ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)
Menu

5
Issue
vol 67 / May, 2024
Article

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

S. V. Porshnev
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

References:
  1. Schmitter D., Delgado-Gonzalo R., Unser M. IEEE Signal Processing, 2015, no. 11(22), рр.2097–2101. DOI: 10.1109/LSP.2015.2461557
  2. Stotsky A. Proc. IMechE, Part I: J. Systems and Control Engineering, 2010, no. 1(224), рр.65–77.
  3. Selva J. IEEE Trans. Signal Processing, 2008, no. 11(56), рр.5465–5477. DOI: 10.1109/TSP.2008.929659
  4. Adzhemov S., Kurakhtenkov L., Romanov E. T-Comm: Telecommunications and transport, 2009, April, рр. 20–22. (in Russ.)
  5. Ziatdinov S.I., Girina N.V. Journal of Instrument Engineering, 2008, no. 5(51), рр. 42–45. (in Russ.)
  6. Zygmund A. Trigonometric Series, Third Edition, Volumes I & II Combined, Cambridge University Press, 2002, рp. 355.
  7. Lucke R.L. Signal processing, 1993, no. 2(34), рр. 223–230.
  8. Baskakov S.I. Radiotekhnicheskie tsepi i signaly (Radio Engineering Chains and Signals), Moscow, 1998, 462 р. (in Russ.)
  9. Turetskiy A.Kh. Teoriya interpolirovaniya v zadachakh (The Theory of Interpolating in Tasks), Minsk, 1968, 320 р. (in Russ.)
  10. http://pmpu.ru/vf4/interpolation/dft. (in Russ.)
  11. Smirnov V.I. Kurs vysshey matematiki (Course of the Higher Mathematics), Moscow, 1974, Vol. 2, 656 р. (in Russ.)
  12. Ryaben'kiy B.C. Vvedenie v vychislitel'nuyu matematiku (Introduction to Computational Mathematics), Moscow, 2000, 296 р. (in Russ.)
  13. Porshnev S.V., Kusaykin D.V. Electrosvyaz, 2017, no. 6. (in Russ.)
  14. IEEE standard for terminology and test methods for analog-to-digital converters, IEEE Std 1241-2000, 2001, 92 p.
  15. Kalitkin N.N. Chislennye metody (Numerical Methods), Moscow, 1978, 512 р. (in Russ.)