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1
Content available Implementation of Goertzel-based frequency estimation for power quality monitoring in embedded measurement systems
Rodrigues Nuno M., Janeiro Fernando M., Ramos Pedro M.
Metrology and Measurement Systems
|
2022
|
Vol. 29, nr 3
455--468
EN
International standards from IEC and IEEE regulate power grid parameters such as the RMS value, frequency, harmonic and interharmonic distortion, unbalance or the presence of transients, that are important to assure the quality of distributed power. Standard IEC 61000-4-30 suggests the zero crossing algorithm for the measurement of the power grid frequency, but also states that different algorithms can be used. This paper proposes a new algorithm, the Fractional Interpolated Discrete Fourier Transform, FracIpDFT, to estimate the power grid frequency, suitable for implementation in resource limited embedded measurement systems. It is based on the non-integer Goertzel algorithm followed by interpolation at non-integer multiples of the DFT frequency resolution. The proposed algorithm is validated and its performance compared with other algorithms through numerical simulations. Implementation details of the FracIpDFT in an ARM Cortex M4 processor are presented along with frequency measurement results performed with the proposed algorithm in the developed system.
2
Content available Fast one-cycle frequency estimation of a single sinusoid in noise using downsampled linear prediction model
Duda Krzysztof, Zieliński Tomasz P.
Metrology and Measurement Systems
|
2021
|
Vol. 28, nr 4
661--672
EN
A new solution to the problem of frequency estimation of a single sinusoid embedded in the white Gaussian noise is presented. It exploits, approximately, only one signal cycle, and is based on the well-known 2nd order autoregressive difference equation into which a downsampling is introduced. The proposed method is a generalization of the linear prediction based Prony method for the case of a single undamped sinusoid. It is shown that, thanks to the proposed downsampling in the linear prediction signal model, the overall variance of the least squares solution of frequency estimation is decreased, when compared to the Prony method, and locally it is even close to the Cramér-Rao Lower Bound, which is a significant improvement. The frequency estimation variance of the proposed solution is comparable with, computationally more complex, the Matrix Pencil and the Steiglitz-McBride methods. It is shown that application of the proposed downsampling to the popular smart DFT frequency estimation method also significantly reduces the method variance and makes it even better than the least squares smart DFT. The noise immunity of the proposed solution is achieved simultaneously with the reduction of computational complexity at the cost of narrowing the range of measured frequencies, i.e. a sinusoidal signal must be sufficiently oversampled to apply the proposed downsampling in the autoregressive model. The case of 64 samples per period with downsampling up to 16, i.e. 1/4th of the cycle, is presented in detail, but other sampling scenarios, from 16 to 512 samples per period, are considered as well.
3
Content available remote Performance analysis of SRF PLL type-3 with dynamic feed forward frequency estimator for abnormal grid conditions
Agrawal Seema, Kumar Mahendra, Palwalia D. K.
Journal of Power Technologies
|
2021
|
Vol. 101, nr 2
87--95
EN
A phase-locked loop (PLL) is a closed-loop feedback control device that synchronizes its output signal with an input signal in both frequency and time. This paper presents a robust method for tracking against adverse conditions of the fundamental sequence component of utility voltage. The proposed phase-locked loop (PLL) is a hybrid configuration of the phase- locked loop type-3 (SRF type-3) synchronous reference frame coupled with a feed-forward frequency estimator using a selective harmonic filtering technique. A SRF type -2 based PLL has a secondary closed path. Under the ramp frequency transition, it has a steady-state step and a frequency error. In the proposed PLL, the constant gain loop filter is used to eliminate the phase and frequency error. Feed-forward operation with selective harmonic pre-filtering enables fast-tracking with a low tracking error of the reference signal. From the results it is evident that the proposed PLL achieves a high bandwidth and quick dynamic response without endangering the stability and filtering capability. The proposed system has been tested through MATLAB Simulink platform under abnormal conditions.
