On polynomial phase signals with time-varying amplitudes

We address the parameter estimation problem for a class of nonstationary signals modeled as polynomial phase signals with time-varying amplitudes. Exponentially damped polynomial phase signals are treated as a special case and are analyzed in detail. High-order instantaneous moments provide the basic analytical tool, but links are shown to exist with either the usually employed FFT-based technique or the high-resolution Kumaresan-Tufts (1982), MUSIC, and matrix pencil methods. Asymptotic properties of the relevant estimators are established, Cramer-Rao lower bounds on the amplitude and phase parameter estimates are derived, and computer simulations are carried out to evaluate the performance of various schemes. We focus on parametric modeling of AM-FM signals, mainly because parametric techniques offer parsimony and allow for theoretically unlimited resolution.