Some Topological Aspects of Sampling Theorem and Reconstruction Formula
Abstract
In this paper, we present 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 transform-ations. 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.References
A. Boggess and F. J. Narcowich, A First Course in Wavelets with Fourier Analysis, New York: John Wiley & Sons, 2011.
R. J. Marks II, Introduction to Shannon Sampling and Interpolation Theory, New York: Springer-Verlag, 1991.
A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, New York: Pearson, 2010.
W. E. Sabin, Discrete-Signal Analysis and Design, New York: John Wiley & Sons, 2008.
K. Sozański, Digital Signal Processing in Power Electronics Control Circuits, London: Springer-Verlag, 2013.
U. Zölzer, Digital Audio Signal Processing, Chichester: John Wiley & Sons, 2008.
Available at: https://en.wikipedia.org/wiki/Leopold_Kronecker, Oct. 2019.
Available at: http://mathworld.wolfram.com/DeltaFunction.html, Oct. 2019.
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