Generally, the response of a second-order system to an impulse excitation can be expressed in terms of a series of exponentially damped sinusoids. This technique is called the singularity expansion method (SEM). Knowing the SEM parameters, it is possible to characterize the system response and to search for conditions required to maximize a particular attribute of the response signal. Thus the goal of this study is to present techniques whereby the SEM parameters can be extracted from measured data, and in particular, data with a low s1gnal-to-noise ratio. A nonlinear digital filter technique that uses a circular serial correlation test is shown to provide a preprocessing technique which allows the classic Prony method to be applied to the data. The technique also estimates the noise level and accomodates the presence of non-stationary noise Results are presented for typical noisy data, as well as for analytical data with added white-Gaussian noise.