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Multitaper estimation on arbitrary domains [article]

Joakim Andén, José Luis Romero
2020 arXiv   pre-print
We also prove a set of performance bounds for multitaper estimators on arbitrary domains.  ...  Multitaper estimators have enjoyed significant success in estimating spectral densities from finite samples using as tapers Slepian functions defined on the acquisition domain.  ...  Section 4 provides a bound for the mean squared error of the multitaper estimator for arbitrary domains.  ... 
arXiv:1812.03225v3 fatcat:x7md4dyv3je75ech2nzq4jolfm

A Multitaper Frequency-Domain Bootstrap Method

Seong-Eun Kim, Demba Ba, Emery N. Brown
2018 IEEE Signal Processing Letters  
The multitaper method is optimal for minimizing the bias-variance tradeoff in spectral estimation.  ...  To develop a statistical inference approach that considers the spectrum as a function defined across frequencies, we combine multitaper spectral methods with a frequency-domain bootstrap (FDB) procedure  ...  Section II reviews multitaper spectral estimation, and Section III presents the proposed multitaper frequency-domain bootstrap (MFDB) method.  ... 
doi:10.1109/lsp.2018.2876606 pmid:32002009 pmcid:PMC6990459 fatcat:g62e4ifgcvbbfdqqgmf4isqkm4

Comparison of the Performance of Two Advanced Spectral Methods for the Analysis of Times Series in Paleoceanography

Eulogio Pardo-Igúzquiza, Francisco Rodríguez-Tovar
2015 Journal of Marine Science and Engineering  
The statistical significance of maximum entropy estimates was assessed by a random permutation test (Pardo-Igúzquiza and Rodríguez-Tovar, 2000), while the statistical significance of the Thomson multitaper  ...  Many studies have revealed the cyclicity of past ocean/atmosphere dynamics at a wide range of time scales (from decadal to millennial time scales), based on the spectral analysis of time series of climate  ...  Figure 4 . 4 Power spectrum estimated by the Thomson multitaper method with 5 tapers. The Nyquist frequency is 0.5 which corresponds to a period of 2 arbitrary units of time.  ... 
doi:10.3390/jmse3030957 fatcat:ffxiinztqjdylmcxehult3kikq

Multitaper Time-Frequency Reassignment

Patrick Flandrin, Jun Xiao
2006 Zenodo  
However, when the area of the domain D is reduced, the situation evolves quite differently for the two estimates: on the one hand, S x,K is smoother that RS x,K ; on the other hand, RS x,K is essentially  ...  Figure 1 illustrates what happens in such a case by comparing the WVD and a sample (reassigned) spectrogram with the corresponding multitaper estimates based on K = 10 Hermite functions.  ... 
doi:10.5281/zenodo.53548 fatcat:nk6wrrxqkjh4hfcmxwhtmojlci

Improving the spatial resolution of effective elastic thickness estimation with the fan wavelet transform

J.F. Kirby, C.J. Swain
2011 Computers & Geosciences  
computationally 21 much faster and requires the arbitrary variation of only one parameter compared to 22 three for the multitaper method.  ...  Finally, we present a modified method to compute the 23 predicted coherence using the multitaper method that, while not improving its spatial 24 resolution, does improve the bias of recovered T e estimates  ...  First, the fan wavelet method only requires the arbitrary 450 variation of one parameter (|k 0 |), whereas the multitaper method requires the variation 451 of three (window size, bandwidth and number of  ... 
doi:10.1016/j.cageo.2010.10.008 fatcat:f2djod4cajc2jmswgoriuv5kvu

Multitaper Time-Frequency Reassignment for Nonstationary Spectrum Estimation and Chirp Enhancement

Jun Xiao, Patrick Flandrin
2007 IEEE Transactions on Signal Processing  
The first one, primarily aimed at nonstationary spectrum estimation, is based on sums of estimates with different tapers, whereas the second one makes use of differences between the same estimates for  ...  The technique consists in combining time-frequency reassignment with multitapering, and two variations are proposed.  ...  However, when the area of the domain D is reduced, the situation evolves quite differently for the two estimates: on the one hand, S x,K is smoother that RS x,K ; on the other hand, RS x,K is essentially  ... 
doi:10.1109/tsp.2007.893961 fatcat:icpyfljl25c5lncqptfvole5mi

Kernels and Multiple Windows for Estimation of the Wigner-Ville Spectrum of Gaussian Locally Stationary Processes

Patrik Wahlberg, Maria Hansson
2007 IEEE Transactions on Signal Processing  
Index Terms-Locally stationary circular symmetric processes, multitaper spectral estimation, optimal estimation, time-frequency analysis, Wigner-Ville spectrum (WVS).  ...  We also treat the equivalent multitaper estimation formulation and the associated problem of eigenvalue-eigenfunction decomposition of a certain Hermitian function.  ...  This means that Hermite functions can be used as window functions in the multitaper estimation.  ... 
doi:10.1109/tsp.2006.882076 fatcat:xbj5lfeh5ngjnaafrefkxuhocm

Localized spectral analysis on the sphere

Mark A. Wieczorek, Frederik J. Simons
2005 Geophysical Journal International  
In order to make robust localized estimates of the admittance and coherence spectra between two fields on the sphere, we propose a method analogous to Cartesian multitaper spectral analysis that uses our  ...  Direct localized spectral estimates on the sphere can be obtained by tapering, or multiplying the data by a suitable windowing function, and expanding the resultant field in spherical harmonics.  ...  Here, we limit ourselves to axisymmetric windows and we refer to Simons et al. (2005) for extensions to arbitrary domains and non-zonal windows.  ... 
doi:10.1111/j.1365-246x.2005.02687.x fatcat:cldgvvbclndepexiueyuju4hom

