Using the method of moments for the approximation of signals containing peak shaped structural elements

In this paper a generalization of the method of moments which was proposed in a recent article for modeling electrocardiogram waves with sets of several Gauss functions is performed. The purpose is to make the method applicable to functions of a more general form, while maintaining the simplicity of its program implementation. For this a series of mathematical transformations were carried out in a general form and sufficiently simple relations were obtained for calculating the parameters of the model signal. This makes it possible to use functions of various types for the approximation of signal regions, dictated by their physical model. The only restriction for the functions used is the existence of the required number of moments, and the moment of zero order must be different from zero. This paper demonstrates several examples of the implementation of the generalized method of moments. It is shown that in practice, depending on the type of function used for modeling, a number of computational features arise concerning the accuracy of the method and its stability with respect to noise. Obtained results can be useful for developing new effective models of biomedical signals, atomic and nuclear spectra, as well as other types of signals that have peak shaped local features.