Exponential signals with time-varying amplitude: Parameter estimation via polar decomposition

Abstract

This paper addresses the estimation of the center frequency of complex exponential signals with time-varying amplitude. A method which requires few assumptions regarding the signal’s envelope is proposed. It is based on the polar decomposition of a certain covariance matrix. The polar decomposition, a generalization to matrices of the complex number representation z= re i θ with r>0, is particularly suitable for the application considered. The notion of truncated polar decomposition is introduced. Simple schemes for estimating the signal’s frequency are presented, based on these decompositions. In contrast to most existing methods, the methods presented herein do not rely on any assumed structure for the time-varying amplitude, and they are shown to possess good performances in a large class of signals. The effectiveness and robustness of our approach are demonstrated on real radar data.