The Measurement of Power Spectra from the Point of View of Communications Engineering - Part II

Blackman, R. B.; Tukey, John W.

doi:10.1002/j.1538-7305.1958.tb01530.x

Cited by 288 publications

(184 citation statements)

References 24 publications

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“…Heikkinen 1981; Barthelmes 1986Barthelmes , 1988Vermeer 1982Vermeer , 1983Vermeer , 1984Vermeer , 1995, the radial multipoles (e.g. Marchenko 1998;Marchenko et al 2001), the Blackman functions of Blackman and Tukey (1958) (Schmidt et al 2004(Schmidt et al , 2005a(Schmidt et al , 2007, and the Poisson wavelets of Holschneider et al (2003) (e.g. Chambodut et al 2005;Panet et al 2006;Klees and Wittwer 2007b), see also Holschneider and Iglewska-Nowak (2007).…”

Section: Introductionmentioning

confidence: 99%

A data-driven approach to local gravity field modelling using spherical radial basis functions

Klees

Tenzer

Prutkin

et al. 2008

J Geod

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We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing potential using least-squares techniques. The latter is represented as a linear combination of spherical radial basis functions (SRBFs). A data-adaptive strategy is used to select the optimal number, location, and depths of the SRBFs using generalized cross validation. Variance component estimation is used to determine the optimal regularization parameter and to properly weight the different data sets. In the second step, the gravimetric height anomalies are combined with observed differences between global positioning system (GPS) ellipsoidal heights and normal heights. The data combination is written as the solution of a Cauchy boundary-value problem for the Laplace equation. This allows removal of the non-uniqueness of the problem of local gravity field modelling from terrestrial gravity data. At the same time, existing systematic distortions in the gravimetric and geometric height anomalies are also absorbed into the combination. The approach is used to compute a height reference surface for the Netherlands. The solution is compared with NLGEO2004, the official Dutch height reference surface, which has been computed using the same data but a Stokes-based approach with kernel modification and a geometric six-parameter "corrector surface" to fit the gravimetric solution to the GPS-levelling points. A direct comparison of both height reference surfaces shows an RMS difference of 0.6 cm; the maximum difference is 2.1 cm. A test at R. Klees (B) · R. Tenzer · I. Prutkin · T. Wittwer

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Section: Introductionmentioning

confidence: 99%

A data-driven approach to local gravity field modelling using spherical radial basis functions

Klees

Tenzer

Prutkin

et al. 2008

J Geod

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“…For a given interval I, the mean solar wind velocity V { AV I S gives the associated spatial lag r p tV I I sw sw at time t; this is assumed, with minimal error, to lie along the heliocentric radial direction. In this way we employ a "Blackman-Tukey" technique (Blackman & Tukey 1958) to compute the correlation functions R I (r), in the same way as done in Milano et al (2004). We choose the maximum computed lag as t max p 16 hr (so for a given interval I, the maximum spatial lag corresponds to r p t max FV F).…”

mentioning

confidence: 99%

Anisotropy in Fast and Slow Solar Wind Fluctuations

Dasso

Milano

Matthaeus

et al. 2005

ApJ

252

253

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Using 5 years of spacecraft data from near Earth orbit, we investigate the correlation anisotropy of solar wind magnetohydrodynamic-scale fluctuations and show that the nature of the anisotropy differs in fast (1500 km s Ϫ1 ) and slow (!400 km s Ϫ1 ) streams. In particular, fast streams are relatively more dominated by fluctuations with wavevectors quasi-parallel to the local magnetic field, while slow streams, which appear to be more fully evolved turbulence, are more dominated by quasi-perpendicular fluctuation wavevectors.

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“…Blackman and Tukey (1958) page 502 ⟨B.5 Particular Pairs of Windows⟩, Blackman and Tukey (1959), page 98 ⟨B.5 Particular Pairs of Windows⟩, Oppenheim and Schafer (1999) page 763, …”

Section: Filteringmentioning

confidence: 99%

Order and Metric Compatible Symbolic Sequence Processing

Greenhoe

2016

Preprint

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A traditional random variable X is a function that maps from a stochastic process to the real line (X,<=,d,+,.), where R is the set of real numbers, <= is the standard linear order relation on R, d(x,y)=|x-y| is the usual metric on R, and (R, +, .) is the standard field on R. has demonstrated that this definition of random variable is often a poor choice for computing statistics when the stochastic process that X maps from has structure that is dissimilar to that of the real line. Greenhoe(2015b) has further proposed an alternative statistical system, that rather than mapping a stochastic process to the real line, instead maps to a weighted graph that has order and metric geometry structures similar to that of the underlying stochastic process. In particular, ideally the structure X maps from and the structure X maps to are, with respect to each other, both isomorphic and isometric.Mapping to a weighted graph is useful for analysis of a single random variable.for example the expectation EX of X can be defined simply as the center of its weighted graph. However, the mapping has limitations with regards to a sequence of random variables in performing sequence analysis (using for example Fourier analysis or wavelet analysis), in performing sequence processing (using for example FIR filtering or IIR filtering), in making diagnostic measurements (using a post-transform metric space), or in making goptimal h decisions (based on gdistance h measurements in a metric space or more generally a distance space). Rather than mapping to a weighted graph, this paper proposes instead mapping to an ordered distance linear space Y=(R^n,<=,d,+,.,R,+,x), where (R,+,x) is a field, + is the vector addition operator on R^n Order and Metric Compatible Symbolic Sequence Processing DANIEL J. GREENHOEAbstract: A traditional random variable is a function that maps from a stochastic process to the "real line" (ℝ, ≤, , +, ⋅), where ℝ is the set of real numbers, ≤ is the standard linear order relation on ℝ, ( , ) ≜ | − | is the usual metric on ℝ, and (ℝ, +, ⋅) is the standard field on ℝ.Greenhoe (2015b) has demonstrated that this definition of random variable is often a poor choice for computing statistics when the stochastic process that maps from has structure that is dissimilar to that of the real line. Greenhoe (2015b) has further proposed an alternative statistical system, that rather than mapping a stochastic process to the real line, instead maps to a weighted graph that has order and metric geometry structures similar to that of the underlying stochastic process. In particular, ideally the structure maps from and the structure maps to are, with respect to each other, both isomorphic and isometric.Mapping to a weighted graph is useful for analysis of a single random variable-for example the expectation of can be defined simply as the center of its weighted graph. However, the mapping has limitations with regards to a sequence of random variables in performing sequence analysis (using for example Fourier analysis or wavelet analysis),...

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The Measurement of Power Spectra from the Point of View of Communications Engineering - Part II

Cited by 288 publications

References 24 publications

A data-driven approach to local gravity field modelling using spherical radial basis functions

A data-driven approach to local gravity field modelling using spherical radial basis functions

Anisotropy in Fast and Slow Solar Wind Fluctuations

Order and Metric Compatible Symbolic Sequence Processing

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