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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