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Grabie na motyla

Nowaczyk E.

Przegląd Komunalny

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2003

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nr 10

78-79

PL

Od 5 lat szrotówek kasztanowcowiaczek bezkarnie "pałaszuje" kasztanowce w całej Polsce. Na razie nie ma skutecznego sposobu na szkodnika. Jak więc pomóc kasztanowcom? Choćby zmniejszając populację szrotówka przez grabienie i niszczenie liści, w których zimują jego poczwarki. O skuteczności grabienia przekonali się poznaniacy, którzy ubiegłej jesieni uczestniczyli w akcji poznańskiej "Gazety Wyborczej" - "Ratujmy nasze kasztanowce".

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Wpływ liczby pobieranych próbek i ich usytuowania w okresie na błąd wyznaczania wartości skutecznej i średniej sygnału poliharmonicznego (Część II)

Nowaczyk E., Nowaczyk J.

Metrology and Measurement Systems

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2002

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Vol. 9, nr 4

413-432

PL

W przentowanej pracy podano zależności matematyczne określające wartość skuteczną sygnału wyliczaną na podstawie próbek pobranych przez przetwornik niesynchroniczny. Przedstawiono wyniki badań modelu takiego przetwornika w środowisku MATLAB-a. Uzyskane rezultaty ilustrują wpływ parametrów sygnału poliharmonicznego i sposobu przeprowadzania próbkowania na błąd wyznaczenia wartości skutecznej i średniej bezwzględnej tego sygnału. W artykule zamieszczono przesłanki odnośnie prawidłowego wyboru częstotliwości próbkowania, a także zalecenia stosowania filtrów antyaliasingowych w torze przetwarzania. Stanowia one zdaniem autorów skuteczne remedium na zmniejszenie błędów omawianych w pracy.

EN

The paper produces an analysis of the accuracy of determination of the root-mean-square (rms) and average value at asynchronous signal sampling. It is an enlargement of the publication [1]. Mathematical equations determining the rms value for pure sine-wave and polyharmonic signals have been presented. The calculation of the average value has been based on the analysis carried out in a general way in many literature items, such as [6]. For both calculated kinds of values, tests were carried out by creating a model of asynchronous converter in MATLAB's environment and applying at its input a pure sine-wave signal or polyharmonic signals of different forms; at the same time the sampling frequency and the number of samples taken were changed. The obtained simulation results, representing the determination of the root-mean-square or average value with regard to the conventional true value, for exemplifying signal forms, have been presented in illustrations. They illustrate the effect of the number of samples taken, of the relative sampling frequency, of the moment of the first sample, and for polyhannonic signals also of harmonic contents, their numbers and phase shift. The phenomenon of result waving and particularly big errors for some ,,unlucky" harmonic numbers have been shown. It was noticed that as the number of the samples taken increases, the intervals are being narrowed where the calculated root-mean-square or average value can be found. However, with an increase of the sampling frequency there is need for drawing a larger and larger number of samples, in order to obtain results not differing from each other more than it is admissible (when calculating the root-mean-square value this occurs for a relative sampling frequency greater than four). If a signal contains, apart from the fundamental frequency, also harmonics ones (and this is always the case in practice), then in selecting sampling frequencies the greatest harmonic numbers should be kept in mind, including also the sum or the difference of their numbers. Neglecting this recommendation that results from Shannon's theorem, may lead to the result waving at a very low frequency and simultaneously with high amplitude. The result of taking a greater number of samples for calculations may be more departing from the correct one than with their smaller number. Application of antialiasing filters in the conversion line was proposed. These filters, damping high frequency components and possible noise enable one to obtain greater repeatability of the results. For the sampling of signals of approximately constant frequency, such as those of the power-line, it was recommended to select a sampling frequency close to an odd multiple of the rated frequency value of the sampled signal, both when calculating the average and the rms value. The presented paper points to the error sources resulting from the way of drawing of samples by sampling converters. It also contains main lines directed at practicians, connected with making use of the obtained results when applying these converters in measurements and automation.

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Wpływ liczby pobieranych próbek i ich usytuowania w okresie na wyznaczanie wartości skutecznej lub średniej sygnału poliharmonicznego

Nowaczyk E., Nowaczyk J.

Metrology and Measurement Systems

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2001

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Vol. 8, nr 3

271-287

PL

W artykule przedstawiono zależności określające wartość skuteczną lub średnią bezwzględną sygnału wyliczaną na podstawie próbek pobranych przez przetwornik synchroniczny. Opisują one wpływ częstotliwości harmonicznych zawartych w próbkowanym sygnale na uzyskany wynik. Otrzymane rezultaty stanowią uzasadnienie, sformułowanej przez autorów w pracy [4], tezy o potrzebie i celowości stosowania filtrów dolnoprzepustowych umieszczonych w torze przetwarzania przed przetwornikiem próbkującym.

