An Unexpected Result on Modelling the Behavior of A/D Converters and the Signals They Produce

• Autorzy: Borys Andrzej

Identyfikatory

DOI

10.24425/ijet.2023.144350

• Języki publikacji: EN

Abstrakty

EN

In this paper, we show that the signal sampling operation considered as a non-ideal one, which incorporates finite time switching and operation of signal blurring, does not lead, as the researchers would expect, to Dirac impulses for the case of their ideal behavior.

Słowa kluczowe

EN

modelling; signal; sampling operation

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: International Journal of Electronics and Telecommunications
• Rocznik: 2023
• Tom: Vol. 69, No. 1
• Strony: 185--191
• Opis fizyczny: Bibliogr. 35 poz., wykr.

Twórcy

autor

Borys Andrzej

• Gdynia Maritime University, Poland

• https://orcid.org/0000-0003-1316-4031

Bibliografia

• [1] J. H. McClellan, R. Schafer, and M. Yoder, DSP First. London, England: Pearson, 2015.
• [2] M. Vetterli, J. Kovacevic, and V. K. Goyal, Foundations of Signal Processing. Cambridge, England: Cambridge University Press, 2014.
• [3] R. Wang, Introduction to Orthogonal Transforms with Applications in Data Processing and Analysis. Cambridge, England: Cambridge University Press, 2010.
• [4] V. K. Ingle and J. G. Proakis, Digital Signal Processing Using Matlab. Stamford, CT, USA: Cengage Learning, 2012.
• [5] A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing. New Jersey: Prentice Hall, 1998.
• [6] R. J. Marks II, Introduction to Shannon Sampling and Interpolation Theory. New York: Springer-Verlag, 1991. https://doi.org/10.1007/978-1-4613-9708-3.
• [7] R. N. Bracewell, The Fourier Transform and Its Applications. New York: McGraw-Hill, 2000.
• [8] R. Brigola, Fourier-Analysis und Distributionen. Hamburg: edition swk, 2013.
• [9] P. Prandoni and M. Vetterli, Signal Processing for Communications. Lausanne: EPFL Press (a Swiss academic publisher distributed by CRC Press), 2008.
• [10] K. B. Howell, Principles of Fourier Analysis. Boca Raton: Chapman and Hall, 2001.
• [11] C. Gasquet and P. Witomski. Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets. Berlin: Springer, 1998.
• [12] R. F. Hoskins, Delta Functions: Introduction to Generalised Functions. Oxford: Woodhead Publishing, 2010.
• [13] 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. http://doi.org/10.24425/ijet.2021.135947.
• [14] A. Dąbrowski, “Fundamentals of systems, signals and information theory: sampling of signals,” (in Polish), January 2008, Accessed on: July 7, 2022. [Online]. Available: http://150.254.27.109/uploaded/dydaktyka/wyklady/podstawy_teorii_systemow_sygnalow_i_informacji/05_probkowanie_www.pdf.
• [15] A. Borys, “On using a stochastic-delay model to estimate solid-cluster velocities in gas-solid streams,” Zeszyty Naukowe ATR seria Telekomunikacja i Elektronika, vol. 8, pp. 43-63, 1997.
• [16] Aggrawal Sir Physics, “Dirac Delta as limiting form of Gaussian function,” Dec. 2021, Accessed on: July 11, 2022. [Online]. Available: https://www.youtube.com/watch?v=1KQX4PKvFl0.
• [17] A. Dotson, “Pushing a Gaussian to the limit,” Sept. 2018, Accessed on: July 11, 2022. [Online]. Available: https://www.youtube.com/watch?v=d09gXC_D_24.
• [18] For the Love of Physics, “Dirac delta as an approximation of normal distribution,” August 2019, Accessed on: July 11, 2022. [Online]. Available: https://www.youtube.com/watch?v=lmpPNvzZdH0.
• [19] A. Borys, “Consideration of Volterra series with excitation and/or impulse responses in form of Dirac impulses,” IEEE Trans. on Circuits and Systems - II: Express Briefs, vol. 57, no. 6, pp. 466-470, June 2010. http://doi.org/10.1109/TCSII.2010.2048376.
• [20] I. Sandberg, “Linear maps and impulse responses,” IEEE Trans. on Circuits and Systems, vol. 35, no. 2, pp. 201-206, Feb. 1988. http://doi.org/10.1109/31.1722.
• [21] I. Sandberg, “Integral representations for linear maps,” IEEE Trans. on Circuits and Systems, vol. 35, no. 5, pp. 536-544, May 1988. http://doi.org/10.1109/31.1781.
• [22] A. Borys and Z. Zakrzewski, “Use of phasors in nonlinear analysis,” Intl Journal of Electronics and Telecommunications, vol. 59, no. 3, pp. 219-228, 2013. http://doi.org/10.2478/eletel-2013-0026.
• [23] A. Borys, “Sandberg’s representation theorem and classification of linear systems,” IEEE Trans. on Circuits and Systems – II: Express Briefs, vol. 55, no. 7, pp. 678- 679, July 2008. http://doi.org/10.1109/TCSII.2008.921598.
• [24] B. Osgood, The Fourier Transform and Its Applications, Lecture Notes EE261. Stanford: Stanford University, 2014.
• [25] L. Zadeh, “Frequency analysis of variable networks,” Proceedings of the IRE, vol. 38, no. 3, pp. 291-299, March 1950.
• [26] T. Kailath, “Time-variant communication channels,” IEEE Transactions on Information Theory, vol. 9, no. 4, pp 233–237, Oct. 1963.
• [27] J. Kudrewicz, J. Osiowski, and M. Piekarski, unpublished notes.
• [28] L. Schwartz, “Sur l’impossibilité de la multiplication des distributions,” Comptes Rendus Acad. Sci. Paris, vol. 239, pp. 847-848, 1954. [29] J. F. Colombeau, Multiplication of Distributions. Berlin: Springer-Verlag, 1992.
• [30] F. Bagarello, “A pedagogical approach to multiplication of distributions in any spatial dimensions,” Zeszyty Naukowe UTP (d. ATR) seria Telekomunikacja i Elektronika, vol. 10, pp. 5-26, 2007.
• [31] A. Borys, A. Kamiński, and S. Sorek, “Volterra systems and powers of Dirac delta impulses,” Integral Transforms and Special Functions, vol. 20, no. 3-4, pp. 301-308, March-April 2009. https://doi.org/10.1080/10652460802565214.
• [32] A. Borys, “Explanation of problems occurring in the analysis of nonlinear circuits with the use of Volterra series (in Polish),” Zeszyty Naukowe Wyższej Szkoły Informatyki (WSInf) w Łodzi, Teoria i zastosowania informatyki, vol. 5, no. 1, pp. 71-114, 2006.
• [33] A. Borys, “The modified nodal formulation for nonlinear circuits with multiple inputs,” Zeszyty Naukowe ATR seria Telekomunikacja i Elektronika, vol. 9, pp. 53-62, 2006.
• [34] A. Borys, “Extended definitions of spectrum of a sampled signal,” Intl Journal of Electronics and Telecommunications, vol. 67, no. 3, pp. 395-401, 2021. http://doi.org/10.24425/ijet.2021.137825.
• [35] 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. http://doi.org/10.24425/ijet.2022.139884.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).