Some useful properties of Teager's energy operators

Teager's energy operators are defined in both the continuous and discrete domains and are very useful tools for analyzing single component signals from an energy point of view. A number of important properties of these operators are shown that make it possible to determine the energy functions of quite complicated functions, provided these functions can be expressed as products of simpler functions, this operation of function multiplication being typical of a modulation process. Some of the eigenfunction properties of the energy operator that illustrate the special role of the trigonometric, Gaussian, and single soliton functions are also given.<>