Abstract
The paper is devoted to the problem of the Fourier transformation effective convergence getting, processing the streaming data. The Fourier transformation that for even values of the variable gives the cosine of the Fourier transformation, and for odd values – the sine of the Fourier transformation has been considered. The properties of this Fourier transformation have been studied. The analysis of certain classes of special polynomials used to construct the summation function has been given. The obtained results can be applied in real signal processing systems based on the Fourier transformation usage. The results of the study allow us to conclude that the application of methods of summation of rectangular linear matrices will increase the rate of convergence of the Fourier transformation compared to triangular matrix methods of summation of Fourier series. This fact will increase the speed of all signal processing systems and the system of recognition and automated texts translation.
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