The Problem of Aliasing and Folding Effects in Spectrum of Sampled Signals in View of Information Theory

• Autorzy: Borys Andrzej

Identyfikatory

DOI

10.24425/ijet.2022.139884

• Języki publikacji: EN

Abstrakty

EN

In this paper, the problem of aliasing and folding effects in spectrum of sampled signals in view of Information Theory is discussed. To this end, the information content of deterministic continuous time signals, which are continuous functions, is formulated first. Then, this notion is extended to the sampled versions of these signals. In connection with it, new signal objects that are partly functions but partly not are introduced. It is shown that they allow to interpret correctly what the Whittaker–Shannon reconstruction formula in fact does. With help of this tool, the spectrum of the sampled signal is correctly calculated. The result achieved demonstrates that no aliasing and folding effects occur in the latter. Finally, it is shown that a Banach–Tarski-like paradox can be observed on the occasion of signal sampling.

Słowa kluczowe

EN

signal sampling; modeling of sampled signal in time domain; signal information content; spectrum aliasing and folding; Banach–Tarski-like paradox in signal sampling

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: International Journal of Electronics and Telecommunications
• Rocznik: 2022
• Tom: Vol. 68, No. 2
• Strony: 315--322
• Opis fizyczny: Bibliogr. 10 poz., wykr.

Twórcy

autor

Borys Andrzej

• Department of Marine Telecommunications, Faculty of Electrical Engineering, Gdynia Maritime University, Gdynia, Poland

Bibliografia

• [1] A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing. New Jersey: Prentice Hall, 1998.
• [2] R. J. Marks II, Introduction to Shannon Sampling and Interpolation Theory, New York: Springer-Verlag, 1991.
• [3] R. N. Bracewell, The Fourier Transform and Its Applications, New York: McGraw-Hill, 2000.
• [4] A. Borys, “Further discussion on modeling of measuring process via sampling of signals,” Intl Journal of Electronics and Telecommunications, vol. 66, no. 3, pp. 507-513, 2020. https://doi.org/10.24425-ijet.2020.134006
• [5] A. Borys, “Spectrum aliasing does not occur in case of ideal signal sampling,” Intl Journal of Electronics and Telecommunications, vol. 67, no. 1, pp. 71-77, 2021. https://doi.org/10.24425-ijet.2021.135946
• [6] A. Borys, “Extended definitions of spectrum of a sampled signal,” Intl Journal of Electronics and Telecommunications, vol. 67, no. 3, pp. 395-401, 2021. https://doi.org/10.24425-ijet.2021.137825
• [7] R. F. Hoskins, Delta Functions: Introduction to Generalised Functions. Oxford: Woodhead Publishing, 2010.
• [8] A. Borys, “Some topological aspects of sampling theorem and reconstruction formula,” Intl Journal of Electronics and Telecommunications, vol. 66, no. 2, pp. 301-307, 2020. https://doi.org/10.24425/ijet.2020.131878
• [9] A. Borys, “Measuring process via sampling of signals, and functions with attributes,” Intl Journal of Electronics and Telecommunications, vol. 66, no. 2, pp. 309-314, 2020. https://doi.org/10.24425-ijet.2020.131879/0
• [10] A. Borys, “Filtering property of signal sampling in general and under-sampling as a specific operation of filtering connected with signal shaping at the same time,” Intl Journal of Electronics and Telecommunications, vol. 66, no. 3, pp. 589-594, 2020. https://doi.org/10.24425-ijet.2020.134016

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).