On frequency estimation of exponential signals with time-varying amplitude via polar decomposition

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/sup i/spl theta// 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. The methods presented herein do not rely on any assumed structure for the time-varying amplitude, and they are shown to possess good performance in a large class of signals. The effectiveness and robustness of our method is demonstrated on real radar data.