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ISSN 2083-6473
ISSN 2083-6481 (electronic version)




Associate Editor
Prof. Tomasz Neumann

Published by
TransNav, Faculty of Navigation
Gdynia Maritime University
3, John Paul II Avenue
81-345 Gdynia, POLAND
A New Result on Description of the Spectrum of a Sampled Signal
1 Gdynia Maritime University, Gdynia, Poland
ABSTRACT: 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.
Prandoni P., Vetterli M. 2008. Signal Processing for Communications, Lausanne: EPFL Press. - doi:10.1201/9781439808009
van de Plassche R. 1994. Integrated Analog-To-Digital and Digital-To-Analog Converters, Berlin: Springer Verlag. - doi:10.1007/978-1-4615-2748-0
Borys A. 2022. Sampled signal description that is used in calculation of spectrum of this signal needs revision, IEEE Signal Processing Letters, submitted for publication.
Oppenheim A. V., Schafer R. W., Buck J. R. 1998. Discrete-Time Signal Processing, New Jersey: Prentice Hall.
Vetterli M., Kovacevic J., Goyal V. K. 2014. Foundations of Signal Processing, Cambridge University Press, Cambridge. - doi:10.1017/CBO9781139839099
de la Rosa J., Perez-Verdu B., Medeiro F., del Rio R., Rodriguez-Vazquez A. 2001. Effect of non-linear settling error on the harmonic distortion of fully-differential switched-current bandpass sigma-delta modulators, Proceedings of the Conference ISCAS’2001, 340-343.
de la Rosa J., Perez-Verdu B., Medeiro F., del Rio R., Rodri-guez-Vazquez A. 2004. Analysis of error mechanisms in switched-current sigma-delta modulators, Analog Integrated Circuits and Signal Processing, vol. 38, 175–201. - doi:10.1023/B:ALOG.0000011167.24521.82
Citation note:
Borys A.: A New Result on Description of the Spectrum of a Sampled Signal. TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 18, No. 2, doi:10.12716/1001.18.02.17, pp. 393-397, 2024
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