Some Topological Aspects of Sampling Theorem and Reconstruction Formula

Andrzej Marek Borys

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.

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References


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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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International Journal of Electronics and Telecommunications
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