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 secondorder 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 timebandwidth 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]}
 Argonne National Lab. (ANL), Lemont, IL (United States)
 Univ. of Chicago, Lemont, Chicago, IL (United States)
 Publication Date:
 Grant/Contract Number:
 AC0206CH11357
 Type:
 Accepted Manuscript
 Journal Name:
 IEEE Signal Processing Letters
 Additional Journal Information:
 Journal Volume: 24; Journal Issue: 11; Journal ID: ISSN 10709908
 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) (SC21)
 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 secondorder 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 timebandwidth 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}
}