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1
Content available On modelling and description of the output signal of a sampling device
Borys Andrzej
Archives of Electrical Engineering
|
2023
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Vol. 72, nr 1
147--155
EN
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.
2
Content available Modelling of non-ideal signal sampling via averaging operation and spectrum of sampled signal predicted by this model
Borys A.
TransNav : International Journal on Marine Navigation and Safety of Sea Transportation
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2022
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Vol. 16 No. 2
274--278
EN
In this paper, a novel model of a non-ideal signal sampling via a local, periodic averaging operation is present-ed. The spectrum of a sampled signal predicted by this model is also analysed as well as compared with a one following from another model.
3
Content available Definition of sampled signal spectrum and shannon’s proof of reconstruction formula
Borys A.
TransNav : International Journal on Marine Navigation and Safety of Sea Transportation
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2022
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Vol. 16 No. 3
473--478
EN
The objective of this paper is to show from another perspective that the definition of the spectrum of a sampled signal, which is used at present by researchers and engineers, is nothing else than an arbitrary choice for what is possibly not uniquely definable. To this end and for illustration, the Shannon’s proof of reconstruction formula is used. As we know, an auxiliary mathematical entity is constructed in this proof by performing periodization of the spectrum of an analog, bandlimited, energy signal. Admittedly, this entity is not called there a spectrum of the sampled signal - there is simply no need for this in the proof – but as such it is used in signal processing. And, it is not clear why just this auxiliary mathematical object has been chosen in signal processing to play a role of a definition of the spectrum of a sampled signal. We show here what are the interpretation inconsistences associated with the above choice. Finally, we propose another, simpler and more useful definition of the spectrum of a sampled signal, for the cases where it can be needed.
4
Content available The Problem of Aliasing and Folding Effects in Spectrum of Sampled Signals in View of Information Theory
Borys Andrzej
International Journal of Electronics and Telecommunications
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2022
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Vol. 68, No. 2
315--322
EN
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.
5
Content available Another Proof of Ambiguity of the Formula Describing Aliasing and Folding Effects in Spectrum of Sampled Signal
Borys Andrzej
International Journal of Electronics and Telecommunications
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2022
|
Vol. 68, No. 1
115--122
EN
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.
6
Content available Simple proof of incorrectness of the formula describing aliasing and folding effects in spectrum of sampled signal in case of Ideal signal sampling
Borys A.
TransNav : International Journal on Marine Navigation and Safety of Sea Transportation
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2021
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Vol. 15 No. 4
873--876
EN
A simple proof of the incorrectness of the formula, which is used in the literature nowadays, for description of the aliasing and folding effects in the spectrum of a sampled signal in the case of an ideal signal sampling, is given in this paper. By the way, it is also shown that such the effects cannot occur at all, when the signal sampling is considered to be performed perfectly.
7
Content available Spectrum Aliasing Does Occur Only in Case of Non-ideal Signal Sampling
Borys Andrzej Marek
International Journal of Electronics and Telecommunications
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2021
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Vol. 67, No. 1
79--85
EN
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.
8
Content available Spectrum Aliasing Does not Occur in Case of Ideal Signal Sampling
Borys Andrzej Marek
International Journal of Electronics and Telecommunications
|
2021
|
Vol. 67, No. 1
71--77
EN
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 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.
9
Content available Filtering Property of Signal Sampling in General and Under-Sampling as a Specific Operation of Filtering Connected with Signal Shaping at the Same Time
Borys Andrzej
International Journal of Electronics and Telecommunications
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2020
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Vol. 66, No. 3
589--594
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.
10
Content available Propagacja błędów losowych w multiplikatywnych algorytmach przetwarzania danych pomiarowych
Jakubiec J., Roj J.
Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej
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2018
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Nr 59
69--72
PL
W artykule opisano propagację błędów losowych w multiplikatywnych algorytmach przetwarzania, cechujących się mnożeniem danych pomiarowych przez siebie. Wyznaczono równania propagacji błędów dla dwóch algorytmów służących do obliczania wartości skutecznej i mocy elektrycznej na podstawie cyfrowych reprezentacji przebiegów. Przeprowadzono analizę propagacji błędów kwantowania i błędów spowodowanych drżeniem próbek przy użyciu równań propagacji błędów oraz metodą Monte Carlo wykorzystując niepewność wyników pomiaru do porównywania ich niedokładności.
