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Matrix operator for the mutual transformation of the Fourier spectrum and the generalized Hartley spectrum

DOI 10.18127/j19997493-201904-05

Keywords:

V.V. Syuzev – Dr.Sc. (Eng.), Professor, Department «Computer systems and networks», Bauman Moscow State Technical University
E-mail: v.suzev@bmstu.ru
V.V. Gurenko – Associate Professor, Department «Computer systems and networks», Bauman Moscow State Technical University
E-mail: wgurenko@bmstu.ru
B.I. Bychkov – Assistant, Department «Computer systems and networks», Bauman Moscow State Technical University
E-mail: bychkovboris@bmstu.ru


The scientific and applied problem of converting the trigonometric Fourier spectrum to the generalized Hartley spectrum in a number system with an arbitrary base is solved. The structure and the basic properties of the mutual spectrum transformations operator are formulated. Original rules for combining the spectral coefficients into independent groups are written. The generalized spectrum analysis procedure is presented as a system of equations that are simpler to implement. An analytical assessment of computational complexity showed that the obtained equations reduce the number of computational operations needed to convert the spectrum.
The achieved results are generalized. Similarly to the Hartley basis, when changing the base of the number system, one can obtain solutions in new basis systems. The results may turn out to be in demand in signal processing using their spectral and energy characteristics instead of traditional trigonometric systems and complex exponential functions of Fourier and Vilenkin-Chrestenson. In particular, spectrum transformation operator can be used in the development of effective algorithms for simulating deterministic and random signals in the framework of correlation theory.

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