Revision of the formula describing the spectrum of output signals at A/D converters

• Autorzy: Borys Andrzej

Identyfikatory

DOI

10.24425/ijet.2024.149529

• Języki publikacji: EN

Abstrakty

EN

This paper crowns efforts, made by its author, aiming in showing and proving that the current formula for calculation of the spectra of output signals at A/D converters requires a correcting factor in it. A number of partial results obtained and published in the last years are referred to here. They paved the way to a fully satisfactory and correct result; it is presented in this work. The corrected formula for spectrum calculation is derived using a description of the output signal of an A/D converter by means of the so-called Dirac comb, however not in a direct form, but with taking into account physical reality. In addition, the paper contains a number of interpretative remarks, comments, and explanations - clarifying those matters that have so far been omitted in analyses of the sampling process, despite the fact that they raised various types of doubts.

Słowa kluczowe

EN

Modelling of output signals of A/D converters forcalculation of their spectra and a corrected formula forperforming this task

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: International Journal of Electronics and Telecommunications
• Rocznik: 2024
• Tom: Vol. 70, No. 1
• Strony: 183--190
• Opis fizyczny: Bibliogr. 22 poz., rys.

Twórcy

autor

Borys Andrzej

• Department of Marine Telecommunications, Faculty of Electrical Engineering, Gdynia Maritime University, Poland

Bibliografia

• [1] A. Borys, “Spectrum aliasing does not occur in case of ideal signal sampling,” Intl Journal of Electronics and Telecommunications, vol. 67, no. 1, pp. 71-77, 2021, doi:10.24425/ijet.2021.135946
• [2] A. Borys, “Spectrum aliasing does occur only in case of non-ideal signal sampling,” Intl Journal of Electronics and Telecommunications, vol. 67, no. 1, pp. 79-85, 2021, doi:10.24425/ijet.2021.135947
• [3] A. Borys, “Extended definitions of spectrum of a sampled signal,” Intl Journal of Electronics and Telecommunications, vol. 67, no. 3, pp. 395-401, 2021, doi:10.24425/ijet.2021.137825
• [4] A. Borys, “Another proof of ambiguity of the formula describing aliasing and folding effects in spectrum of sampled signal,” Intl Journal of Electronics and Telecommunications, vol. 68, no. 1, pp. 115-122, 2022, doi:10.24425/ijet.2022.139858
• [5] A. Borys, “The problem of aliasing and folding effects in spectrum of sampled signals in view of Information Theory,” Intl Journal of Electronics and Telecommunications, vol. 68, no. 2, pp. 315-322, 2022, doi:10.24425/ijet.2022.139884
• [6] A. Borys, “Simple proof of incorrectness of the formula describing aliasing and folding effects in spectrum of sampled signal in case of ideal signal sampling,” Intl Journal on Marine Navigation and Safety of Sea Transportation, vol. 15, no. 4, pp. 873-876, 2021, doi:10.12716/1001.15.04.20
• [7] A. Borys, “Modelling of non-ideal signal sampling via averaging operation and spectrum of sampled signal predicted by this model,” Intl Journal on Marine Navigation and Safety of Sea Transportation, vol. 16, no. 2, pp. 273-278, 2022, doi:10.12716/1001.16.02.10
• [8] A. Borys, “Definition of sampled signal spectrum and Shannon’s proof of reconstruction formula,” Intl Journal on Marine Navigation and Safety of Sea Transportation, vol. 16, no. 3, pp. 473-478, 2022, doi:10.12716/1001.16.03.08
• [9] A. Borys, “On modelling and description of the output signal of a sampling device,” Archives of Electrical Engineering, vol. 72, no. 1, pp. 147-155, 2023.
• [10] A. Borys, “Some topological aspects of sampling theorem and reconstruction formula,” Intl Journal of Electronics and Telecommunications, vol. 66, no. 2, pp. 301-307, 2020, doi:10.24425-ijet.2020.131878
• [11] A. Borys, “An unexpected result on modelling the behavior of A/D converters and the signals they produce,” Intl Journal of Electronics and Telecommunications, vol. 69, no. 1, pp. 193-198, 2023, doi:10.24425-ijet.2023.144350
• [12] A. Borys, “Sampled signal description that is used in calculation of spectrum of this signal needs revision,” Intl Journal of Electronics and Telecommunications, vol. 69, no. 2, pp. 319-324, 2023, doi:10.24425-ijet.2023.144367
• [13] A. Borys, “A new result on description of the spectrum of a sampled signal,” Intl Journal on Marine Navigation and Safety of Sea Transportation, submitted for publication, 2023, doi:10.12716/1001.18.02.17
• [14] R. van de Plassche, “Integrated Analog-To-Digital and Digital-To-Analog Converters,” Berlin, Germany: Springer Verlag, 1994.
• [15] A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing. New Jersey: Prentice Hall, 1998.
• [16] E. Zappa, private communication.
• [17] R. Yan, private communication.
• [18] A. Mertins, Signaltheorie: Grundlagen der Signalbeschreibung, Filterbänke, Wavelets, Zeit-Frequenz-Analyse, Parameter- und Signalschätzung. Berlin, Germany: Springer Verlag, 2020, doi:10.1007/978-3-658-29648-3
• [19] S. Zozor, private communication.
• [20] A. Yeredor, private communication.
• [21] M. Vetterli, P. Marziliano, and T. Blu, “Sampling signals with finite rate of innovation,” IEEE Transactions on Signal Processing, vol. 50, no. 6, pp. 1417-1428, 2002, doi:10.1109/TSP.2002.1003065
• [22] M. Vetterli, J. Kovacevic, and V. K. Goyal, Foundations of Signal Processing. Cambridge, England: Cambridge University Press, 2014, doi: 10.1017/CBO9781139839099

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).