Wavelet-polyspectra: Principles and properties

We present a stringent definition of higher-order evolutionary spectra. On this basis, we define wavelet-polyspectral densities as a way of dealing with non-stationarities in higher-order statistics. We propose a simple wavelet-polyspectral estimator, and we discuss its statistical properties. The proposed wavelet-polyspectral analysis tool is demonstrated by a numerical example. It is concluded that the wavelet-poly-spectra have desirable properties for the analysis of data that are simultaneously non-stationary and non-Gaussian/non-linear.