The higher order statistics of energy operators with application to neurological signals

Statistics for detecting changes in signal energy are developed for generalized energy estimation algorithms. The Teager energy operator (TEO) is a method for quantifying signal energy, a product of both frequency as well as amplitude. Using second and third order autocorrelation-based tests for dependence, we examine time domain methods of energy detection of sinusoids. To quantify signal energy we exploit the whiteness of the output of the TEO. The C-statistics examine the level of second order whiteness in a time series. The newly developed H-statistics test confirms the presence of third order whiteness or independence. A pure noise exhibits both second and third order whiteness. A power analysis of these tests for energy detection are also shown to be sensitive to changes in both sinusoidal amplitude and frequency. The Cand H-statistics allow for quantification of distortion in the TEO output as well. Distortion in an energy operator results from poor cancellation of cross-terms or from second harmonic distortion as typified by a traditional square law device. Fluctuations in band-specific EEG (electroencephalogram) energy also are amenable to practical analysis using the TEO. An example of an EEG signal with a large harmonic content are spindle signals taken from animal experiments dealing with recovery from hypoxic-asphyxic injury.