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2 TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

2 Borys A.

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Definition of sampled signal spectrum and shannon’s proof of reconstruction formula

Borys A.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

2022

Vol. 16 No. 3

473--478

The objective of this paper is to show from another perspective that the definition of the spectrum of a sampled signal, which is used at present by researchers and engineers, is nothing else than an arbitrary choice for what is possibly not uniquely definable. To this end and for illustration, the Shannon’s proof of reconstruction formula is used. As we know, an auxiliary mathematical entity is constructed in this proof by performing periodization of the spectrum of an analog, bandlimited, energy signal. Admittedly, this entity is not called there a spectrum of the sampled signal - there is simply no need for this in the proof – but as such it is used in signal processing. And, it is not clear why just this auxiliary mathematical object has been chosen in signal processing to play a role of a definition of the spectrum of a sampled signal. We show here what are the interpretation inconsistences associated with the above choice. Finally, we propose another, simpler and more useful definition of the spectrum of a sampled signal, for the cases where it can be needed.

Simple proof of incorrectness of the formula describing aliasing and folding effects in spectrum of sampled signal in case of Ideal signal sampling

Borys A.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

2021

Vol. 15 No. 4

873--876

A simple proof of the incorrectness of the formula, which is used in the literature nowadays, for description of the aliasing and folding effects in the spectrum of a sampled signal in the case of an ideal signal sampling, is given in this paper. By the way, it is also shown that such the effects cannot occur at all, when the signal sampling is considered to be performed perfectly.