On testing for impropriety of complex-valued Gaussian vectors
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Widely linear estimation algorithms for second-order stationary signals
IEEE Transactions on Signal Processing
Bivariate instantaneous frequency and bandwidth
IEEE Transactions on Signal Processing
A statistical analysis of morse wavelet coherence
IEEE Transactions on Signal Processing
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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 rotational 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 influence 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.