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Dirac delta as a useful technical Tool in modelling signals but hard to think about It as a physical signal itself

Borys A.

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

2024

Vol. 18 No. 2

387--392

In this paper, we show that the Dirac delta is a useful technical tool in modelling signals but hard to think about it as a physical signal itself. This thesis is supported here by an example coming from the field of measuring physical quantities and measurement theory.

A new result on description of the spectrum of a sampled signal

Borys A.

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

2024

Vol. 18 No. 2

393--397

It is explained, in introduction of this paper, why the description of the output signal at an A/D converter in the form that is presented in such respected textbooks as: a one written by Prandoni and Vetterli, and another one by van de Plassche is appropriate and correct. Unlike all others, especially those using in it the so-called comb of Dirac deltas. The latter ones do not lead to getting a correct formula for the spectrum of the output waveform of an A/D converter, or they yield no formula at all. Using the description of the A/D output signal in form of a step function (as in the textbooks mentioned above), a new, correct formula for calculating the spectrum of the sampled signal is derived in this paper. It is a revised version of the formula currently used in the literature, that is of the so-called Discrete-Time Fourier Transform (DTFT), and it is a product of this DTFT and a certain correction factor. Finally, some literature items are referred to in which the designers of integrated circuits (containing A/D converters) point out discrepancies that arise in designs when the multiplying factor mentioned above is not taken into account.