Statistical analysis of the Tufts-Kumaresan and principal Hankel components methods for estimating damping factors of single complex exponentials

A statistical analysis of the estimates of the damping factor of a single complex exponential in additive white Gaussian noise is presented. The analysis is done for two of the more popular methods, namely, the system identification method of principal Hankel components (PHC) and the Tufts-Kumaresan (TK) method of linear prediction. Assuming a high signal-to-noise ratio, closed form expressions for the variances of the damping factor are derived. These analytical solutions are confirmed with computer simulations. The analysis indicates that both the TK method and the PHC method perform well in comparison to the Cramer-Rao bound. Theoretically, however, the PHC method slightly outperforms the TK method