How to search?
advanced search

Search results

Filters

  • Journals
  • Authors
  • Keywords
  • Date
  • Type

Search results

Number of results: 9
items per page: 25 50 75
Sort by:

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

Andrzej Borys
International Journal of Electronics and Telecommunications | 2023 | vol. 69 | No 1 | 193-198 | DOI: 10.24425/ijet.2023.144350
Keywords modelling of signal sampling operation
Download PDF Download RIS Download Bibtex

Abstract

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.
Go to article

Authors and Affiliations

Andrzej Borys
1
ORCID: ORCID
  1. Gdynia Maritime University, Poland

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

Andrzej Borys
International Journal of Electronics and Telecommunications | 2020 | vol. 66 | No 3 | 589-594 | DOI: 10.24425/ijet.2020.134016
Keywords Signal sampling filtering discrete-time Fourier transform
Download PDF Download RIS Download Bibtex

Abstract

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 wideranging 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.

Go to article

Authors and Affiliations

Andrzej Borys
ORCID: ORCID

Spectrum Aliasing Does Occur Only in Case of Non-ideal Signal Sampling

Andrzej Borys
International Journal of Electronics and Telecommunications | 2021 | vol. 67 | No 1 | 79-85 | DOI: 10.24425/ijet.2021.135947
Keywords Signal sampling occurrence of spectrum aliasing and folding modelling of non-ideal signal sampling operation
Download PDF Download RIS Download Bibtex

Abstract

In this paper, it has been shown that the spectrum aliasing and folding effects occur only in the case of non-ideal signal sampling. When the duration of the signal sampling is equal to zero, these effects do not occur at all. In other words, the absolutely necessary condition for their occurrence is just a nonzero value of this time. Periodicity of the sampling process plays a secondary role.
Go to article

Authors and Affiliations

Andrzej Borys
1
ORCID: ORCID
  1. Department of Marine Telecommunications, Faculty of Electrical Engineering, Gdynia Maritime University, Gdynia, Poland

Spectrum Aliasing Does not Occur in Case of Ideal Signal Sampling

Andrzej Borys
International Journal of Electronics and Telecommunications | 2021 | vol. 67 | No 1 | 71-77 | DOI: 10.24425/ijet.2021.135946
Keywords Signal sampling occurrence of spectrum aliasing and folding modelling of signal sampling operation Kronecker time function Kronecker comb
Download PDF Download RIS Download Bibtex

Abstract

A new model of ideal signal sampling operation is developed in this paper. This model does not use the Dirac comb in an analytical description of sampled signals in the continuous time domain. Instead, it utilizes functions of a continuous time variable, which are introduced in this paper: a basic Kronecker time function and a Kronecker comb (that exploits the first of them). But, a basic principle behind this model remains the same; that is it is also a multiplier which multiplies a signal of a continuous time by a comb. Using a concept of a signal object (or utilizing equivalent arguments) presented elsewhere, it has been possible to find a correct expression describing the spectrum of a sampled signal so modelled. Moreover, the analysis of this expression showed that aliases and folding effects cannot occur in the sampled signal spectrum, provided that the signal sampling is performed ideally.
Go to article

Authors and Affiliations

Andrzej Borys
1
ORCID: ORCID
  1. Department of Marine Telecommunications, Faculty of Electrical Engineering, Gdynia Maritime University, Gdynia, Poland

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

Andrzej Borys
International Journal of Electronics and Telecommunications | 2022 | vol. 68 | No 1 | 115-122 | DOI: 10.24425/ijet.2022.139858
Keywords signal sampling occurrence of spectrum aliasing and folding modelling of non-ideal signal sampling operation Vetterli’s model
Download PDF Download RIS Download Bibtex

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 as well as fundamental errors that are made in perception and description of sampled signals are considered.
Go to article

Authors and Affiliations

Andrzej Borys
1
ORCID: ORCID
  1. Department of Marine Telecommunications, Faculty of Electrical Engineering, Gdynia Maritime University, Gdynia, Poland

Further Discussion on Modeling of Measuring Process via Sampling of Signals

Andrzej Borys
International Journal of Electronics and Telecommunications | 2020 | vol. 66 | No 3 | 507-513 | DOI: 10.24425/ijet.2020.134006
Keywords measuring process sampling of signals smearing and averaging of signal samples
Download PDF Download RIS Download Bibtex

Abstract

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.

