Further Discussion on Modeling of Measuring Process via Sampling of Signals

Andrzej Marek Borys


In this paper, we continue a topic of modeling measuring processes by perceiving them as a kind of signal sampling. And, in this respect, note that an ideal model was developed in a previous work. Whereas here, we present its nonideal version. This extended model takes into account an effect, which is called averaging of a measured signal. And, we show here that it is similar to smearing of signal samples arising in nonideal signal sampling. Furthermore, we demonstrate in this paper that signal averaging and signal smearing mean principally the same, under the conditions given. So, they can be modeled in the same way. A thorough analysis of errors related to the signal averaging in a measuring process is given and illustrated with equivalent schemes of the relationships derived. Furthermore, the results obtained are compared with the corresponding ones that were achieved analyzing amplitude quantization effects of sampled signals used in digital techniques. Also, we show here that modeling of errors related to signal averaging through the so-called quantization noise, assumed to be a uniform distributed random signal, is rather a bad choice. In this paper, an upper bound for the above error is derived. Moreover, conditions for occurrence of hidden aliasing effects in a measured signal are given.

Full Text:



A. Borys, “Measuring process via sampling of signals, and functions with attributes,” submitted to Int. Journal of Telecommunications and Electronics (JET).

P. A. Lynn, Chapter 8: Modulation and Sampling in An Introduction to the Analysis and Processing of Signals, London: Palgrave, 1982.

M. Vetterli, J. Kovacevic, and V. K. Goyal, Chapter 5: Sampling and Interpolation in Foundations of Signal Processing, Cambridge: Cambridge University Press, 2014.

A. Boggess and F. J. Narcowich, A First Course in Wavelets with Fourier Analysis, New York: John Wiley & Sons, 2011.

R. Strichartz, Chapter 1: What are Distributions? in A Guide to Distribution Theory and Fourier Transforms, Boca Raton: CRC Press, 1994.

J. G. Proakis, Digital Communications, New York: McGraw-Hill, Inc., 1995.

R. F. Hoskins, Chapter 1: Results from Elementary Analysis in Delta Functions: An Introduction to Generalised Functions, Oxford: Woodhead Publishing, 2010.

U. Zölzer, Digital Audio Signal Processing, Chichester: John Wiley & Sons, 2008.

K. Sozański, Digital Signal Processing in Power Electronics Control Circuits, London: Springer-Verlag, 2013.

B. Widrow, “Statistical analysis of amplitude-quantized sampled-data systems”, Trans. AIEE, Pt. II, vol. 79, pp. 555–568, January 1961.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, New York: Pearson, 2010.


  • There are currently no refbacks.

International Journal of Electronics and Telecommunications
is a periodical of Electronics and Telecommunications Committee
of Polish Academy of Sciences

eISSN: 2300-1933