Filtering Property of Signal Sampling in General and Under-Sampling as a Specific Operation of Filtering Connected with Signal Shaping at the Same Time

• Autorzy: Borys Andrzej

Identyfikatory

DOI

10.24425/ijet.2020.134016

• Języki publikacji: EN

Abstrakty

EN

In this paper, we show that signal sampling operation can be considered as a kind of all-pass filtering in the time domain, when the Nyquist frequency is larger or equal to the maximal frequency in the spectrum of a signal sampled. We demonstrate that this seemingly obvious observation has wide-ranging implications. They are discussed here in detail. Furthermore, we discuss also signal shaping effects that occur in the case of signal under-sampling. That is, when the Nyquist frequency is smaller than the maximal frequency in the spectrum of a signal sampled. Further, we explain the mechanism of a specific signal distortion that arises under these circumstances. We call it the signal shaping, not the signal aliasing, because of many reasons discussed throughout this paper. Mainly however because of the fact that the operation behind it, called also the signal shaping here, is not a filtering in a usual sense. And, it is shown that this kind of shaping depends upon the sampling phase. Furthermore, formulated in other words, this operation can be viewed as a one which shapes the signal and performs the low-pass filtering of it at the same time. Also, an interesting relation connecting the Fourier transform of a signal filtered with the use of an ideal low-pass filter having the cut frequency lying in the region of under-sampling with the Fourier transforms of its two under-sampled versions is derived. This relation is presented in the time domain, too.

Słowa kluczowe

EN

signal sampling; filtering; discrete-time Fourier transform

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: International Journal of Electronics and Telecommunications
• Rocznik: 2020
• Tom: Vol. 66, No. 3
• Strony: 589--594
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Borys Andrzej

• Department of Marine Telecommunications, Faculty of Electrical Engineering, Gdynia Maritime University, Gdynia, Poland

Bibliografia

• [1] J. H. McClellan, R. Schafer, and M. Yoder, DSP First. London, England: Pearson, 2015.
• [2] Ch. A. Bouman, Digital Image Processing I - Lecture 11 - DTFT, DSFT, Sampling, and Reconstruction. https://cosmolearning.video-lectures/dtft-dsft-sampling-reconstruction/, accessed December 2019.
• [3] H. C. So, Signals and Systems - Lecture 6 - Discrete-Time Fourier Transform. www.ee.cityu.edu.hk/~hcso/ee3210.html, accessed December 2019.
• [4] M. Vetterli, J. Kovacevic, and V. K. Goyal, Foundations of Signal Processing. Cambridge, England: Cambridge University Press, 2014.
• [5] R. Wang, Introduction to Orthogonal Transforms with Applications in Data Processing and Analysis. Cambridge, England: Cambridge University Press, 2010.
• [6] V. K. Ingle and J. G. Proakis, Digital Signal Processing Using Matlab. Stamford, CT, USA: Cengage Learning, 2012.
• [7] W. K. Jenkins, Fourier Methods for Signal Analysis and Processing in W. K. Chen, Fundamentals of Circuits and Filters. Boca Raton, FL, USA: CRC Press, 2009.
• [8] A. Borys, “Some topological aspects of sampling theorem and reconstruction formula,” Intl Journal of Electronics and Telecommunications, accepted for publication in 2020.
• [9] A. Borys, “Some useful results related with sampling theorem and reconstruction formula,” Intl Journal of Electronics and Telecommunications, vol. 65, no. 3, pp. 471-475, 2019.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).