Polarization Ellipse Analysis of Nonstationary Random Signals

We present a novel way of extending rotary-component and polarization analysis to nonstationary random signals. If a complex signal is resolved into counterclockwise and clockwise rotating phasors at one particular frequency only, it traces out an ellipse in the complex plane. Rotary-component analysis characterizes this ellipse in terms of its shape and orientation. Polarization analysis looks at the coherence between counterclockwise and clockwise rotating phasors and whether there is a preferred rotation direction of the ellipse (counterclockwise or clockwise). In the nonstationary case, we replace this ellipse with a time-dependent local ellipse that, at a given time instant, gives the best local approximation of the signal from a given frequency component. This local ellipse is then analyzed in terms of its shape, orientation, and degree of polarization. A time-frequency coherence measures how well the local ellipse approximates the signal. The ellipse parameters and the time-frequency coherence can be expressed in terms of the Rihaczek time-frequency distribution. Under coordinate rotation, the ellipse shape, the degree of polarization, and the time-frequency coherence are invariant, and the ellipse orientation is covariant. The methods presented in this paper provide an alternative to ellipse decompositions based on wavelet ridge analysis.