A recursive approach to prony parameter estimation

Abstract The Prony series method of fitting a series of complex exponentials to a time series can be applied to many acoustic and vibration signals. For example, in the analysis of a structure's response to transient excitation the Prony series method can be used to find the natural frequencies, damping ratios, amplitudes and relative phases of the modes of the structure. One of the main problems with this method is the need to calculate and invert matrices. In this paper an algorithm that combines the Prony series method with the recursive least squares algorithm is described. This eliminates the need to invert any matrices and also requires only part of the data to be available at one particular time. The method is applied to analyze a simulated structure's response and also to analyze the response of a beam to transient excitation.