Signals Recovery by Means of Three-Harmonic Equations Solutions
Andrii P. Musienko, Andriy Makarchuk, Yu. I. Kharkevych, Inna V. Kal’chuk, Galyna Kharkevych, Maryna V. Hrysenko · 2022
An intensive development of signal theory has been taking place for the last decades. Therefore, the range of such problems has expanded considerably. Problems closely related to the mathematical methods have become especially important. We can include here problems related to image processing, filtering audio and other signals, etc. It should be noted that these problems are often related to the methods of systems analysis and approximation theory. In particular, in many digital signal processing problems, interpolation is one of the classic methods of their solution. When we talk about the usage of interpolation polynomials in signal theory, we are used to using standard methods of spline-type interpolation, Lagrange interpolation polynomials or Hermite polynomials. However, signals are known to be approximated the best by periodic functions. Trigonometric analogues of Lagrange interpolation polynomials are the standard examples of interpolation that could be used in practice. But such methods do not always give good results or are not easy to use. To solve this problem, we should keep in mind that signals are harmonic functions. Therefore, the discrete Fourier transformation has been used in many scientific works. However, this approach does not always give the desired effect, so the question of constructing alternative interpolation polynomials arises. In this paper, we propose a new approach to signal recovery, which allows getting better signal recovery than that given by the most common methods of signal recovery. The usage of interpolation polynomials proposed in this paper provides an improvement in signal recovery compared to their classical counterparts.