EN
Multiplicative algorithm, used for example for calculation of electrical power on the basis of digital representations of a voltage and current signal, characterize occurrence of products of measurement results. Accuracy of the results in the output of the algorithm can be analyzed by using error propagation equations for different kinds of the algorithm input errors. The alternative way consist in application of Monte Carlo method especially in sophisticated measurement condition. The general form of the multiplication algorithms is described in the paper and, for two kinds of the algorithm, the propagation equations have been determined. Error analysis of the algorithms applied for calculation of effective value and electric power has been performed for two basic errors caused by sampling jitter and quantization of samples.
11
Content available remote Influence of signal sampling period in the control system on optimal settings of PI and PID controllers
Laskawski M., Wcislik M.
Przegląd Elektrotechniczny
|
2018
|
R. 94, nr 4
83--86
EN
The work covers the issues connected with selection of optimal settings of PID controllers and the influence of sampling frequency of the control signal on their values. The methods used to select the sampling frequency of the control signal were reviewed. In this paper, we determined the ITAE optimum settings of continuous and discrete PID regulators. The influence of the frequency of control signal sampling on the optimum settings of the regulator was analyzed.
PL
Praca porusza zagadnienia związane z doborem optymalnych nastaw regulatorów PID i wpływu częstotliwości próbkowania sygnału sterującego na ich wartości. Dokonano przeglądu stosowanych metod doboru częstotliwości próbkowania sygnału sterującego. W pracy określono optymalne względem kryterium ITAE nastawy ciągłych i dyskretnych regulatorów PID. Dokonano analizy wpływu częstotliwości próbkowania sygnału sterującego na wartości optymalnych nastaw regulatora.
12
Content available Wyznaczanie granicznych błędów pomiaru parametrów sygnału sinusoidalnego spowodowanych kwantyzacją
Kontorski K.
Pomiary Automatyka Kontrola
|
2014
|
R. 60, nr 11
975--977
PL
Często w celu wyznaczenia amplitudy i fazy pewnej harmonicznej sygnału próbkowanego przetwornikiem A/C korzysta się z DFT. Dokładność pomiaru wyznacza się numerycznie stosując metodę Monte-Carlo przy założeniu, że próbki nie są skorelowane między sobą. Założenie to jest błędne, gdy próbkuje się sygnał sinusoidalny. W artykule zostanie wyznaczony zbioru sygnałów sinusoidalnych, na podstawie którego można wyznaczyć amplitudę i fazę sygnału mono-harmonicznego próbkowanego. Przeprowadzono badania dokładności transformaty DFT.
EN
Signals probed with finite resolution ADC's are affected by quantization errors. If we assume that value of each probe is uncorrelated with the value of each other probe then we may assess the accuracy of the first harmonic determined by DFT using Monte-Carlo method [1]. But if we probe a sinusoidal signal it is an incorrect assumption. In the paper we analyze the set of the sinusoidal signals that are inevitably connected with acquired single harmonic signal probes. In the Figure 1 we can see that the set of probes may be generated by a few different signals. We prove that set of signals that give the same set of the probes represents a non-fragmented surface on the amplitude and phase angle plane (Fig. 2). Secondly we determine the set of signals for the specified set of probes D3 acquired by the simulated ADC. We construct function F represented by equation (9) which consists of the function which block diagram is presented in the Fig. 3. This function F is discrete so statistical methods must be used to determine the set of signals (A, φ) which give the maximal value [2]. Final shape of the set is given on the Fig. 5. Some experiment was conducted to check the accuracy of the DFT algorithm. The Figure 6 represent values of amplitudes acquired by DFT (triangles), amplitudes from the computed sets (dots) against number of acquired probes of the 1 V sinusoidal signal. The error bars corresponds to the extreme amplitudes (Fig. 6) in the set. The results differ, because DFT computes parameters of the first harmonic of the probes which only approximately represents the input signal. This method with modifications may be applied to the multi-harmonic signals. Keywords: signal sampling, ADC, periodic signal, amplitude and phase angle, mathematical analysis, DFT.
13
Modeling of digital control systems of power electronics converters
Krystkowiak M.
Poznan University of Technology Academic Journals. Electrical Engineering
|
2011
|
No. 66
77--85
EN
In this paper one of the modeling method of digital control systems of power electronics converters is presented. The main task depends on precise mapping phenomenon occurred in real experimental systems. So, we have to take into account for example delays, which are carried in control system by signal sampling, as well as delays of algorithms realized by processor. The chosen results of simulation and also experimental research are shown.
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