On the positivity of Teager-Kaiser's energy operator

This paper is devoted to the problem of positivity conditions of Teager-Kaiser energy operator in one dimension. This operator and its extended versions form a class of energy operators that are well adapted for non-stationary signals and images processing and thus, are well suitable for a large range of domains and applications. However, negativity of the operator is essentially meaningfulness and thus prevents it from having some useful mathematical properties. We tackle this problem of positivity, and we show that it can be formulated logarithmically in terms of attenuation and phase of the input signal, rather than the more conventional AM-FM model. A more detailed analysis of the positivity conditions of the operator is presented, which extends and generalizes the findings reported in the literature. We highlight the existence of a critical interval over which the positivity is depending on the initial phase of the input signal. Outside this critical interval, the positivity is guaranteed. Positivity conditions are illustrated and analyzed on synthetic and real signals. (C) 2022 Elsevier B.V. All rights reserved.