Minimum bias multiple taper spectral estimation

By K. Riedel, Alexander Sidorenko. IEEE Transactions on Signal Processing, 2018

334 citations recorded by the source corpus.

Two families of orthonormal tapers are proposed for multitaper spectral analysis: minimum bias tapers, and sinusoidal tapers {/spl upsisup (k/)}, where /spl upsisub nsup (k/)=/spl radic/(2/(N+1))sin(/spl pi/kn/N+1), and N is the number of points. The resulting sinusoidal multitaper spectral estimate is S/spl circ/(f)=(1/2K(N+1))/spl Sigmasub j=1sup K/|y(f+j/(2N+2))-y(f-j/(2N+2))|/sup 2/, where y(f) is the Fourier transform of the stationary time series, S(f) is the spectral density, and K is the number of tapers. For fixed j, the sinusoidal tapers converge to the minimum bias tapers like 1/N. Since the sinusoidal tapers have analytic expressions, no numerical eigenvalue decomposition is necessary. Both the minimum bias and sinusoidal tapers have no additional parameter for the spectral bandwidth. The bandwidth of the jth taper is simply 1/N centered about the frequencies (/spl plusmn/j)/(2N+2). Thus, the bandwidth of the multitaper spectral estimate can be adjusted locally by simply adding or deleting tapers. The band limited spectral concentration, /spl intsub -wsup w/|V(f)|/sup 2/df of both the minimum bias and sinusoidal tapers is very close to the optimal concentration achieved by the Slepian (1978) tapers. In contrast, the Slepian tapers can have the local bias, /spl intsub - 1/2 sup 1/2 /f/sup 2/|V(f)|/sup 2/df, much larger than of the minimum bias tapers and the sinusoidal tapers. >

Subfields: Analytical Chemistry, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/0a3157c12166dfec8cb023f26e80e72cb516e2ed

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In Analytical Chemistry

1. Alexei Kuvshinov
2. Jon M. Jenkins
3. Usik Lee
4. Jérôme Antoni
5. Dong Wang

In Computer Vision and Pattern Recognition

1. Alexei Kuvshinov
2. Jon M. Jenkins
3. Usik Lee
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In Signal Processing

1. Alexei Kuvshinov
2. Jon M. Jenkins
3. Usik Lee
4. Jérôme Antoni
5. Dong Wang
6. Kwok Leung Tsui
7. Qiang Miao

Citations in the corpus

• Spatiospectral Concentration on a Sphere (2004, neutral): “, [19, 51], the optimally concentrated signal is considered to be the one with the least energy outside the interval:”
• 3-D Global Induction in the Oceans and Solid Earth: Recent Progress in Modeling Magnetic and Electric Fields from Sources of Magnetospheric, Ionospheric and Oceanic Origin (2008, methodology): “Riedel and Sidorenko 1995 ) as applied to hourly mean time series of the geomagnetic field components recorded at Hermanus observatory in 1957–1958.”
• The Impact of Solar-like Variability on the Detectability of Transiting Terrestrial Planets (2002, background): “Several choices for tapers are available, including sinusoidal families (Riedel & Sidorenko 1995), which approximate optimal tapers minimizing the asymptotic bias of the estimate.”
• Cyclic spectral analysis in practice (2007, background): “which yields nearly minimum bias estimates and are also more efficient from the computational point of view [15].”
• Spectral Analysis of Signals (2009, methodology): “Such an approach was introduced in [Thomson 1982] and was further developed in [Mullis and Scharf 1991] (more recent references on this approach include [Bronez 1992; Onn and Steinhardt 1993; Riedel and Sidorenko 1995]).”