On the Problem of the Effectiveness of the Use of Trigonometric Polynomials in Signal Theory

At the stage of analysis of the efficiency of complex systems of automated signal processing there is a need to select parameters that would optimize a number of processes. The paper considers the effectiveness of the use of trigonometric polynomials for digital signal processing. We investigate matrix summation methods with rectangular matrices and their efficiency in comparison with methods based on the use of trigonometric polynomials. We propose a new approach to the construction of the trigonometric series of the function. The question of Lebesgue convergence of the constructed trigonometric series for an arbitrary summable periodic function in terms of a system of numerical coefficients is also investigated. The obtained results can be used in digital signal processing systems.