Go to article

Authors and Affiliations

Andrzej Borys
ORCID: ORCID

The Problem of Aliasing and Folding Effects in Spectrum of Sampled Signals in View of Information Theory

Andrzej Borys
International Journal of Electronics and Telecommunications | 2022 | vol. 68 | No 2 | 315-322 | DOI: 10.24425/ijet.2022.139884
Keywords signal sampling modeling of sampled signal in the time domain signal information content spectrum aliasing and folding Banach–Tarski-like paradox in signal sampling
Download PDF Download RIS Download Bibtex

Abstract

In this paper, the problem of aliasing and folding effects in spectrum of sampled signals in view of Information Theory is discussed. To this end, the information content of deterministic continuous time signals, which are continuous functions, is formulated first. Then, this notion is extended to the sampled versions of these signals. In connection with it, new signal objects that are partly functions but partly not are introduced. It is shown that they allow to interpret correctly what the Whittaker– Shannon reconstruction formula in fact does. With help of this tool, the spectrum of the sampled signal is correctly calculated. The result achieved demonstrates that no aliasing and folding effects occur in the latter. Finally, it is shown that a Banach–Tarski-like paradox can be observed on the occasion of signal sampling.
Go to article

Authors and Affiliations

Andrzej Borys
1
ORCID: ORCID
  1. Department of Marine Telecommunications, Faculty of Electrical Engineering, Gdynia Maritime University, Gdynia, Poland

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

Andrzej Borys
Archives of Electrical Engineering | 2023 | vol. 72 | No 1 | 147-155 | DOI: 10.24425/aee.2023.143694
Keywords signal sampling modelling of ideal or non-ideal sampling via averaging operation Dirac and Kronecker deltas
Download PDF Download RIS Download Bibtex

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.
Go to article

Authors and Affiliations

Andrzej Borys
1
ORCID: ORCID
  1. Department of Marine Telecommunications, Electrical Engineering Faculty, Gdynia Maritime University, ul. Morska 81-87, 81-225 Gdynia, Poland

Extended Definitions of Spectrum of a Sampled Signal

Andrzej Borys
International Journal of Electronics and Telecommunications | 2021 | vol. 67 | No 3 | 395-401 | DOI: 10.24425/ijet.2021.137825
Keywords spectrum of sample signal ideal versus non-ideal sampling modelling of signal sampling process
Download PDF Download RIS Download Bibtex

Abstract

It is shown that a number of equivalent choices for the calculation of the spectrum of a sampled signal are possible. Two such choices are presented in this paper. It is illustrated that the proposed calculations are more physically relevant than the definition currently in use.
Go to article