4
Content available remote Mining Cardinality Restrictions in OWL
Potoniec Jędrzej
Foundations of Computing and Decision Sciences
|
2020
|
Vol. 45, No. 3
195--216
EN
We present an approach to mine cardinality restriction axioms from an existing knowledge graph, in order to extend an ontology describing the graph. We compare frequency estimation with kernel density estimation as approaches to obtain the cardinalities in restrictions. We also propose numerous strategies for filtering obtained axioms in order to make them more available for the ontology engineer. We report the results of experimental evaluation on DBpedia 2016-10 and show that using kernel density estimation to compute the cardinalities in cardinality restrictions yields more robust results that using frequency estimation. We also show that while filtering is of limited usability for minimum cardinality restrictions, it is much more important for maximum cardinality restrictions. The presented findings can be used to extend existing ontology engineering tools in order to support ontology construction and enable more efficient creation of knowledge-intensive artificial intelligence systems.
5
Content available remote Właściwości wybranych algorytmów do estymacji częstotliwości w dokładnych pomiarach napięcia sinusoidalnego
Krajewski M., Sienkowski S., Kawecka E.
Przegląd Elektrotechniczny
|
2018
|
R. 94, nr 12
52--55
PL
W artykule przedstawiono wyniki badań symulacyjnych właściwości wybranych cyfrowych algorytmów do estymacji częstotliwości w warunkach pracy przyrządów do dokładnych pomiarów napięcia sinusoidalnego. Zastosowano opracowany algorytm do pomiaru częstotliwości, oparty o pomiar przesunięcia fazowego z zastosowaniem DFT (Dyskretnej Transformaty Fouriera) oraz znane z literatury trzy algorytmy z interpolacją widma i algorytm zupełnych kwadratów błędów TLS (Total Least Squares) . Wyniki badań wskazują, że opracowany algorytm cechuje się najlepszymi właściwościami.
EN
The article presents the results of the simulation properties of selected digital algorithms to estimate the frequency, in the operating conditions of instruments for accurate measurements of sinusoidal voltage. A developed algorithm based on a phase shift measurement with a use of DFT (Discrete Fourier Transform) and four algorithms known from literature, three with spectral interpolation and a total least squares (TLS), were applied. The research results indicate that the developed algorithm is characterized by the best properties.
6
Content available remote Czasowo-dyskretne algorytmy czteropunktowe do śledzenia częstotliwości sygnału sinusoidalnego
Sienkowski S., Krajewski M.
Przegląd Elektrotechniczny
|
2018
|
R. 94, nr 11
30--33
PL
W artykule przedstawiono nowe czasowo-dyskretne algorytmy czteropunktowe umożliwiające śledzenie częstotliwości sygnału sinusoidalnego. Opracowane algorytmy porównano z czasowo-dyskretnym algorytmem trzypunktowym zaproponowanym przez Vizireanu. W celu porównania algorytmów wykonano symulacje polegające na śledzeniu częstotliwości sygnału sinusoidalnego zakłóconego szumem Gaussa. Pokazano, że opracowane algorytmy umożliwiają śledzenie częstotliwości z większą dokładnością.
EN
The article presents new discrete-time four-point algorithms that enable tracking the sinusoidal signal frequency. The developed algorithms have been compared with the discrete-time three-point algorithm proposed by Vizireanu. In order to compare the algorithms, simulations have been performed, consisting in tracking the sinusoidal signal frequency disturbed by Gaussian noise. It has been shown that the developed algorithms allow frequency tracking with greater accuracy.
7
Content available remote Assessment of power frequency estimation methods in distributed generation in islanding condition
Sanca H. S., Campos J. T. L. S., Souza F. C., Costa F. B., Souza B. A.
Przegląd Elektrotechniczny
|
2018
|
R. 94, nr 5
1--6
EN
In this paper, a method for evaluation of power frequency estimation during transient operation in distributed generation (DG) in islanding conditions is presented. For this end, five methods of fundamental frequency estimation are evaluated in a distribution system with distributed generation in islanding operation, such as: (a) zero crossing, (b) adjustment of points to a pure sinusoidal waveform, (c) hybrid method, (d) discrete Fourier transform method based, and (e) Prony-Fourier-based algorithm. The estimators are compared and evaluated in two different ways, using two analytical functions, and in an electric power distributed system with DG in islanding condition. The evaluation methodology for the frequency estimators are based in statistical errors, taking into account mean, mean square error. The zero-crossing and discrete Fourier transform based estimator presented better results in comparison with the other evaluated algorithms. However, the discrete Fourier transform presented good results in the estimated frequency in the three evaluated cases.
