Orthogonal Chebyshev Polynomials in Signal Processing

Systems of automatic process signals need constant improvement and increasing efficiency, taking into account the peculiarity of a specific practical task and the real current situation. It is proposed to use new improved methods of approximation of continuous functions in signal processing in this paper. They are based on expanding in a series according to the orthogonal system of Chebyshev polynomials of the first kind. Herewith, Chebyshev - Poisson partial sums and Chebyshev - Poisson integrals built on the basis of this orthogonal system of polynomials naturally arise. The conditions of convergence of series are investigated depending on the chosen system of numerical coefficients. Estimation of the accuracy of approximation of the function for different cases is also compared. The obtained results can be used in digital signal processing systems, which are based on Fourier series decomposition of functions with some modifications.