Some useful properties of cross-ΨBΨB-energy operator

In this paper, some useful properties of cross-ΨBΨB-energy operator, which measures the interaction between two signals, are provided. We show that ΨBΨB is a generalization of some extensions of Teager–Kaiser operator to complex signals. Due to its bilinearity, ΨBΨB satisfies the quadratic superposition principle. We point out the link between the ΨBΨB and the Lie bracket, which measures the instantaneous differences in the relative change between two signals. We show how the ΨBΨB operator can handle wideband signals using bandpass filtering. We also show how the quadratic superposition law can be used for detection purpose.