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Instruments and Systems: Monitoring, Control, and Diagnostics

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Harmonic Representation of Two-Dimensional Signals in the Basis of Trigonometric Functions
V.V. SYUZEV, V.V. GURENKO, B.I. BYCHKOV, A.A. SHUMAKOV

The work is devoted to the harmonic representation of two-dimensional continuous and discrete signals in the spectral region of the trigonometric basis. The system of two-dimensional trigonometric functions is considered. The components of the two-dimensional continuous and discrete trigonometric spectrum of signals are determined. Mathematical algorithms are formulated for simulating twodimensional continuous and discrete deterministic and random signals in a system of trigonometric functions. The correctness of the signal representation in this basis is confi rmed. The simulation accuracy is estimated experimentally by calculating the errors of the two-dimensional autocorrelation functions. The conclusion is made about the correct representation of two-dimensional signals in the considered basis with acceptable accuracy. The results of the work can be used in the development of real-time simulation systems. The resulting harmonic representation can serve as a basis for developing effi cient algorithms for simulating two-dimensional signals in the spectral region of other function systems.
Keywords: simulation of signal, simulation algorithm, spectrum, two-dimensional signal, harmonic representation, basis of trigonometric functions, continuous and discrete signals, deterministic and random signals, computational complexity.


DOI: 10.25791/pribor.4.2023.1401

Pp. 15-22.

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