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.
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.
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