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EN
In this paper the analysis of backlash influence on the spectrum of torque at the output shaft of a cycloidal gearbox has been performed. The model of the single stage cycloidal gearbox was designed in the MSC Adams. The analysis for the excitation with the torque and the analysis with constant angular velocity of the input shaft were performed. For these analyses, the amplitude spectrums of the output torque for different backlashes was solved using FFT algorithm. The amplitude spectrums of the combined sine functions composed of the impact to impact times between the cycloidal wheel and the external sleeves were computed for verification. The performed studies show, that the backlash has significant influence on the output torque amplitude spectrum. Unfortunately the dependencies between the components of the spectrum and the backlash could not be expressed by linear equations, when vibrations of the output torque in the range of (350 Hz – 600 Hz) are considered. The gradual dependence can be found in the spectrum determined for the combined sine functions with half-periods equal impact-to-impact times. The spectrum is narrower for high values of backlash.
EN
Accurate prediction of preterm birth is a global, public health priority. This necessitates the need for an efficient technique that aids in early diagnosis. The objective of this study is to develop an automated system for an effective detection of preterm (weeks of gestation < 37) condition using Electrohysterography (EHG) and topological features associated with the frequency components of signals. The EHG signals recorded prior to gestational age of 26 weeks are considered. The pre-processed signals are subjected to discrete Fourier transform to obtain the Fourier coefficients. The envelope is computed from the boundary of the complex Fourier coefficients identified using the a-shape method. Topological features namely, area, perimeter, circularity, convexity, ellipse variance and bending energy are extracted from the envelope. Classifications based on threshold-determination method and machine learning algorithms namely, naïve Bayes, decision tree and random forest are employed to differentiate the term and preterm conditions. The results show that the Fourier coefficients of EHG signals exhibit different shapes in the term and preterm conditions. The regularity of signals is found to increase in preterm condition. All the features are found to have significant differences between these two conditions. Bending energy as a single biomarker achieves a maximum accuracy of 80.7%. The random forest model based on the topological features detects the conditions with the maximum accuracy and positive predictive value of about 98.6%. Therefore, the proposed automated system seems to be effective and could be used for the accurate detection of term and preterm conditions.
EN
A novel symmetric cryptosystem of the substitution permutation network type is presented for image encryption in 14 rounds. An algorithm is developed to generate 15 keys to encrypt images where each key is the image size. These keys are calculated using an elliptic curve with a constant zero value. The proposed curve is non-singular, non-supersingular, nor trace one. Chaos is employed to find a generating element in a cyclic subgroup and it is produced using the logistic map equation. In addition, a 16 × 16 substitution box is constructed using both chaos and an algorithm that defines a bijective function. The following tools are used in order to measure the degree of randomness of the encrypted figures: entropy, correlation, the discrete Fourier transform and a goodness-of-fit test with the chi-square distribution. Furthermore, an image size variable permutation is applied in the first round, and its inverse in the fourteenth.
4
Content available remote On the existence of complex Hadamard submatrices of the Fourier matrices
EN
We use a theorem of Lam and Leung to prove that a submatrix of a Fourier matrix cannot be Hadamard for particular cases when the dimension of the submatrix does not divide the dimension of the Fourier matrix. We also make some observations on the trace-spectrum relationship of dephased Hadamard matrices of low dimension.
5
Content available Discrete Fourier transform and permutations
EN
It is well known that the magnitudes of the coefficients of the discrete Fourier transform (DFT) are invariant under certain operations on the input data. In this paper, the effects of rearranging the elements of an input data on its DFT are studied. In the one-dimensional case, the effects of permuting the elements of a finite sequence of length N on its Discrete Fourier transform (DFT) coefficients are investigated. The permutations that leave the unordered collection of Fourier coefficients and their magnitudes invariant are completely characterized. Conditions under which two different permutations give the same DFT coefficient magnitudes are given. The characterizations are based on the automorphism group of the additive group ZN of integers modulo N and the group of translations of ZN. As an application of the results presented, a generalization of the theorem characterizing all permutations that commute with the discrete Fourier transform is given. Numerical examples illustrate the obtained results. Possible generalizations and open problems are discussed. In higher dimensions, results on the effects of certain geometric transformations of an input data array on its DFT are given and illustrated with an example.
