On the perturbation analysis of a Prony-based algorithm

A Prony-based algorithm for the estimation of frequencies embedded in noise is discussed. The performance of this algorithm is known to depend on the signal-to-noise ratio. A perturbation analysis of this algorithm is carried out to assess this performance. The estimation accuracy, measured in terms of the bias and variance of the estimated frequencies, is discussed. The expressions for the variance are obtained for cases when L=M and L>M, where L is the order of the coefficient polynomial and M is the number of complex sinusoidals. It is found that as L increases the variance decreases and thus improves the frequency estimates