The higher order statistics of energy operators with application to neurological signals
David L. Sherman, Melvin J. Hinich, Nitish V. Thakor · 2002
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.