EN

A general pricniple in signal sampling is taking the minimum sampling rate more than twice the highest frequency contained in the signal. Does it matter, if on the basis of the collected samples, a root-mean-square (rms) or average signal value is calculated? A synchronous sampling was considered and an effect of sample number on the calculated value was analyzed in this paper. No account was taken - for clarity of the results - of the influence of other factors, such as resolution of converter, aperture time, etc. which also determine accuracy. For the considerationscarried out a stationary input signal and sampling with constant rate equal to multiple of input signal frequency were assumed. In the paper the mathematical equations for the rms value calculated on the basis of sampling were given and the circumstances for the obtainment of a correct rms value were determined. It has been ascertained that for a definite sample number per period of the fundamental frequency, there are a lot of harmonics that do not have to satisfy Shannon's requirement to get a correct result of calculation. But there exist "unlucky" numners of harmonics among them which are determined by a relation between the harmonic number and the number of samples per signal period. Their lowest frequency is equal to half of sampling rate. In this case the error of calculation of rms value can be quite significant. The error value depends on the moment of the first sample taking and on harmonic amplitude, also on itsphase shift in relation to the fundamental. For more than one harmonic contained in the signal, additional errors will come into being, if the sum or the difference of harmonic numbers is a multiple of the sample number in signal period. Calculating of average value on the basis of the taken samples can be done by one of the numerical integration methods. The rectangular method was applied in the paper. From the developed dependencies and computer reckoning it follows that in most cases the calculating error first of all depends on sample number in the signal period. A smaller error is received when the sample number is odd. Just as in calculating the rms, the error value is conditioned by the moment of taking of the first sample as well as by the amplitude and phase of various component harmonics included in the signal. The described examples show that if the frequency of the sampling rate is too low, then the error of computations can be significant under certain circumstances. Also in average value calculating the "unlucky" harmonics occur. Their existence in the signal can lead to big errors which can be even bigger than in the case of removing of a part pf high frequency components from the signal. Then a low-pass filter is desirable in the converter track. Both with the calculation of the rms and the average value, the low-pass filter will not be necessary, provided there is full guarantee that "unlucky" harmonics do not appear in the band of the converted signal. The verification of mathematical dependences was accomplished in MATLAB's environment. The obtained results were presented in the figures. Finally one should answer the questions: "Can the described phenomena be called an aliasing?" and "Can the low-pass filter placed before sampling converter be given the name of antialiasing filter?". Taking into account the opinions presented in the references, e.g. [2], the authors think so.

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Przetwornik wartości skutecznej napięcia zmiennego z aproksymacją sygnału wejściowego za pomocą trapezu

Kriszniewski K., Nowaczyk E.

Pomiary Automatyka Kontrola

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2000

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R. 46, nr 2

16-19

PL

Ograniczona szybkość działania, przy równoczesnym wymaganiu dość dobrej rozdzielczości przetworników a/c powoduje, źe nie moga one sprostać ciągle rosnącym wymaganiom w zakresie przetwarzania sygnałów. W artykule opisano sposób w jaki można, przy niewielkiej rozbudowie układu elektronicznegourządzenia, znacznie poprawić dokładność pomiaru wartości skutecznej napięcia (lub prądu) sygnału niesinusoidalnego.

EN

A limited possible sampling rate with simultaneous requirement for high resolution of A/D converters effects that they often will not be up the still fast grover demand of the signal conversion quality. This problem will occur in the conversion of non-sinusoidal signals, if their frequency are in supersonic of higher range. Using of nonstandard hardware and software solutions take place in this case. This paper presents a way of this problem solution with the help of little building up of the electronic circuit. The additional fast, but not very much accurate A/D converter is used. This converter samples an input signal in order to determination of parameters which approximate the converted non-sinusoidal signal by a trapezoid-form signal. On the base of the parameter values the correction is estimated and used for decreasing the final uncertainty of the measurement.

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Aproksymacja sygnałem trapezowym kształtu sygnałów niesinusoidalnych do oceny niedokładności przetworników wartości skutecznej

Nowaczyk E.

Metrologia i Systemy Pomiarowe

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1998

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T. 5, z. 1-2

15-22

PL

Pomiarowi wartości skutecznej napięć niesinusoidalnych towarzyszy problem określenia niedokładności uzyskiwanego wyniku, jeżeli sygnał mierzony ma kształt niesinusoidalny. Wykazano, że aproksymowanie różnych kształtów sygnałów trapezem ułatwia wyznaczenie nieznanego błędu przetwarzania. Zastosowanie dodatkowego przetwornika a/c pozwala na oszacowanie wartości wszystkich potrzebnych parametrów trapezu i obliczenie poszukiwanego błędu przetworników wartości skutecznej.

EN

The paper discusses a problem of determination of additional error resulting from finite frequency response of true root-meansquare (rms) to "dc" converter when nonsinusoidal signals are convertered. It is shown that various waveforms approximation to a trapezoid-form signal makes calculation of unknow error easier. Application of additional a/c converter allows for the estimation values of all necessery parameters of the trapezoid and investigating errors computation.