M.P. Slichenko1

1 JSC «Concern «Sozvezdie» (Voronezh, Russia)

Periodic functions describe phenomena of various nature and are used in various fields of science and technology. In practice, the problem of restoring such periodic functions from their discrete non-equidistant samples is widespread, especially when processing the results of measurements of such functions. However, the existing approach to interpolation by the non-equidistant Kotelnikov series leads to errors due to the truncation of the infinite series. To eliminate this error and improve the accuracy of interpolation will allow the modification of the Kotelnikov series based on the periodicity of the original function.

The purpose of this paper is to obtain an exact closed analytical representation of periodic functions with a finite Fourier spectrum modified by a non-equidistant Kotelnikov series.

The problem of exact analytical representation of the infinite Kotelnikov interpolation series for periodic functions with a finite Fourier spectrum is solved as a weighted sum of non-equidistant samples on a period. The use of this representation in the class of periodic functions with a non-finite Fourier spectrum makes it possible to nullify the truncation error, leaving the value of the overlay error unchanged. The resulting expressions are a modification of the Kotelnikov interpolation series and are valid in the general case for vector complex functions that satisfy the conditions of the sampling theorem.

The application of the proven theorem in practice makes it possible to restore periodic functions of various nature (for example, the directivity characteristics of antenna systems, image contours) with a zero truncation error from their non-equidistant readings. In particular, this makes it possible to implement the resampling of the results of measurements of the characteristics of antenna systems and the formation of data directly used in radio monitoring equipment in the direction finding mode of radio emission sources.

Slichenko M.P. Representation of periodic functions with a finite Fourier spectrum by a modified non-equidistant Kotelnikov series. Radiotekhnika. 2023. V. 87. № 5. P. 123−133. DOI: https://doi.org/10.18127/j00338486-202305-13 (In Russian)

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