"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 6, 2017

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Peculiar properties of interpolation band-limited signals


A. V. Kokoshkin, V. A. Korotkov, K. V. Korotkov, E. P. Novichikhin

Kotel'nikov Institute of Radio-engineering and Electronics of RAS, Fruazino Branch, Vvedensky Sq.1, Fryazino Moscow region 141120, Russia


The paper is received on June 8, 2017


Abstract. To achieve the objectives of experimental signal research, it is often necessary to know its values outside the measured points. The interpolation results (interpolation errors) depend both on the correspondence of the type of interpolation to the signal, and on the location of the measured points. Unlike other methods, the Fourier series interpolation errors do not depend on the location of the interpolation nodes, but depend on the spectrum of the measured signal. In this paper, we consider the features of interpolation of spectrally-bounded signals. The experimental data are assumed to be obtained as a result of several series of measurements with a constant step, but with an arbitrary arrangement of the starting point. The obtained results make it possible to get interpolated values that depend weakly on the initial measurement points. As applied to digital image processing, this is equivalent to trying to increase spatial resolution in the presence of several low-quality source frames. In our work, we paid special attention to verifying the correspondence between the type of interpolation (Fourier series) and signal properties (spectral limitation). Usually, the analysis of spectrally limited signals is performed on the basis of the Kotel'nikov series without using the signal spectrum. In this paper, the computation of the signal spectrum is an important difference from other works, which makes it possible to estimate the real limitation of the spectrum of the measured data (if any). This ensures the reliability of interpolation by the Fourier series. In spite of the fact that the measured experimental data can be non-periodic, we shall consider them (within the Fourier series) as periodic with a period equal to the time of measurement. In this article we compare the results of interpolation by the Kotel'nikov and Fourier series and the cubic spline. A certain advantage of interpolation of the Fourier series for a periodic spectral-limited signal is shown. Expressions are obtained for calculating the spectra of experimentally measured signals for several series of measurements with a constant step, but with an arbitrary arrangement of the starting point.

Key words: spectrally limited signal, interpolation, Kotelnikov series, Fourier series.


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For citation:

A. V. Kokoshkin, V. A. Korotkov, K. V. Korotkov, E. P. Novichikhin. Peculiar properties of interpolation band-limited signals. Zhurnal Radioelektroniki - Journal of Radio Electronics, 2017, No. 6. Available at http://jre.cplire.ru/jre/jun17/6/text.pdf. (In Russian)