PL
W pracy krótko scharakteryzowano ideę pomiaru natężenia prądu przy użyciu czujnika polarymetrycznego ze światłowodową cewką pomiarową. Zaprezentowano definicję oraz podstawowe właściwości dyskretnego przekształcenia Fouriera. Omówiono technikę wyznaczania wartości poszczególnych harmonicznych sygnału na wejściu i wyjściu polarymetrycznego czujnika natężenia prądu. Wyznaczono wartości błędów pomiaru oraz współczynnika zawartości harmonicznych – THD, a następnie sformułowano ogólne wnioski dotyczące wprowadzania zniekształceń towarzyszących procesowi przetwarzania realizowanemu w polarymetrycznym czujniku natężenia prądu. Dodatkowo określono wpływ stężenia molowego domieszki GeO2 w rdzeniu światłowodu (na przykładzie trzech standardów jednomodowych światłowodów telekomunikacyjnych wg ITU-T G.652, G.653 i G.655) oraz wpływ liczby zwojów pomiarowej cewki światłowodowej na zniekształcenia towarzyszące procesowi przetwarzania.
EN
In this paper briefly characterised the idea of measure of current using polarimetric current sensor with optical fiber coil. It shows the definition and basic properties of the Discrete Fourier Transform. It discusses the technique of determining the value of each harmonic of signal at the input and output polarimetric sensor current. Calculated the value of measurement errors and total harmonic distortion – THD, and formulated a general request for placing a distortion accompanying of processing realized in polarimetric current sensor. In addition, the impact of the molar concentration of the dopant GeO2 in the core of fiber (for example, three standards of single mode optical fiber ITU-T G.652, G.653 and G.655) and the impact of the number of turns of the measuring coil on the distortion accompanying the process of processing, have been determined.
EN
The achieved discrete trigonometric transform allows building of adaptive filters to suit their area of application. By varying the phase shift can be achieved improved quality of source data recovery in case the frequency coefficients undergo distortion. This transformation is well manifested itself in the problem of image compression, showing better results than the discrete cosine transform.
8
Content available remote Comparative assessment of digital filters for microprocessorbased relay protection
EN
This article presents the implementation of digital filters used in microprocessor-based (digital) relay protection current measuring elements. It has been shown that in order to reliable estimate the digital filter performance its input signals waveforms must be close to the actual secondary current waveform of the current transformer (CT) to which the digital protection with the estimated digital filter is connected. Ways of digital filtering improvement based on the window functions usage are proposed.
PL
W pracy przedstawiono przykład wdrożenia filtrów cyfrowych stosowanych w elementach pomiarowych zabezpieczenia przekażnika prądowego na bazie mikroprocesora cyfrowego. Wykazano, że w celu wiarygodnego oszacowania wydajności filtrów cyfrowych ich przebiegi sygnałów wejściowych powinny być zbliżone do rzeczywistego przebiegu prądu wtórnego transformatora prądowego do którego jest podłączono zabezpieczenie cyfrowe z pomiarowym filtrem cyfrowym. Zaproponowano sposoby poprawy filtracji cyfrowej w oparciu o wykorzystanie funkcji okna.
9
Content available remote Virtual phase shift meter
EN
The paper presents the possibility of using virtual instrument for the phase shift measurement. The hardware is built on the basis of National Instrument data acquisition card and PC. The software is based on LabVIEW. The measurement results were compared with results obtained from simulation.
PL
W artykule przedstawiono możliwość zastosowania przyrządu wirtualnego do pomiaru kąta przesunięcia fazowego. Część sprzętowa zbudowanego przyrządu to karta pomiarowa firmy National Instruments oraz komputer PC. Część programowa powstała w oparciu o środowisko LabVIEW. Otrzymane wyniki pomiarów porównano z wynikami otrzymanymi z symulacji.
PL
W artykule przedstawiono wyniki zastosowania okna czasowego o płaskiej charakterystyce amplitudowej do obliczania fazora w sieciach elektroenergetycznych. Otrzymane wyniki porównano do wyników uzyskanych dla okna prostokątnego i okna Hanna. Do określenia właściwości porównywanych metod obliczeniowych wykorzystano niektóre z testów zgodności standardu IEEE Standard for Synchrophasor Measurements for Power Systems, oraz zdefiniowane tam błędy TVE (total vector error) i FE (frequency error). Otrzymane wyniki wskazują, że okna o płaskiej charakterystyce widmowej pozwalają istotnie poprawić dokładność estymacji fazora zwłaszcza w stanie ustalonym.
EN
This paper presents results of direct phasor estimation by DFT with application of flat-top windows. Results obtained with rectangular window and Hann window are also presented for comparison. The quality of the phasor estimation is evaluated by TVE (total vector error) and FE (frequency error) as defined in the IEEE Standard for Synchrophasor Measurements for Power Systems. The application of flat-top windows resulted in significant reduction of TVE in steadystate compliance tests. For actual frequency fin=50±2,5 Hz maximum TVE was reduced about 30 times as compare to Hann window. The smallest maximum FE errors were also obtained for flat-top window. In dynamic compliance tests flat-top windows performed only slightly better than Hann window and rectangular window in frequency estimation, and maximum TVE error is even slightly higher than for rectangular window for modulating frequency above 2,5 Hz. Straightforward computation of the phasor based on one DFT bin has computational complexity N. Application of FFT algorithms is not advised, because only one DFT bin is required. The phasor may be computed on sample by sample basis by discrete time convolution with FIR filter. In that case reporting frequency is the same as the sampling frequency of the signal.
