A NOTE ON ANALYTIC SIGNALS WITH NONLINEAR PHASE

Instantaneous frequency, defined as the derivative of the phase of a complex analytic representation of the signal, is a basic concept and plays an important role in communication and information processing. It is not unusual to expect that the instantaneous frequency of an analytic signal is nonnegative. In this note, we exhibit new families of analytic signals with band-limited amplitudes and positive nonlinear instantaneous frequencies. The structures of analytic signals with band-limited amplitude and rational as well as linear plus periodic instantaneous frequencies have been analyzed.