On modelling and description of the output signal of a sampling device

Authors

DOI:

https://doi.org/10.24425/aee.2023.143694

Abstract

The problem of an inconsistent description of an “interface” between the A/D converter and the digital signal processor that implements, for example, a digital filtering (described by a difference equation) – when a sequence of some hypothetical weighted Dirac deltas occurs at its input, instead of a sequence of numbers – is addressed in this paper. Digital signal processors work on numbers, and there is no “interface” element that converts Dirac deltas into numbers. The output of the A/D converter is directly connected to the input of the signal processor. Hence, a clear conclusion must follow that sampling devices do not generate Dirac deltas. Not the other way around. Furthermore, this fact has far-reaching implications in the spectral analysis of discrete signals, as discussed in other works referred to in this paper.

References

[1] Borys A., Spectrum aliasing does occur only in case of non-ideal signal sampling, International Journal of Electronics and Telecommunications, vol. 67, no. 1, pp. 79–85 (2021), DOI: 10.24425/ijet.2021.135947.

[2] Shannon C.E., Communications in the presence of noise, Proceedings of the IRE, vol. 37, pp. 10–21 (1949).

[3] Oppenheim A.V., Schafer R.W., Buck J.R., Discrete-Time Signal Processing, New Jersey: Prentice Hall (1998).

[4] Marks R.J. II, Introduction to Shannon Sampling and Interpolation Theory, New York: Springer-Verlag (1991).

[5] Bracewell R.N., The Fourier Transform and Its Applications, New York: McGraw-Hill (2000).

[6] McClellan J.H., Schafer R., Yoder M., DSP First, London, England: Pearson (2015).

[7] Brigola R., Fourier-Analysis und Distributionen, Hamburg: edition swk (2013).

[8] So H.C., Signals and Systems – Lecture 6 – Discrete-Time Fourier Transform, www.ee.cityu.edu.hk/~hcso/ee3210.html, accessed December 2019.

[9] Vetterli M., Kovacevic J., Goyal V.K., Foundations of Signal Processing, Cambridge, England: Cambridge University Press (2014).

[10] Wang R., Introduction to Orthogonal Transforms with Applications in Data Processing and Analysis, Cambridge, England: Cambridge University Press (2010).

[11] Ingle V.K., Proakis J.G., Digital Signal Processing Using Matlab, Stamford, CT, USA: Cengage Learning (2012).

[12] Borys A., 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), DOI: 10.24425-ijet.2020.134006.

[13] Borys A., Measuring process via sampling of signals, and functions with attributes, International Journal of Electronics and Telecommunications, vol. 66, no. 2, pp. 309–314 (2020), DOI: 10.24425-ijet.2020.131879.

[14] Strichartz R., A Guide to Distribution Theory and Fourier Transforms, Boca Raton, USA: CRC Press (1994).

[15] Borys A., Extended definitions of spectrum of a sampled signal, International Journal of Electronics and Telecommunications, vol. 67, no. 3, pp. 395–401 (2021), DOI: 10.24425-ijet.2021.137825.

[16] Borys A., Definition of sampled signal spectrum and Shannon’s proof of reconstruction formula, submitted for publication in the International Journal on Marine Navigation and Safety of Sea Transportation.

[17] Borys A., On derivation of discrete time Fourier transform from its continuous counterpart, International Journal of Electronics and Telecommunications, vol. 66, no. 2, pp. 355–368 (2020), DOI: 10.24425/ijet.2020.13188.

[18] Peters K.H., Schönheit, Exaktheit, Wahrheit: Der Zusammenhang von Mathematik und Physik am Beispiel der Geschichte der Distributionen, Diepholz, Germany: GNT-Verlag (2004).

[19] Vetterli M., Marziliano P., Blu T., 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.

[20] Borys A., Some topological aspects of sampling theorem and reconstruction formula, International Journal of Electronics and Telecommunications, vol. 66, no. 2, pp. 301–307 (2020), DOI: 10.24425/ijet.2020.131878.

[21] Borys A., Filtering property of signal sampling in general and under-sampling as a specific operation of filtering connected with signal shaping at the same time, International Journal of Electronics and Telecommunications, vol. 66, no. 3, pp. 589–594 (2020), DOI: 10.24425-ijet.2020.134016.

[22] Borys A., 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), DOI: 10.24425/ijet.2021.135946.

