ON AMPLITUDE AND FREQUENCY DEMODULATION USING ENERGY OPERATORS

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.