Using of Chebyshev-Hermite functions for analytical device signals processing

The paper deals with the development of theoretical and applied approaches for synthesis fast and compact analytical data processing algorithms which can be used to estimate analytical peaks parameters. These algorithms are based on analytical data decomposition, the Chebyshev-Hermite polynomials are used as decomposition basis. The goal of using data decomposition is possibility of simple estimating of analytical peaks parameters by reconstructing different data transforms directly from decomposition coefficients. These transforms can be obtained by using corresponding bases. In this article considered following bases: basis for reconstruction initial data, bases for reconstruction smoothed first and second derivative of initial data. Examples of using these bases are given. Limitations of this approach are described. Relation between values of decomposition coefficients and modeled analytical peak parameters are obtained, Gauss function used for peak model. The Mathematica 11.3 computer algebra system was used to calculations and graph the results.