Abstract
When developing automatic signal processing systems, it is important to determine a set of parameters in order to optimize them and increase their efficiency. In the paper the modified Fourier transformation methods for digital signal processing have been used. A new approach to the construction of special polynomials has been offered by means of which the summing function is realized. The matrix methods of summation with rectangular matrices and their efficiency in comparison with the methods based on the use of triangular matrices have been investigated. Necessary and sufficient conditions for uniform convergence of the constructed trigonometric series for any continuous function on a segment in terms of a system of numerical coefficients have been established. The Lebesgue convergence of the constructed series for any summable periodic function has been studied. The obtained results can be used in digital signal processing systems based on the use of Fourier transformations.
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