Parameter Estimation of the Exponentially Damped Sinusoid for Noisy Signals*

Abstract The damped sinusoid equation is a common model for many scientific processes involving damped periodic signals. Here we present two methods for estimating the damped sinusoid parameters for noisy signals. Both methods are based upon an exact, closed form solution to fit the parameters for signals without noise, and they estimate the parameters for the noisy signals by the statistical maximum likelihood criterion. The first method relies on an optimizer to minimize the mean square signal error. The second method estimates the parameters by direct calculation and is suitable when the signal noise is small and the frequencies are sufficiently far from the integer and half integer values.