Optimal Bandwidth for Multitaper Spectrum Estimation

doi:10.1109/LSP.2017.2719943

Title: Optimal Bandwidth for Multitaper Spectrum Estimation

Article Details
Other Related Research

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:

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

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

Publication Date:: 2017-07-04

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.

Copy to clipboard


                    Haley, Charlotte L., & Anitescu, Mihai. Optimal Bandwidth for Multitaper Spectrum Estimation.  United States.  doi:10.1109/LSP.2017.2719943.

Copy to clipboard


                    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.

Copy to clipboard


                    
@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}

}

Copy to clipboard

Free Publicly Accessible Full Text
Accepted Manuscript (DOE)
Publisher's Version of Record
10.1109/LSP.2017.2719943
https://doi.org/10.1109/LSP.2017.2719943

Similar Records

Similar records in DOE PAGES and OSTI.GOV collections:

Optimal Spectrum Estimation in Statistical Mechanics

Journal Article - in OSTI.gov collection Wheeler, Ralph ; Haitao, Dong November 2002 - Chemphyschem

In statistical mechanics, spectrum estimation is traditionally done by computing Fourier transforms of time-correlation functions[1]-[3] to find the amplitudes of frequency components that fit best the observed data (assuming each component is the only one present). Examples of important time correlation functions include the van Hove, dipole density, and magnetization correlation functions, whose Fourier transforms are related to the structure factor, infrared lineshape, and NMR signal lineshape, respectively.[4],[5] Although the Fourier transform is extremely general, crucial restrictions limiting its applications in statistical mechanics include assumptions of periodic or stationary time series and a linear system, so that data may bemore »« less
Bandwidth optimization of femtosecond pure-rotational coherent anti-Stokes Raman scattering by pump/Stokes spectral focusing.

Journal Article Kearney, Sean Patrick July 2014 - Applied Optics

A simple spectral focusing scheme for bandwidth optimization of gas-phase rotational coherent anti-Stokes Raman scattering (CARS) spectra is presented. The method is useful when femtosecond pump/Stokes preparation of the Raman coherence is utilized. The approach is of practical utility when working with laser pulses that are not strictly transform limited, or when windows or other sources of pulse chirp may be present in the experiment. A delay between the femtosecond preparation pulses is introduced to shift the maximum Raman preparation away from zero frequency and toward the Stokes or anti-Stokes side of the spectrum with no loss in total preparationmore »« less
Cited by 9Full Text Available
Nanometer resolution optical coherence tomography using broad bandwidth XUV and soft x-ray radiation

Journal Article Fuchs, Silvio ; Rödel, Christian ; Blinne, Alexander ; ... February 2016 - Scientific Reports

Optical coherence tomography (OCT) is a non-invasive technique for cross-sectional imaging. It is particularly advantageous for applications where conventional microscopy is not able to image deeper layers of samples in a reasonable time, e.g. in fast moving, deeper lying structures. However, at infrared and optical wavelengths, which are commonly used, the axial resolution of OCT is limited to about 1 μm, even if the bandwidth of the light covers a wide spectral range. Here, we present extreme ultraviolet coherence tomography (XCT) and thus introduce a new technique for non-invasive cross-sectional imaging of nanometer structures. XCT exploits the nanometerscale coherence lengthsmore »« less
Cited by 5Full Text Available
Low Group Delay Dispersion Optical Coating for Broad Bandwidth High Reflection at 45° Incidence, P Polarization of Femtosecond Pulses with 900 nm Center Wavelength

Journal Article Bellum, John C. ; Field, Ella S. ; Winstone, Trevor B. ; ... March 2016 - Coatings

We describe an optical coating design suitable for broad bandwidth high reflection (BBHR) at 45° angle of incidence (AOI), P polarization (Ppol) of femtosecond (fs) laser pulses whose wavelengths range from 800 to 1000 nm. The design process is guided by quarter-wave HR coating properties. Our design must afford low group delay dispersion (GDD) for reflected light over the broad, 200 nm bandwidth in order to minimize temporal broadening of the fs pulses due to dispersive alteration of relative phases between their frequency components. The design should also be favorable to high laser-induced damage threshold (LIDT). We base the coatingmore »« less
Cited by 4Full Text Available
Significantly Improving Regional Seismic Amplitude Tomography at Higher Frequencies by Determining S -Wave Bandwidth

Journal Article Fisk, Mark D. ; Pasyanos, Michael E. May 2016 - Bulletin of the Seismological Society of America

Characterizing regional seismic signals continues to be a difficult problem due to their variability. Calibration of these signals is very important to many aspects of monitoring underground nuclear explosions, including detecting seismic signals, discriminating explosions from earthquakes, and reliably estimating magnitude and yield. Amplitude tomography, which simultaneously inverts for source, propagation, and site effects, is a leading method of calibrating these signals. A major issue in amplitude tomography is the data quality of the input amplitude measurements. Pre-event and prephase signal-to-noise ratio (SNR) tests are typically used but can frequently include bad signals and exclude good signals. The deficiencies ofmore »« less
Cited by 1Full Text Available

Access journal articles and accepted manuscripts resulting from DOE research funding

Title: Optimal Bandwidth for Multitaper Spectrum Estimation

Access journal articles and accepted manuscripts
resulting from DOE research funding