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Abstrakty
It is common knowledge that no signals having the form of a sequence of weighted Dirac deltas, as they are currently modelled so, are present, in reality, at the output of analog-to-digital converters (ADC). No such signals are available in the otherwise large variety of physical signals. This has been illustrated in many works and shown by means of measurements. However, it is highly intriguing that the same papers (with the exception of this article) consider it necessary to model the signals at the output of ADC via sequences of Dirac deltas because only such an approach allows to describe the aliasing effect occurring in the spectra of these signals. But due to this incorrect description such an approach is obviously incomprehensible to everyone. In accepting this, however, it has been overlooked that this does not have to be the case at all. The effect of aliasing in the spectrum of a sampled signal may be explained by modeling this signal as a weighted step function. Moreover, such an approach offers also a quantitatively more accurate result for this spectrum than the one obtained using the current method. All that is illustrated in this paper that focuses on this specific theme.
Słowa kluczowe
Rocznik
Tom
Strony
15--22
Opis fizyczny
Bibliogr. 27 poz., rys., wykr.
Twórcy
autor
- Faculty of Electrical Engineering Gdynia Maritime University, Gdynia, Poland
Bibliografia
- [1] A. Borys, “Some Topological Aspects of Sampling Theorem and Reconstruction Formula”, International Journal of Electronics and Telecommunications, vol. 66, no. 2, pp. 301–307, 2020 (https://doi.org/10.24425/ijet.2020.131878).
- [2] A. Borys, “Measuring Process via Sampling of Signals, and Functions with Attributes”, International Journal of Electronics and Telecommunications, vol. 66, no. 2, pp. 309–314, 2020 (https://doi.org/10.24425/ijet.2020.131879).
- [3] A. Borys, “Further Discussion on Modeling of Measuring Process via Sampling of Signals”, International Journal of Electronics and Telecommunications, vol. 66, no. 3, pp. 507–513, 2020 (https://doi.org/10.24425/ijet.2020.134006).
- [4] R. van de Plassche, Integrated Analog-To-Digital and Digital-To-Analog Converters, Berlin: Springer Verlag, 501 p., 1994 (https://doi.org/10.1007/978-1-4615-2748-0).
- [5] MIT, OpenCourseWare, “Signal Processing – Continuous and Discrete”, [Online]. Available: https://ocw.mit.edu/courses/2-161-signal-processing-continuous-and-discrete-fall-2008/pages/readings/.
- [6] J.H. McClellan, R. Schafer, and M. Yoder, DSP First, London: Pearson, 2015 (ISBN: 9780136019251).
- [7] V.K. Ingle and J.G. Proakis, Digital Signal Processing Using Matlab, 3rd ed., Stamford: Cengage Learning, 672 p., 2011 (ISBN: 9781111427375).
- [8] R.J. Marks II, Introduction to Shannon Sampling and Interpolation Theory, New York: Springer-Verlag, 324 p., 1991 (https://doi.org/10.1007/978-1-4613-9708-3).
- [9] R.N. Bracewell, The Fourier Transform and Its Applications, 3rd ed., New York: McGraw-Hill, 640 p., 2000 (ISBN: 9780073039381).
- [10] R. Brigola, Fourier-Analysis und Distributionen: Eine Einführung mit Anwendungen, Hamburg: Tredition, 448 p., 2013 (ISBN:9783847287421) (in German).
- [11] A. Borys, “Spectrum Aliasing does not Occur in Case of Ideal Signal Sampling”, International Journal of Electronics and Telecommunications, vol. 67, no. 1, pp. 71–77, 2021 (https://doi.org/10.24425/ijet.2021.135946).
- [12] S.C. Gupta, “Delta Function”, IEEE Transactions on Education, vol. 7, no. 1, pp. 16–22, 1964 (https://doi.org/10.1109/TE.1964.4321835).
- [13] R.F. Hoskins, Delta Functions: An Introduction to Generalized Functions, Oxford: Woodhead Publishing, 280 p., 2010 (ISBN: 9781904275398).
- [14] A. Borys, “Spectrum Aliasing does Occur only in Case of Nonideal Signal Sampling”, International Journal of Electronics and Telecommunications, vol. 67, no. 1, pp. 79–85, 2021 (https://doi.org/10.24425/ijet.2021.135947).
- [15] A. Dąbrowski, “Fundamentals of Systems, Signals and Information Theory: Sampling of Signals”, Department of Control and Systems Engineering, Technical University of Poznań, Poland, 2008.
- [16] A. Borys, “An Unexpected Result on Modelling the Behavior of A/D Converters and the Signals They Produce”, International Journal of Electronics and Telecommunications, vol. 69, no. 1, pp. 193–198, 2023 (https://doi.org/10.24425/ijet.2023.144350).
- [17] A. Borys, “Sampled Signal Description That is Used in Calculation of Spectrum of This Signal Needs Revision”, International Journal of Electronics and Telecommunications, vol. 69, no. 2, pp. 319–324, 2023 (https://doi.org/10.24425/ijet.2023.144367).
- [18] P. Prandoni and M. Vetterli, Signal Processing for Communications, Lausanne: EPFL Press, 371 p., 2008 (ISBN: 9781420070460).
- [19] N. Ma et al., “Influence of Sampling Frequency on Magneto-optical Imaging under Alternating Magnetic Field Excitation”, IEEE Sensors Journal, vol. 19, no. 23, pp. 11591–11600, 2019 (https://doi.org/10.1109/JSEN.2019.2937629).
- [20] K. Sozański, Digital Signal Processing in Power Electronics Control Circuits, London: Springer-Verlag, 285 p., 2013 (ISBN: 9781447152668).
- [21] T.S. Low and C. Bi, “Design of A/D Converters with Hierarchic Networks”, IEEE Transactions on Industrial Electronics, vol. 43, no. 1, pp. 184–191, 1996 (https://doi.org/10.1109/41.481424).
- [22] MathWorks, “Switched Capacitor Analog to Digital Converter”, [Online]. Available: https://www.mathworks.com/help/sps/ug/switched-capacitor-analog-to-digital-converter.html.
- [23] A. Mertins, Signaltheorie: Grundlagen der Signalbeschreibung, Filterbänke, Wavelets, Zeit-Frequenz-Analyse, Parameter- und Signalschätzung. Berlin: Springer Verlag, 461 p., 2020 (https://doi.org/10.1007/978-3-658-29648-3) (in German).
- [24] U. Zölzer, Digital Audio Signal Processing, Chichester: Wiley & Sons, 340 p., 2008 (ISBN: 9780470997857).
- [25] C. Marven and G. Ewers, A Simple Approach to Digital Signal Processing, Hoboken: Wiley-Interscience, 236 p., 1996 (ISBN: 9780471152439).
- [26] SlideServe, “Analog/Digital Conversion”, [Online]. Available: https://www.slideserve.com/papaj/analog-digital-conversion-powerpoint-ppt-presentation.
- [27] A. Borys, “A New Result on Description of the Spectrum of a Sampled Signal”, International Journal on Marine Navigation and Safety of Sea Transportation, vol. 18, no. 2, 2024 (https://doi.org/10.12716/1001.18.02.17).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-91f1c860-90c1-4de7-8724-6a1e0493bd89
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