Assessing instantaneous energy in the EEG: a non-negative, frequency-weighted energy operator

Signal processing measures of instantaneous energy typically include only amplitude information. But measures that include both amplitude and frequency do better at assessing the energy required by the system to generate the signal, making them more sensitive measures to include in electroencephalogram (EEG) analysis. The Teager-Kaiser operator is a frequency-weighted measure that is frequently used in EEG analysis, although the operator is poorly defined in terms of common signal processing concepts. We propose an alternative frequency-weighted energy measure that uses the envelope of the derivative of the signal. This simple envelope- derivative operator has the advantage of being nonnegative, which when applied to a detection application in newborn EEG improves performance over the Teager-Kaiser operator: without post-processing filters, area-under the receiver-operating characteristic curve (AUC) is 0.57 for the Teager-Kaiser operator and 0.80 for the envelope-derivative operator. The envelope-derivative operator also satisfies important properties, similar to the Teager-Kaiser operator, such as tracking instantaneous amplitude and frequency.