On the pre-constant signals of the Teager-Kaiser operator

The set of root signals of a nonlinear filter is an important step for its analysis. In addition, in the case of the Teager-Kaiser operator (a discrete, nonlinear filter of the moving-window type) the characterization of the signals that when filtered become constant, is particularly interesting. In fact, the operator was originally proposed as having the property that, for a sinusoidal input, the output is a constant signal of value the energy of the signal. The rich class of pre-constant signals of the Teager-Kaiser operator, which includes the sinusoids, hyperbolic sinusoids and several pre-null signals, is characterized here.