Rubin-Delanchy, P

Walden, AT

IEEE Transactions on Signal Processing

Rubin-Delanchy, Patrick T G

Walden, Andrew T

Explore Bristol Research

Kinematics of complex-valued time series

Spiral - Imperial College Digital Repository

Abstract—The contribution to a stationary complex-valued time series at a single frequency magnitude takes the form of a random ellipse, and its properties such as aspect ratio (which includes rota-tional direction) and orientation are of great interest in science. A case when both the aspect ratio and orientation are fixed is found, and their variability, in general, results from the additional influ-ence of an orthogonal ellipse. It is shown how a magnitude squared coherence coefficient controls both the relative influences of these components and the variation of both the orientation and aspect ratio of the resultant ellipse. Realizations of random ellipses are recovered very accurately from simulated time series. The mean orientation of the random ellipse is formally derived. Index Terms—Aspect ratio, azimuth, coherence, complex-valued processes, random ellipse, simulation. I

Patrick Rubin-delanchy

Andrew T. Walden

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http://spiral.imperial.ac.uk/bitstream/10044/1/1336/1/RDWaldenKin.pdf

Kinematics of complex-valued time series

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Spiral - Imperial College Digital Repository

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