EN
This paper deals with the amplitude estimation in the frequency domain of low-level sine waves, i.e. sine waves spanning a small number of quantization steps of an analog-to-digital converter. This is a quite common condition for high-speed low-resolution converters. A digitized sine wave is transformed into the frequency domain through the discrete Fourier transform. The error in the amplitude estimate is treated as a random variable since the offset and the phase of the sine wave are usually unknown. Therefore, the estimate is characterized by its standard deviation. The proposed model evaluates properly such a standard deviation by treating the quantization with a Fourier series approach. On the other hand, it is shown that the conventional noise model of quantization would lead to a large underestimation of the error standard deviation. The effects of measurement parameters, such as the number of samples and a kind of the time window, are also investigated. Finally, a threshold for the additive noise is provided as the boundary for validity of the two quantization models.
EN
Modern production technology requires new ways of surface examination and a special kind of surface profile parameters. Industrial quality inspection needs to be fast, reliable and inexpensive. In this paper it is shown how stochastic surface examination and its proper parameters could be a solution for many industrial problems not necessarily related with smoothing out a manufactured surface. Burnishing is a modern technology widely used in aircraft and automotive industries to the products as well as to process tools. It gives to the machined surface high smoothness, and good fatigue and wear resistance. Every burnished material behaves in a different manner. Process conditions strongly influence the final properties of any specific product. Optimum burnishing conditions should be preserved for any manufactured product. In this paper we deal with samples made of conventional tool steel – Sverker 21 (X153CrMoV12) and powder metallurgy (P/M) tool steel – Vanadis 6. Complete investigations of product properties are impossible to perform (because of constraints related to their cost, time, or lack of suitable equipment). Looking for a global, all-embracing quality indicator it was found that the correlation function and the frequency analysis of burnished surface give useful information for controlling the manufacturing process and evaluating the product quality. We propose three new indicators of burnishing surface quality. Their properties and usefulness are verified with the laboratory measurement of material samples made of the two mentioned kinds of tool steel.
PL
Przedstawiono wyniki symulacji pokazujące skutki stosowania okien przy wyznaczaniu widma, za pomocą MDFT, sygnałów próbkowanych niesynchronicznie. Symulacje przeprowadzono dla okna prostokątnego, okna Hanninga i zsynchronizowanego okna Hanninga. Najlepsze wyniki uzyskano dla zsynchronizowanego okna Hanninga, które pozwala w pełni wykorzystać zalety MDFT wynikające z synchronizacji funkcji bazowych szeregu Fouriera z harmonicznymi sygnału.
EN
The paper presents simulation results showing effects of application of windows when determining the spectrum by means of MDFT of signals sampled asynchronously. Simulations were performed for a rectangular window, Hanning window, and a synchronized Hanning window. The best results were obtained for the synchronized Hanning window, which allows to take full advantage of MDFT arising from synchronization of basis functions of the Fourier series with harmonics of the signal.
14
Content available remote Zastosowanie IpDFT do diagnostyki silników asynchronicznych
PL
W niniejszej pracy przedstawiono porównanie dokładności estymacji parametrów dla sygnału wieloharmonicznego dla klasycznej metody DFT oraz dwupunktowej metody interpolowanego DFT (IpDFT). Analizy dokonano dla wybranych okien Rife’a-Vincenta klasy I (RVCI). W artykule skupiono się również na skuteczności niwelowania przecieku widma, w zależności od wybranej metody estymacji, rodzaju użytego okna oraz długości czasu pomiaru. Zmiana wartość błędu pomiaru dla estymacji częstotliwości, amplitudy i fazy została przedstawiona w postaci graficznej. Ponieważ jedną z metod oceny stanu klatki silnika indukcyjnego, jest analiza składowej widma o częstotliwości poślizgowej, niniejszy artykuł może stanowić podstawę do dalszych badań dotyczących diagnostyki silnika indukcyjnego.
EN
This paper presents a comparison of the accuracy of parameter estimation of multifrequency signal for classic DFT method and the method of two-point interpolated DFT (IpDFT). The analysis was performed for selected windows Rife-Vincent Class I (RVCI). The article focuses on the effectiveness of eliminating the leakage of the spectrum, depending on the selected estimation method, used types of time windows and length of measurement time. The value of the measurement error of the frequency, the amplitude and the phase estimation are presented in graphical form. As one of the methods of assessing cage induction motor is analysis of slip spectrum component, this article can be used as a basis for further studies on the diagnosis of the induction motor.