Bibliography

[1] 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.
[2] J. H. McClellan, R. Schafer, M. Yoder, DSP First. London, England: Pearson, 2015.
[3] M. Vetterli, J. Kovacevic, V. K. Goyal, Foundations of Signal Processing. Cambridge, England: Cambridge University Press, 2014.
[4] A. V. Oppenheim, R. W. Schafer, J. R. Buck, Discrete-Time Signal Processing. New Jersey, USA: Prentice Hall, 1998.
[5] R. J. Marks, Introduction to Shannon Sampling and Interpolation Theory. New York, USA: Springer-Verlag, 1991.
[6] R. N. Bracewell, The Fourier Transform and Its Applications. New York, USA: McGraw-Hill , 2000.
[7] V. K. Ingle, J. G. Proakis, Digital Signal Processing Using Matlab. Stamford, CT, USA: Cengage Learning, 2012.
[8] P. Prandoni, M. Vetterli, Signal Processing for Communications. Lausanne, Switzerland: EPFL Press, 2008.
[9] N.T. Thao, M. Vetterli, “Deterministic analysis of oversampled A/D conversion and decoding improvement based on consistent estimates”, IEEE Transactions on Signal Processing, vol. 42, no. 3, pp. 519-531, 1994.
[10] K. Adam, A. Scholefield, M. Vetterli, “Encoding and Decoding Mixed Bandlimited Signals Using Spiking Integrate-and-Fire Neurons”, 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 9264-9268, May 2020.
[11] R. Alexandru, P. L. Dragotti, “Reconstructing classes of non-bandlimited signals from time encoded information”, IEEE Transactions on Signal Processing, vol. 68, pp. 747-763, 2020.
[12] A. Lazar, L. T. Toth, “Perfect recovery and sensitivity analysis of time encoded bandlimited signals,” IEEE Transactions on Circuits and Systems – I: Regular Papers, vol. 51, no. 10, pp. 2060-2073, 2004.
[13] J. A. Urigueen, T. Blu, P. L. Dragotti, “FRI Sampling with arbitrary kernels”, IEEE Transactions on Signal Processing, vol. 61, pp. 5310-5323, 2013.
[14] 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.
[15] P. L. Dragotti, M. Vetterli, and T. Blu, “Sampling moments and recon- structing signals of finite rate of innovation: Shannon meets strang-fix,” IEEE Transactions on Signal Processing, vol. 55, no. 5, pp. 1741-1757, 2007.
[16] R. Tur, Y. C. Eldar, Z. Friedman, “Innovation rate sampling of pulse streams with application to ultrasound imaging,” IEEE Transactions on Signal Processing, vol. 59, no. 4, pp. 1827-1842, 2011.
[17] M. Unser, “Sampling – 50 years after Shannon,” Proceedings of the IEEE, vol. 88, no. 4, pp. 569-587, 2000.
[18] G. Ortiz-Jimenez, M. Coutino, S. P. Chepuri, G. Leus, “Sparse sampling for inverse problems with tensors”, IEEE Transactions on Signal Processing, vol. 67, no. 12, pp. 3272-3286, 2019.
[19] S. P. Chepuri, G. Leus, “Graph sampling for covariance estimation”, IEEE Transactions on Signal and Information Processing over Networks, vol. 3, no. 3, pp. 451-466, 2017.
[20] M. R. D. Rodrigues, Y. C, Eldar, Information-Theoretic Methods in Data Science. Cambridge, England: Cambridge University Press, 2021.
[21] M. R. D. Rodrigues, H. Bölcskei, S. Draper, Y. Eldar, V. Tan, “Introduction to the issue on information-theoretic methods in data acquisition, analysis, and processing”, IEEE Journal on Selected Topics in Signal Processing, vol. 66, no. 9, pp. 2314-2329, 2018.
[22] G. Matz, H. Bölcskei, and F. Hlawatsch, “Time-frequency foundations of communications”, IEEE Signal Processing Magazine, vol. 30, no. 6, pp. 87-96, 2013.
[23] Y. Eldar, H. Bölcskei, “Geometrically uniform frames”, IEEE Transactions on Information Theory, vol. 49, no. 4, pp. 993-1006, 2003.
[24] Y. Kopsinis, K. Slavakis, S. Theodoridis “On line sparse system identification and signal reconstruction using projections onto weighted l1 balls”, IEEE Transactions on Signal Processing, vol. 59, no. 3, pp. 936-952, 2011.
[25] A. Morgado, R. del Río, J.M. de la Rosa, “High-efficiency cascade sigma-delta modulators for the next generation software-defined-radio mobile systems,” IEEE Trans. on Instrumentation and Measurement, vol. 61, pp. 2860-2869, 2012.
[26] L. Zhao, Z. Chen, Y. Yang, L. Zou, Z. J. Wang, “ICFS clustering with multiple representatives for large data”, IEEE Transactions on Neural Networks and Learning Systems, vol. 30, no. 3, pp. 728-738, 2019.