Minimum-Variance Multitaper Spectral Estimation on the Sphere

Mark A. Wieczorek, Frederik J. Simons
2007 Journal of Fourier Analysis and Applications  
We develop a method to estimate the power spectrum of a stochastic process on the sphere from data of limited geographical coverage.  ...  We describe how the weights applied to the individual spectral estimates in forming the multitaper estimate can be chosen such that the variance of the estimate is minimized.  ...  Software for performing the computations in this article can be found on the authors' web sites. This is IPGP contribution 2236.  ... 
doi:10.1007/s00041-006-6904-1 fatcat:epxknnf5zrcdtgifpoj2vszble

Complementary envelope estimation for frequency-modulated random signals

Pascal Clark, Ivars Kirsteins, Les Atlas
2013 2013 IEEE International Conference on Acoustics, Speech and Signal Processing  
We propose a new complementary envelope estimator based on modified multitaper spectral analysis, and use it to reveal previously unseen FM-like behavior in ship propeller noise.  ...  However, frequency modulation estimators typically impose temporal smoothness constraints that limit their general use for stochastic signals.  ...  In the following, we propose a practical estimator based on a new complementary extension of Thomson's classic multitaper technique [23] .  ... 
doi:10.1109/icassp.2013.6638687 dblp:conf/icassp/ClarkKA13 fatcat:atv25vwjm5h5lnhc7wfkgfavsa

Application of optimal band-limited control protocols to quantum noise sensing

V. M. Frey, S. Mavadia, L. M. Norris, W. de Ferranti, D. Lucarelli, L. Viola, M. J. Biercuk
2017 Nature Communications  
Our results, based on experiments with trapped ions using modulation in the form of discrete prolate spheroidal sequences (aka Slepian functions), demonstrate reduction of spectral leakage by orders of  ...  To characterize the frequency response of a qubit-based sensor undergoing an arbitrary control protocol in the presence of multi-axis classical noise, we rely on the filter transfer function formalism  ...  In an ideal scenario, for frequency domain spectral estimation applications, the chosen control protocol would be sensitive only within a user-determined band.  ... 
doi:10.1038/s41467-017-02298-2 pmid:29259153 pmcid:PMC5736660 fatcat:bxk6c2iltbgz5c65wgwrmojwnq

Adaptive Kernel Estimation of the Spectral Density with Boundary Kernel Analysis [article]

Alexander Sidorenko, Kurt S. Riedel
2018 arXiv   pre-print
When the spectral density is discontinuous, one sided smoothing estimates are used.  ...  A hybrid estimator of the log-spectral density of a stationary time series is proposed. First, a multiple taper estimate is performed, followed by kernel smoothing the log-multitaper estimate.  ...  When the spectral density is discontinuous at a point, the kernel estimate must be one-sided. We present new "boundary" kernels for one-sided estimation. §2.  ... 
arXiv:1803.03906v1 fatcat:rlwpzg5rfjhv7asq7q7mwz3ice

Spacing and shape of random peaks in non-parametric spectrum estimates

D. J. Thomson, C. L. Haley
2014 Proceedings of the Royal Society A  
Spectrum estimation Following its nineteenth-century origins with Stokes [27] , Kelvin [28] , Schuster [1] and Rayleigh [29] , the computational effort associated with statistical spectrum estimation  ...  Indirect estimates begin with sample autocovariances, tapers them with a 'lag window' and then takes their Fourier transform to estimate the spectrum, producing a smoothed periodogram.  ...  Because one can place bounds on the broad-band bias of the multitaper estimate (using nothing more than the properties of the tapers and the Cauchy inequality; see [40] ), the multitaper estimate cannot  ... 
doi:10.1098/rspa.2014.0101 pmid:25002827 pmcid:PMC4032558 fatcat:ximirpo5r5hkxehmejtf4d5x3i

Multitaper estimates of phase-amplitude coupling [article]

Kyle Q. Lepage, Cavan N. Fleming, Mark Witcher, Sujith Vijayan
2021 bioRxiv   pre-print
Finally, asymptotic statistical assessment of the multitaper estimator is introduced to address issue (iv).  ...  In this work, a multitaper phase-amplitude coupling estimator is proposed that addresses issues (i)-(iv) above.  ...  The multitaper method uses the optimal in-band energy concentrated discrete prolate spheroidal sequences 1 (DPSSs) as data tapers applied prior to estimating Fourier-domain related quantities.  ... 
doi:10.1101/2021.03.02.433586 fatcat:633ln6vn5jcwpgzr34y5cbt7i4

Sampling Properties of the Spectrum and Coherency of Sequences of Action Potentials

M. R. Jarvis, P. P. Mitra
2001 Neural Computation  
In addition, new work is presented that builds on the framework established in the review section. This work investigates how the estimates and their error bars are modified by finite sample sizes.  ...  This article begins with a review of these quantities, their interpretation, and how they may be estimated.  ...  Multitaper Estimates.  ... 
doi:10.1162/089976601300014312 pmid:11255566 fatcat:z52w4cxyqrgdtea4qb4qv32hwm
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