Matrix Pencil Method for Estimating Parameters of Exponentially Damped/Undamped Sinusoids in Noise

We present a study of a matrix pencil method for estimating parameters (frequencies and damping factors) of exponentially damped and/or undamped sinusoids in noise. Comparison of this method to a polynomial method (SVD-Prony method) shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach but the pencil method is more efficient in computation and less restrictive about signal poles. It is found through perturbation analysis and simulation that, for signals with un- known damping factors, the pencil method is less sensitive to noise than the polynomial method. In Appendix A, a new expression of the Cramer-Rao bound for the exponential signals is presented.