Some Topological Aspects of Sampling Theorem and Reconstruction Formula

• Autorzy: Borys Andrzej

Identyfikatory

DOI

10.24425/ijet.2020.131878

• Języki publikacji: EN

Abstrakty

EN

We present here a few thoughts regarding topological aspects of transferring a signal of a continuous time into its discrete counterpart and recovering an analog signal from its discrete-time equivalent. In our view, the observations presented here highlight the essence of the above transformations. Moreover, they enable deeper understanding of the reconstruction formula and of the sampling theorem. We also interpret here these two borderline cases that are associated with a time quantization step going to zero, on the one hand, and approaching its greatest value provided by the sampling theorem, on the other.

Słowa kluczowe

EN

topological issues; reconstruction formula; sampling theorem

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: International Journal of Electronics and Telecommunications
• Rocznik: 2020
• Tom: Vol. 66, No. 2
• Strony: 301--307
• Opis fizyczny: Bibliogr. 8 poz., wykr.

Twórcy

autor

Borys Andrzej

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

Bibliografia

• [1] A. Boggess and F. J. Narcowich, A First Course in Wavelets with Fourier Analysis, New York: John Wiley & Sons, 2011.
• [2] R. J. Marks II, Introduction to Shannon Sampling and Interpolation Theory, New York: Springer-Verlag, 1991.
• [3] A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, New York: Pearson, 2010.
• [4] W. E. Sabin, Discrete-Signal Analysis and Design, New York: John Wiley & Sons, 2008.
• [5] K. Sozański, Digital Signal Processing in Power Electronics Control Circuits, London: Springer-Verlag, 2013.
• [6] U. Zölzer, Digital Audio Signal Processing, Chichester: John Wiley & Sons, 2008.
• [7] Available at: https://en.wikipedia.org/wiki/Leopold_Kronecker, Oct. 2019.
• [8] Available at: http://mathworld.wolfram.com/DeltaFunction.html, Oct. 2019.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).