Decomposition based on the Prony transform is widely used to solve various engineering and scientific problems, representing a discrete dataset in the form of a linear combination of complex exponentials or damped sinusoids. Each of these functions is determined by four real parameters: amplitude, attenuation, frequency and phase. In this article, we propose a new workflow, based on the classic Prony and Matrix Pencil methods to determine the damped signals considering their locality and frequency heterogeneity. After estimating the parameters a certain procedure is constructed. This procedure selects the parameters using different criteria and can be called as Prony filtering. We have demonstrated the capabilities of the proposed algorithms and workflow, which provide an optimal set of damped terms for the Prony decomposition for an arbitrary window. The results obtained show good accuracy in the selection of the decomposition components and posterior approximation of damped signals. The accuracy of the results is guaranteed by the quasi-orthogonality of the basis functions of the Prony decomposition on finite intervals.
Предметные области OECD FOS+WOS
- 1.05.GC ГЕОХИМИЯ И ГЕОФИЗИКА