Implementation of the Prony Method for Signal Deconvolution

Modern implementations of the Prony method have been used in the statistical analysis of sinusoidal and/or exponential signals distorted with noise. Modern implementations are auto-regressive, using a series of matrix calculations and least-squares to calculate the values of interest from a signal; the frequency, decay constant, initial amplitude, and phase. In cavity ring-down spectroscopy, the frequency and decay constant of an exponentially decaying sinusoidal signal need to be obtained, in order to identify molecules and the chirality of these molecules, which may be applied in, for instance, development of pharmaceuticals. This method is applicable to signals from other fields - signals which are sinusoidal or exponential in nature. An implementation of the Prony method for cavity ring-down spectroscopy has been developed and characterised in Python.