A method for the estimation of phase and amplitude of polynomial phase signals with time-varying amplitude

We investigate the parameter estimation problem of polynomial phase signals with time-varying amplitudes. For many models of polynomial phase signals with time-varying amplitudes, the parameters can be expressed by the coefficients of its finite-order Taylor series expansion. And the estimation of phase and amplitude parameters can be converted to the estimation of the Taylor coefficients. We propose a linear transform—polynomial to Hermite polynomial transform, which can transform a polynomial signal in time-domain into a Hermite polynomial signal with the same order in frequency-domain. The Taylor coefficients can be estimated easily by utilizing the orthogonality of Hermite polynomial.