DOI 10.17586/0021-3454-2017-60-6-504-512
UDC 621.391.833.64
RECONSTRUCTION OF FINITE-LENGTH PERIODIC DISCRETE-TIME SIGNALS WITH THE USE OF TRIGONOMETRIC INTERPOLATION
B. N. Yeltsin Ural Federal University, Institute of Radio-Electronics and Information Systems; Department of Radio-Electronics and Information Systems; Professor
D. V. Kusaykin
Ural Technical Institute of Communication and Computer Science — Branch of Siberian State University of Telecommunications and Information Sciences, Department of Multi-channel Electrical Communication; Associate Professor
Abstract. Results of a research on the accuracy of finite-length discrete-time signal (DS) reconstruction by means of trigonometric interpolation are presented. The case when a non-integer number of discrete counts is placed in one period of the signal is considered. Formal increase in the number of counts of discrete signal is found not to provide always a reduction in interpolation error. The relations between the frequency of the periodic signal, the sampling frequency and the number of counts of DS, providing the least error recovery of the signal, are derived. It is demonstrated that the increase in the number of DS counts used for reconstruction the original signal, may decrease reconstruction accuracy of the continuous signal; the effect is explained by the Gibbs phenomenon when the repair interval of the periodic signal fits a non-integer number of its periods.
Keywords: discrete signal, trigonometric interpolation, discrete signal reconstruction, interpolation error, Gibbs phenomenon
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