Using of Chebyshev - Poisson's Orthogonal Operators in Signal Processing

The tasks of security, management and control of air traffic, identification and recognition of moving objects are becoming increasingly important today. Efficiency and accuracy of positioning, reliability and resistance to external conditions are the main important characteristics of navigation systems. Modern radar and navigation systems require fast and accurate signal detection, recognition and analysis. Methods based on the processing of one-dimensional signals using the theory of function approximation have shown themselves to be well-proven. In this case, the signal is considered as a continuous function of the time parameter. This paper investigates and compares methods for approximating continuous functions using orthogonal Chebyshev-Poisson's polynomials. In particular, the biharmonic Chebyshev-Poisson's integral and the Abel-Poisson's integral are considered. The convergence and accuracy estimation are investigated.