Revision of the Formula Describing the Spectrum of Output Signals at A/D Converters
Abstract
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.References
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.
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.
A. Borys, “Extended definitions of spectrum of a sampled signal,” Intl Journal of Electronics and Telecommunications, vol. 67, no. 3, pp. 395-401, 2021.
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.
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.
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.
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.
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.
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.
A. Borys, “Some topological aspects of sampling theorem and reconstruction formula,” Intl Journal of Electronics and Telecommu-nications, vol. 66, no. 2, pp. 301-307, 2020.
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.
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.
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.
R. van de Plassche, Integrated Analog-To-Digital and Digital-To-Analog Converters. Berlin, Germany: Springer Verlag, 1994.
A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing. New Jersey: Prentice Hall, 1998.
E. Zappa, private communication.
R. Yan, private communication.
A. Mertins, Signaltheorie: Grundlagen der Signalbeschreibung, Filterbänke, Wavelets, Zeit-Frequenz-Analyse, Parameter- und Signalschätzung. Berlin, Germany: Springer Verlag, 2020.
S. Zozor, private communication.
A. Yeredor, private communication.
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.
M. Vetterli, J. Kovacevic, and V. K. Goyal, Foundations of Signal Processing. Cambridge, England: Cambridge University Press, 2014.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 International Journal of Electronics and Telecommunications
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
1. License
The non-commercial use of the article will be governed by the Creative Commons Attribution license as currently displayed on https://creativecommons.org/licenses/by/4.0/.
2. Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s. The undersigned also warrants that the manuscript (or its essential substance) has not been published other than as an abstract or doctorate thesis and has not been submitted for consideration elsewhere, for print, electronic or digital publication.
3. User Rights
Under the Creative Commons Attribution license, the author(s) and users are free to share (copy, distribute and transmit the contribution) under the following conditions: 1. they must attribute the contribution in the manner specified by the author or licensor, 2. they may alter, transform, or build upon this work, 3. they may use this contribution for commercial purposes.
4. Rights of Authors
Authors retain the following rights:
- copyright, and other proprietary rights relating to the article, such as patent rights,
- the right to use the substance of the article in own future works, including lectures and books,
- the right to reproduce the article for own purposes, provided the copies are not offered for sale,
- the right to self-archive the article
- the right to supervision over the integrity of the content of the work and its fair use.
5. Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.
6. Termination
This agreement can be terminated by the author or the Journal Owner upon two months’ notice where the other party has materially breached this agreement and failed to remedy such breach within a month of being given the terminating party’s notice requesting such breach to be remedied. No breach or violation of this agreement will cause this agreement or any license granted in it to terminate automatically or affect the definition of the Journal Owner. The author and the Journal Owner may agree to terminate this agreement at any time. This agreement or any license granted in it cannot be terminated otherwise than in accordance with this section 6. This License shall remain in effect throughout the term of copyright in the Work and may not be revoked without the express written consent of both parties.
7. Royalties
This agreement entitles the author to no royalties or other fees. To such extent as legally permissible, the author waives his or her right to collect royalties relative to the article in respect of any use of the article by the Journal Owner or its sublicensee.
8. Miscellaneous
The Journal Owner will publish the article (or have it published) in the Journal if the article’s editorial process is successfully completed and the Journal Owner or its sublicensee has become obligated to have the article published. Where such obligation depends on the payment of a fee, it shall not be deemed to exist until such time as that fee is paid. The Journal Owner may conform the article to a style of punctuation, spelling, capitalization and usage that it deems appropriate. The Journal Owner will be allowed to sublicense the rights that are licensed to it under this agreement. This agreement will be governed by the laws of Poland.
By signing this License, Author(s) warrant(s) that they have the full power to enter into this agreement. This License shall remain in effect throughout the term of copyright in the Work and may not be revoked without the express written consent of both parties.
