Another Proof of Ambiguity of the Formula Describing Aliasing and Folding Effects in Spectrum of Sampled Signal

Authors

Abstract

In this paper, a new proof of ambiguity of the formula describing the aliasing and folding effects in spectra of sampled signals is presented. It uses the model of non-ideal sampling operation published by Vetterli et al. Here, their model is modified and its black-box equivalent form is achieved. It is shown that this modified model delivers the same output sequences but of different spectral properties. Finally, a remark on two possible understandings of the operation of non-ideal sampling is enclosed.

References

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing. New Jersey: Prentice Hall, 1998.

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

R. N. Bracewell, The Fourier Transform and Its Applications, New York: McGraw-Hill, 2000.

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.

M. Vetterli, P. Marziliano, T. Blu, “Sampling signals with finite rate of innovation”, IEEE Transactions on Signal Processing, vol. 50, no. 6, pp. 1417-1428, 2002.

M. Vetterli, J. Kovacevic, V. K. Goyal, Foundations of Signal Processing. Cambridge, England: Cambridge University Press, 2014.

A. Borys, “Some useful results related with sampling theorem and reconstruction formula,” Intl Journal of Electronics and Telecommu-nications, vol. 65, no. 3, pp. 471-475, 2019.

A. Borys, “Filtering property of signal sampling in general and under-sampling as a specific operation of filtering connected with signal shaping at the same time,” Intl Journal of Electronics and Telecommu-nications, vol. 66, no. 3, pp. 589-594, 2020.

A. Borys, “Some topological aspects of sampling theorem and reconstruction formula,” Intl Journal of Electronics and Telecommu-nications, vol. 66, no. 2, pp. 301-307, 2020.

A. Borys, “On derivation of discrete time Fourier transform from its continuous counterpart,” Intl Journal of Electronics and Telecommu-nications, vol. 66, no. 2, pp. 355-368, 2020.

A. Borys, “Spectrum aliasing does occur only in case of non-ideal signal sampling,” Intl Journal of Electronics and Telecommunications, vol. 67, no. 1, pp. 79-85, 2021.

Downloads

Published

2024-04-19

Issue

Section

Signals, Circuits, Systems