Approximation of experimental data by solving linear difference equations with constant coefficients (in particular, by exponentials and exponential cosines)

Abstract

This paper proposes a method for approximating experimental data points by the curves representing the solutions of linear difference equations with constant coefficients, in particular, by the curves of the expcos class. An algorithm for finding the coefficients and initial conditions of this approximation is described. The proposed approach minimizes the root mean square (RMS) deviation. The method is tested on some model examples, including the refinement of the beginning of QRS complexes on a three-dimensional ECG loop (in the form of Frank leads).