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Highlighting problems occurring in analysis of critical sampling of cosinusoidal signal

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EN
Abstrakty
EN
When the sampling of an analog signal uses the sampling rate equal to exactly twice the value of a maximal frequency occurring in the signal spectrum, it is called a critical one. As known from the literature, this kind of sampling can be ambiguous in the sense that the reconstructed signal from the samples obtained by criti-cal sampling is not unique. For example, such is the case of sampling of a cosinusoidal signal of any phase. In this paper, we explain in very detail the reasons of this behavior. Furthermore, it is also shown here that manipulating values of the coefficients of the transfer function of an ideal rectangular reconstruction filter at the transition edges from its zero to non-zero values, and vice versa, does not eliminate the ambiguity mentioned above.
Twórcy
autor
  • Gdynia Maritime University, Gdynia, Poland
autor
  • AGH University of Science and Technology, Kraków, Poland
Bibliografia
  • 1. Marks II R. J. 1991. Introduction to Shannon Sampling and Interpolation Theory, Springer-Verlag, New York.
  • 2. Vetterli M., Kovacevic J., Goyal V. K. 2014. Foundations of Signal Processing, Cambridge University Press, Cambridge.
  • 3. Landau H. J. 1967. Sampling, data transmission, and the Nyquist rate, Proceedings of the IEEE, vol. 55, no. 10, 1701 – 1706.
  • 4. Korohoda P., Borgosz J. 1999. Explanation of sampling and reconstruction at critical rate, Proceedings of the 6th International Conference on Systems, Signals, and Image Processing (IWSSIP), Bratislava, Slovakia, 157-160.
  • 5. Osgood B. 2014. The Fourier Transform and Its Applications, Lecture Notes EE261, Stanford University.
  • 6. Borys A., Korohoda P. 2017. Analysis of critical sampling effects revisited, Proceedings of the 21st International Conference Signal Processing: Algorithms, Architectures, Arrangements, and Applications SPA2017, Poznań, Poland, 131 – 136.
  • 7. Borys A., Korohoda P. 2020. Impossibility of perfect recovering cosinusoidal signal of any phase sampled with Nyquist rate, TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, submitted for publication.
  • 8. Dirac P. A. M. 1947. The Principles of Quantum Mechanics, 3rd Ed., Oxford Univ. Press, Oxford.
  • 9. Hoskins R. F. 2009. Delta Functions: An Introduction to Generalised Functions, Horwood Pub., Oxford.
  • 10. Brigola R. 2013. Fourier-Analysis und Distributionen, edition swk, Hamburg.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020)
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-71b5a786-c25e-4681-b17f-6dccf7fbb939
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