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1

Some Topological Aspects of Sampling Theorem and Reconstruction Formula

Borys Andrzej

International Journal of Electronics and Telecommunications

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2020

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Vol. 66, No. 2

301--307

EN

We present here a few thoughts regarding topological aspects of transferring a signal of a continuous time into its discrete counterpart and recovering an analog signal from its discrete-time equivalent. In our view, the observations presented here highlight the essence of the above transformations. Moreover, they enable deeper understanding of the reconstruction formula and of the sampling theorem. We also interpret here these two borderline cases that are associated with a time quantization step going to zero, on the one hand, and approaching its greatest value provided by the sampling theorem, on the other.

2

Some Useful Results Related with Sampling Theorem and Reconstruction Formula

Borys Andrzej

International Journal of Electronics and Telecommunications

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2019

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Vol. 65, No. 3

471--475

EN

In this paper, we present some useful results related with the sampling theorem and the reconstruction formula. The first of them regards a relation existing between bandwidths of interpolating functions different from a perfectreconstruction one and the bandwidth of the latter. Furthermore, we prove here that two non-identical interpolating functions can have the same bandwidths if and only if their (same) bandwidth is a multiple of the bandwidth of an original unsampled signal. The next result shows that sets of sampling points of two nonidentical (but not necessarily interpolating) functions possessing different bandwidths are unique for all sampling periods smaller or equal to a given period (calculated in a theorem provided). These results are completed by the following one: in case of two different signals possessing the same bandwidth but different spectra shapes, their sets of sampling points must differ from each other.

3

Interpretation of Fractional Derivatives as Reconstruction from Sequence of Integer Derivatives

Tarasov V. E.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

431--442

EN

In this paper, we propose an “informatic” interpretation of the Riemann-Liouville and Caputo derivatives of non-integer orders as reconstruction from infinite sequence of standard derivatives of integer orders. The reconstruction is considered with respect to orders of derivatives.

4

Efektywne wyznaczenie częstotliwości interwencji w cyfrowych quasi-ciągłych systemach sterowania w transporcie

Wacławski T.

Logistyka

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2015

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nr 6

1361--1366, CD

PL

W pracy przeprowadzono analizę procesu dyskretyzacji sygnału ciągłego. Następnie, twierdzenie Shannona o próbkowaniu i analiza niektórych błędów dyskretyzacji zostały przyjęte jako podstawa przedstawionej metody wyboru wartości okresu próbkowania (częstotliwości interwencji) w syntezie quasi-ciągłych układów sterowania w transporcie. Analiza wartości błędów dyskretyzacji została przeprowadzona w dziedzinie częstotliwości dla wybranych sygnałów testowych.

EN

In this paper there has been taken up the investigation of the continuous signal’s conversion.Then, the sampling theorem and analysis some of discretization errors have been assumed to be basis of the suggested method sampling time’s evaluation during synthesis of a quasi-continuous control systems in transportation. These analysis of value of the errors has been carried out in a frequency-domain for selected signals.

5

Energoelektroniczne szerokopasmowe źródła sterowane napięć i prądów realizowane w oparciu o przekształtniki wielokanałowe

Gwóźdź M.

Przegląd Elektrotechniczny

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2012

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R. 88, nr 10a

132-134

PL

W artykule zaprezentowano koncepcję energoelektronicznych szerokopasmowych źródeł sterowanych napięć i prądów wykorzystujących przekształtniki wielokanałowe. Nowe podejście do realizacji algorytmów sterowania układem na bazie rozszerzenia klasycznej teorii próbkowania Whittakera-Kotielnikowa-Shannona oraz rozwiązania części silnoprądowej pozwoliło na znaczące polepszenie jakości energetycznego sygnału wyjściowego – w sensie odwzorowania w nim sygnału zadanego. W artykule zaprezentowana zasady działania oraz wyniki wybranych badań symulacyjnych układów tego typu.

EN

Enlarged technical requirements are connected with precise of control, speed of reaction as well as resistance onto disturbances from receiver or power supply of power electronics inverters. It causes trom demand grows up onto power electronic arrangements small and large power, linear in view of input and output, acting in real time. A kind of power electronics equipment tulfilling these demanding are wideband controlled voltage and current sources. The paper presents concept of these with utilization of multi-channel inverters and contral algorithms based on expansion of Whittaker-Kotelnikov-Shannon sampling theorem. (Wide-Band Power Electronics Controlled Current And Voltage Sources With Multichannel lnverters).

6

Wavelet characterization of Sobolev spaces with variable exponent

Izuki M.

Journal of Applied Analysis

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2011

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Vol. 17, nr 1

37-49

EN

Our aim is to get characterizations and unconditional bases of variable Sobolev spaces Lp (·),s(Rn) in terms of wavelets. As an application, we obtain the sampling theorem in Lp (·),s(Rn).