[23] Dewantoro G., Rizky I., Murtianta B., Frequency response analysis of microcontroller-based discretetime lead-lag compensators, Archives of Electrical Engineering, vol. 69, no. 4, pp. 937950 (2020).

[24] Sozański K., Digital Signal Processing in Power Electronics Control Circuits, London: Springer-Verlag (2013).

[25] Wepman J.A., Analog-to-digital converters and their applications in radio receivers, IEEE Commun. Mag., vol. 33, no. 5, pp. 39–45 (1995).

[26] Walden R.H., Analog-to-digital converter survey and analysis, IEEE Journal on Selected Areas in Communications, vol. 17, no. 4, pp. 539–550 (1999).

[27] Kinniment D., Yakovlev A., Gao B., Synchronous and asynchronous A-D conversion, IEEE Transactions on VLSI Systems, vol. 8, no. 2, pp. 217–220 (2000), DOI: 10.1109/92.831441.

[28] Robert J., Temes G.C., Valencic V., Dessoulavy R., Deval P., A 16-bit low-voltage CMOS A/D converter, IEEE Journal of Solid-State Circuits, vol. 22, no. 2, pp. 157–163 (1987).

[29] Low T.S., Bi C., Design of A/D converters with hierarchic networks, IEEE Transactions on Industrial Electronics, vol. 43, no. 1, pp. 184–191 (1996).

[30] Miller M.R., Petrie C.S., A multibit sigma-delta ADC for multimode receivers, IEEE Journal Solid-State Circuits, vol. 38, no. 3, pp. 475–482 (2003), DOI: 10.1109/JSSC.2002.808321.

[31] Gulati K., Lee H.S., A low-power reconfigurable analog-to-digital converter, IEEE Journal Solid-State Circuits, vol. 36, no. 12, pp. 1900–1911 (2001), DOI: 10.1109/4.972140.

[32] Jerri A.J., The Shannon sampling theorem-its various extensions and applications: A tutorial review, Proc. IEEE, vol. 65, no. 11, pp. 1565–1597 (1977).

[33] Brown J.L., On the error in reconstructing a nonbandlimited function by means of the band pass sampling theorem, J. Math. Anal. Appl., vol. 18, pp. 75–84 (1967).

[34] Brown J.L., Multi-channel sampling of lowpass-pass signals, IEEE Trans. Circuits Syst., vol. 28, no. 2, pp. 101–106 (1981).

[35] Papoulis A., Generalized sampling expansion, IEEE Trans. Circuits Syst., vol. 24, no. 11, pp. 652654 (1977).

[36] Unser M., Aldroubi A., A general sampling theory for non-ideal acquisition devices, IEEE Trans. Signal Processing, vol. 42, no. 11, pp. 2915–2925 (1994).

[37] Unser M., Zerubia J., Generalized sampling: Stability and performance analysis, IEEE Trans. Signal Processing, vol. 45, no. 12, pp. 2941–2950 (1997).

[38] Unser M., Zerubia J., A generalized sampling without bandlimiting constraints, IEEE Trans. Circuits Syst., vol. 45, no. 8, pp. 959–969 (1998).

[39] Xia G., Zhang Z., On sampling theorem, wavelets, and wavelet transforms, IEEE Trans. Signal Processing, vol. 41, no. 12, pp. 3524–3535 (1993).

[40] Djokovic I., Vaidyanathan P.P., Generalized sampling theorems in multiresolution subspaces, IEEE Trans. Signal Processing, vol. 45, no. 3, pp. 583–599 (1997).

[41] Cheung K.F., Marks R.J II., Ill-posed sampling theorems, IEEE Trans. Circuits Syst., vol. 32, no. 5, pp. 481–484 (1985).

[42] Butzer P.L., A survey of the Whittaker–Shannon sampling theorem and some of its extensions, J. Math. Res. Exposit., vol. 3, pp. 185–212 (1983).

[43] Butzer P.L., Stens R.L., Sampling theory for not-necessarily band-limited functions: A historical overview, SIAM Rev., vol. 34, pp. 40–53 (1992).

Downloads

Published

2023-03-30

How to Cite

Borys, Andrzej. “On Modelling and Description of the Output Signal of a Sampling Device”. Archives of Electrical Engineering , vol. 72, no. 1, Mar. 2023, pp. 147-55, doi:10.24425/aee.2023.143694.

Issue

Section

Articles

Similar Articles

<< < 1 2 3 4 5 6 > >> 

You may also start an advanced similarity search for this article.