15
Content available remote Directional Image Filtering Based on the Fourier Transform
EN
An algorithm to design the small size 2-D filter masks with arbitrarily selected rotation angle has been proposed. The classical filter mask of size 3 × 3 is obtained from the reference Fourier space characteristics, rotated in the Fourier domain. The efficiency of the suggested method was illustrated with examples based on the Sobel gradient mask and two test images. Comparative computations indicated that the accuracy of the filtering result with use of the small size filters is noticeably better when the filter has been designed with use of the Fourier characteristics rotation than after direct rotation of the mask in the pixel domain.
PL
Przedstawiono krótko zasady funkcjonowania systemów opartych na urządzeniach klasy PMU, ich charakterystyki i pola zastosowań, takie jak: monitorowanie pracy systemu, oceny stabilności pracy systemu, oceny jakości energii elektrycznej, a także w układach zabezpieczeń. Podano także ocenę jakości samych urządzeń typu PMU.
EN
Presented are shortly operation principles of control systems based on the PMU class devices, their characteristics and field of applications like monitoring of a power system work, system stability evaluation, evaluation of electric energy quality and the work in power system protection schemes. Given is also a short assessment of the PMU devices quality.
PL
Przedstawiono opis metod pomiaru przesunięcia fazowego i analizę ich efektywności pod kątem niepewności pomiaru.
EN
The paper presents a description of methods used for measurement of phase shift. Analysis of their effectiveness pays special attention to measurement uncertainty.
EN
This paper presents a distributed measuring system for on-line monitoring of dielectric loss factor tan δ, and capacitance of HV apparatus. The method employs the Discrete Fourier Transform (DFT) which is performed on the scaled down analog voltage and current signals obtained using digital signal processing (DSP) technology. The measuring unit of the on-line monitoring system takes a series of measures in the hardware circuit design to improve the effectiveness of the DFT algorithm. The lab test results of measuring unit show that the measuring unit has high precision of measurement based on the DFT method. Field tests at a regional substation to evaluate the insulation of two groups of 220kV current transformer units using the developed system.
PL
W artykule opisano system pomiaru rozproszonego do monitorowania on-line współczynnika strat dielektrycznych i pojemności w aparatach HV. W metodzie wykorzystano Dyskretną Transformatę Fouriera. W celu poprawy dokładności i skuteczności DFT, dokonywana jest seria pomiarów. Wyniki badań laboratoryjnych oraz w rzeczywistej podstacji, wykazały wysoką precyzję rozwiązania.
PL
Przedstawiono krótkookresową analizę widmową prądów udarowych, prądu zwarciowego w czasie rzeczywistym z zastosowaniem procesora FFT zrealizowanego w FPGA.
EN
The paper presents short-term spectral analysis of surge currents, short-circuit current at actual time using FFT processor realized with FPGA technology.
EN
The work describes the sensor subsystem for the magnetic signals of vehicles based on measuring the magnetic flux density as well as denoising unit. For this purpose a set of wireless magnetic sensors is used that allows to monitor the movement of vehicles at airports, seaports and border check-points. The measured signalls serve for detection and identification of vehicles. Since every vehicle is built of ferromagnetic components it perturbs the uniformity of the Earth magnetic field. This perturbation can be measured with the use of fluxgate sensors. In order to improve the signal-to-noise ratio the differential setting of the sensorsand the matched filtering based on the FFT FPGA core are applied. Such approach makes easier the detection and identification of objects. In this work the measurement subsystem, the realization of the matched filter based on the FFT FPGA processor and the results of simulation and experimental research are presented.
PL
W artykule przedstawiono podsystem czujników do pomiaru sygnałów magnetycznych od pojazdów, oparty na pomiarze indukcji magnetycznej. Do tego celu zastosowano zestaw czujników magnetycznych pracujących bezprzewodowo, który pozwala na monitorowanie ruchu pojazdów na lotniskach, w portach i punktach kontroli granicznej. Mierzone sygnały pozwalają na wykrywanie i identyfikację pojazdów. Ze względu na fakt, że każdy pojazd jest zbudowany z elementów ferromagnetycznych, które zaburzają pole magnetyczne Ziemi, zaburzenie to można zmierzyć przy zastosowaniu trójosiowych magnetometrów transduktorowych. W celu poprawienia stosunku sygnału do szumu zastosowano pomiar różnicowy i filtrację dopasowaną zrealizowaną w oparciu o procesor wykorzystujący jądro FFT w układzie FPGA. Takie podejście ułatwia wykrywanie i identyfikację obiektów. W pracy opisano system pomiarowy, realizację filtru dopasowanego wykorzystującego procesor FFT oraz rezultaty symulacji i badań eksperymentalnych (Pomiar sygnałów magnetycznych od pojazdów z odszumianiem wspomaganym filtracją dopasowaną z użyciem procesora FFT w technologii FPGA)
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