[27] V. Poor, An Introduction to Signal Detection and Estimation. Berlin, Germany: Springer-Verlag, 1994.
[28] T. Kailath, V. Poor, “Detection of stochastic processes”, IEEE Transactions on Information Theory, vol. 44, no. 6, pp. 2230-2231, 1998.
[29] A. Yeredor, “Blind channel estimation using first and second derivatives of the characteristic function”, IEEE Signal Processing Letters, vol. 9, no. 3 pp. 100-103, 2002.
[30] J.J. Clark, M.R. Palmer, P.D. Lawrence, “A transformation method for the reconstruction of functions from non-uniformly spaced samples,” IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 33, pp. 1151-1165, 1985.
[31] L. Heyoung, Z.Z. Bien, “A variable bandwidth filter for estimation of instantaneous frequency and reconstruction of signals with time-varying spectral content,” IEEE Transactions on Signal Processing, vol. 59, pp. 2052-2071, 2011.
[32] E. Lee, D. Messerschmitt, Digital Communication. Boston, USA: Kluwer, 1994.
[33] S. Mallat, A Wavelet Tour of Signal Processing. San Diego, USA: Aca-demic, 1998.
[34] P. Stoica, R. Moses, Introduction to Spectral Analysis. Englewood Cliffs, USA: Prentice-Hall, 2000.
[35] H. P. E. Stern, S.A. Mahmoud, Communication Systems: Analysis and Design. Upper Saddle River, USA: Prentice-Hall, 2004.
[36] M. Vetterli, J. Kovacevic, Wavelets and Subband Coding. Englewood Cliffs, USA: Prentice-Hall, 1995.
[37] E. J. Candè, M. B. Wakin, “An introduction to compressive sampling”, IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 21-30, 2008.
[38] A. Zayed, Advances in Shannon’s Sampling Theory. Boca Raton, USA: CRC Press, 1993.
[39] R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE Journal on Selected Areas in Communications, vol. 17, no. 4, pp. 539–550, 1999.
[40] P. P. Vaidyanathan, “Generalizations of the sampling theorem: seven decades after Nyquist,” IEEE Trans. Circuits Systems I: Fundamental Theory and Applications, vol. 48, no. 9, pp. 1094–1109, 2001.
[41] H. J. Landau, “Sampling, data transmission, and the Nyquist rate”, Proceedings of the IEEE, vol. 55, no. 10, pp. 1701-1706, 1967.
[42] R.G. Lyons, Understanding Digital Signal Processing. Reading, USA: Addison-Wesley, 1997.
[43] A. J. Jerri, “The Shannon sampling theorem - its various extensions and applications: a tutorial review,” Proceedings of the IEEE, vol. 65, no. 11, pp. 1565–1596, 1977.
[44] Y. C. Eldar, T. Michaeli, “Beyond bandlimited sampling,” IEEE Signal Processing Magazine, vol. 26, no. 3, pp. 48–68, 2009.
[45] A. Papoulis, “Error analysis in sampling theory,” Proceedings of the IEEE, vol. 54, no. 7, pp. 947–955, 1966.
[46] A. Papoulis, “Generalized sampling expansion,” IEEE Transactions on Circuits and Systems, vol. 24, no. 11, pp. 652–654, 1977.
[47] R. G. Vaughan, N. L. Scott, D. R. White, “The theory of bandpass sampling,” IEEE Transactions on Signal Processing, vol. 39, no. 9, pp. 1973–1984, 1991.
[48] Y. M. Lu, M. N. Do, “A theory for sampling signals from a union of subspaces,” IEEE Transactions on Signal Processing, vol. 56, no. 6, pp. 2334–2345, 2008.
[49] C. Herley, P. W. Wong, “Minimum rate sampling and reconstruction of signals with arbitrary frequency support,” IEEE Transactions on Information Theory, vol. 45, no. 5, pp. 1555–1564, 1999.
[50] L. Schwartz, Théorie des Distributions. Paris, France: Hermann, 1950-1951.
[51] 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.
[52] S. Boyd, L. Chua, “Fading memory and the problem of approximating nonlinear operators with Volterra series,” IEEE Transactions on Circuits and Systems, vol. 32, no. 11, pp. 1150-1161, 1985.
[53] L. V. Kantorovich, G. P. Akilov, Functional Analysis. Oxford, England: Pergamon Press, 1982.
[54] I. W. Sandberg, “Linear maps and impulse responses,” IEEE Transactions on Circuits and Systems, vol. 35, no. 2, pp. 201-206, 1988.
[55] I. W. Sandberg, “Causality and the impulse response scandal,” IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications, vol. 50, no. 6, pp. 810-813, 2003.

Go to article

Authors and Affiliations

Andrzej Borys
1
ORCID: ORCID
  1. Department of Marine Telecommunications, Faculty of Electrical Engineering, Gdynia Maritime University, Gdynia, Poland

This page uses 'cookies'. Learn more