Conditions for positivity of an energy operator

The authors present necessary and sufficient conditions such that the output from the Teager-Kaiser (1989) energy operator [s˙(t)=ds(t)/dt] Ψ_c[s(t)]=s˙²(t)-s(t)s¨(t) for continuous-time signals s(t) and the output from the corresponding discrete-time energy operator Ψ_d[s(n)]=s²(n)-s(n+1)s(n-1) be non-negative everywhere. These operators have been shown to be effective for AM and FM demodulation in several useful classes of signals, such as speech and image signals