Estimation and statistical analysis for exponential polynomial signals

Abstract

In this paper we approximate arbitrary complex signals by modeling both the logarithm of the amplitude and the phase of the complex signal as finite-order polynomials in time. We refer to a signal of this type as an exponential polynomial signal (EPS). We propose an algorithm to estimate any desired coefficient for this signal model. We also show how the mean-squared error of the estimate can be determined by using a first-order perturbation analysis. A Monte Carlo simulation is used to verify the validity of the perturbation analysis. The performance of the algorithm is illustrated by comparing the mean-squared error of the estimate to the Cramer-Rao bound for a particular example.