Techniques for Extracting the Complex Resonances of a System Directly from Its Transient Response.

Abstract
An approach for extracting the singularities of a system from its transient response to a given excitation is discussed. The method developed is based on Prony's algorithm. Some basic problems which are associated with the use of Prony's algorithm are discussed and solutions are obtained. The singularities thus identified are useful in the singularity expansion method (SEM) of describing system response. It is demonstrated that Prony's method is applicable to systems with multiple as well as simple pole singularities. Two techniques are presented for systematically determining the number of poles contained in a transient response. Several numerical examples are presented to demonstrate these capabilities. The dependence of Prony's method on the noise level in the transient response is considered in detail and the results of several statistical tests are presented. The Pade approximation is suggested as an alternative to Prony's method but is demonstrated to be unsatisfactory. (Author)

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