Amplitude-modulation (AM) and frequency-modulation (FM) systems are wi
dely applicable to the modeling and transmission of information in sig
nals. In this paper it is shown that the nonlinear energy-tracking sig
nal operator PSI (x) = (x)2 - xx and its discrete-time counterpart can
estimate the AM and FM modulating signals. Specifically, PSI can appr
oximately estimate the amplitude envelope of AM signals and the instan
taneous frequency of FM signals. Bounds are derived for the approximat
ion errors, which are negligible under general realistic conditions. T
hese results, coupled with the simplicity of PSI, establish the useful
ness of the energy operator for AM and FM signal demodulation. These i
deas are then extended to a more general class of signals that are sin
e waves with a time-varying amplitude and frequency and thus contain b
oth an AM and an FM component; for such signals it is shown that PSI c
an approximately track the product of their amplitude envelope and the
ir instantaneous frequency. The theoretical analysis is done for both
continuous- and discrete-time signals.