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The Problem of Aliasing and Folding Effects in Spectrum of Sampled Signals in View of Information Theory
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The Problem of Aliasing and Folding Effects in Spectrum of Sampled Signals in View of Information Theory
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Journal Article
The Problem of Aliasing and Folding Effects in Spectrum of Sampled Signals in View of Information Theory
2022
Overview
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.
Publisher
Polish Academy of Sciences
