.
Authors:
 [1] ;  [2]
  1. Argonne National Lab. (ANL), Lemont, IL (United States)
  2. Univ. of Chicago, Lemont, Chicago, IL (United States)
Publication Date:
Grant/Contract Number:
AC02-06CH11357
Type:
Accepted Manuscript
Journal Name:
IEEE Signal Processing Letters
Additional Journal Information:
Journal Volume: 24; Journal Issue: 11; Journal ID: ISSN 1070-9908
Publisher:
IEEE Signal Processing Society
Research Org:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Bandwidth; Cepstrum; Multitaper; Spectrum Analysis
OSTI Identifier:
1402465

Haley, Charlotte L., and Anitescu, Mihai. Optimal Bandwidth for Multitaper Spectrum Estimation. United States: N. p., Web. doi:10.1109/LSP.2017.2719943.
Haley, Charlotte L., & Anitescu, Mihai. Optimal Bandwidth for Multitaper Spectrum Estimation. United States. doi:10.1109/LSP.2017.2719943.
Haley, Charlotte L., and Anitescu, Mihai. 2017. "Optimal Bandwidth for Multitaper Spectrum Estimation". United States. doi:10.1109/LSP.2017.2719943. https://www.osti.gov/servlets/purl/1402465.
@article{osti_1402465,
title = {Optimal Bandwidth for Multitaper Spectrum Estimation},
author = {Haley, Charlotte L. and Anitescu, Mihai},
abstractNote = {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.},
doi = {10.1109/LSP.2017.2719943},
journal = {IEEE Signal Processing Letters},
number = 11,
volume = 24,
place = {United States},
year = {2017},
month = {7}
}