A DFT BASED ALTERNATING PROJECTION ALGORITHM FOR PARAMETER-ESTIMATIONOF SUPERIMPOSED COMPLEX SINUSOIDS

In this paper, we consider the alternating projection algorithm sugges tcd by Ziskind and Wax for parameter estimation of superimposed comple x sinusoids (cisoids) embedded in noise, and show how the objective fu nction being maximized at each step can be expressed as a non-linear f unction of the Fourier transforms of the observed data and discrete ci soids. We obtain elegant expressions for the objective functions for t he case when the number of cisoids is two and develop a discrete Fouri er transform based algorithm for this case. The expressions for the ca se of three or more cisoids are quite cumbersome, but have a nice recu rsive structure that is illustrated by taking the case of three cisoid s as an example. The details of the recursion for the general case are given in the appendix. We discuss some of the approximations and simp lifications that lead to substantial reduction in computation. Simulat ion results are presented to show how the developed algorithm performs in comparison with the other techniques.