Second-order analysis of improper complex random vectors and processes

Schreier, Peter J.; Scharf, Louis L.

doi:10.1109/tsp.2002.808085

Cited by 339 publications

(227 citation statements)

References 27 publications

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“…(Schreier & Scharf [13] use the terminology 'wide-sense stationary' rather than SOS.) We note that s Z,τ = s * Z,−τ , and r Z,τ = r Z,−τ , i.e.…”

Section: Rotary Components Modelmentioning

confidence: 99%

Rotary components, random ellipses and polarization: a statistical perspective

Walden

2013

Phil. Trans. R. Soc. A.

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Rotary analysis decomposes vector motions on the plane into counter-rotating components, which have proved particularly useful in the study of geophysical flows influenced by the rotation of the Earth. For stationary random signals, the motion at any frequency takes the form of a random ellipse. Although there are numerous applications of rotary analysis, relatively little attention has been paid to the statistical properties of the random ellipses or to the estimated rotary coefficient, which measures the tendency to rotate counterclockwise or clockwise. The precise statistical structure of the ellipses is reviewed, including the random behaviour of the ellipse orientation, aspect ratio and intensity. Special attention is then paid to spectral matrix estimation from physical data and to hypothesis testing and confidence intervals computed using the estimated matrices.

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“…(Schreier & Scharf [13] use the terminology 'wide-sense stationary' rather than SOS.) We note that s Z,τ = s * Z,−τ , and r Z,τ = r Z,−τ , i.e.…”

Section: Rotary Components Modelmentioning

confidence: 99%

Rotary components, random ellipses and polarization: a statistical perspective

Walden

2013

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…that is commonly used, and in addition, the pseudo-covariance [81] matrix-also called the complementary covariance [101] or the relation matrix [92]-given by…”

Section: Statistics Of Complex-valued Random Variables and Random Promentioning

confidence: 99%

“…z C [ C 2N given in (1.13) can be used to define a single matrix summarizing the second-order properties of a random vector X, which is called the augmented correlation matrix [92,101] …”

Section: Statistics Of Complex-valued Random Variables and Random Promentioning

confidence: 99%

“…To completely define the second-order statistics, as in the case of random variables, we also define the pseudo-covariance function [81]-also called the complementary covariance [101] and the relation function [91]-as…”

Section: Differential Entropy Of Complex Random Vectorsmentioning

confidence: 99%

“…It can be shown that the performance of the two filters can be equal even for cases where the input is highly noncircular (see Problems 1.6 and 1.7). However, when certain circularity properties do not hold, widely linear filters provide important advantages in terms of performance [23,94,101] by including the complete statistical information.…”

Section: Linear and Widely Linear Mean-square Error Filtermentioning

confidence: 99%

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