PL
W artykule oceniono metody badania częstotliwości w stanach przejściowych rozproszonych sieci energetycznych w warunkach tworzenia się wysp. Zbadano pięć metod: zero crossing, APPSW, hybrydową, DFT iProny. Najlepszy wyniki osiągnięto przy stosowaniu metody zero-crossing (Przeciecia osi zero) I DFT.
8
Content available Simple, fast and accurate four-point estimators of sinusoidal signal frequency
Sienkowski S., Krajewski M.
Metrology and Measurement Systems
|
2018
|
Vol. 25, nr 2
359--376
EN
In this paper, two new sinusoidal signal frequency estimators calculated on the basis of four equally spaced signal samples are presented. These estimators are called four-point estimators. Simulation and experimental research consisting in signal frequency estimation using the invented estimators have been carried out. Simulation has also been performed for frequency tracking. The simulation research was carried out applying the MathCAD computer program that determined samples of a sinusoidal signal disturbed by Gaussian noise. In the experimental research, sinusoidal signal samples were obtained by means of a National Instruments PCI-6024E data acquisition card and an Agilent 33220A function generator. On the basis of the collected samples, the values of four-point estimators invented by the authors and, for comparison, the values of three- and four-point estimators proposed by Vizireanu were determined. Next, estimation errors of the signal frequency were determined. It has been shown that the invented estimators can estimate a signal frequency with greater accuracy.
9
Algorytm określania momentu rozpoczęcia odbioru sygnału użytecznego na potrzeby pomiaru odległości w systemach radiowych
Piotrowski P., Zieliński R.
Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne
|
2015
|
nr 4
143--146
PL
Zaprezentowano wyniki prac nad algorytmem umożliwiającym pomiar odległości w systemach radiowych metodami czasowymi. Precyzja pomiaru odległości takiego systemu zależy wprost od dokładności pomiaru czasu propagacji sygnału testowego. Przedstawiono koncepcję algorytmu określania momentu odebrania sygnału użytecznego z zastosowaniem estymatorów częstotliwość chwilowej oraz wyniki działania z zastosowaniem różnych estymatorów.
EN
The article presents research results on algorithm that can be used to estimate the distance in multipath environment in wireless systems based on radio signal propagation delay. Precision of the estimation highly depends on signal propagation time estimation error. Authors present new approach to determine the moment of signal reception based on instantaneous frequency estimators as well as results of simulations using various frequency estimators.
10
Content available Accurate Frequency Estimation Based On Three-Parameter Sine-Fitting With Three FFT Samples
Liu X., Ren Y., Chu C., Fang W.
Metrology and Measurement Systems
|
2015
|
Vol. 22, nr 3
403--416
EN
This paper presents a simple DFT-based golden section searching algorithm (DGSSA) for the single tone frequency estimation. Because of truncation and discreteness in signal samples, Fast Fourier Transform (FFT) and Discrete Fourier Transform (DFT) are inevitable to cause the spectrum leakage and fence effect which lead to a low estimation accuracy. This method can improve the estimation accuracy under conditions of a low signal-to-noise ratio (SNR) and a low resolution. This method firstly uses three FFT samples to determine the frequency searching scope, then – besides the frequency – the estimated values of amplitude, phase and dc component are obtained by minimizing the least square (LS) fitting error of three-parameter sine fitting. By setting reasonable stop conditions or the number of iterations, the accurate frequency estimation can be realized. The accuracy of this method, when applied to observed single-tone sinusoid samples corrupted by white Gaussian noise, is investigated by different methods with respect to the unbiased Cramer-Rao Low Bound (CRLB). The simulation results show that the root mean square error (RMSE) of the frequency estimation curve is consistent with the tendency of CRLB as SNR increases, even in the case of a small number of samples. The average RMSE of the frequency estimation is less than 1.5 times the CRLB with SNR = 20 dB and N = 512.
11
Content available Influence of A/D quantization in an interpolated DFT based system of power control with a small delay
Borkowski J., Kania D., Mroczka J.
Metrology and Measurement Systems
|
2014
|
Vol. 21, nr 3
423--432
EN
Fast and accurate grid signal frequency estimation is a very important issue in the control of renewable energy systems. Important factors that influence the estimation accuracy include the A/D converter parameters in the inverter control system. This paper presents the influence of the number of A/D converter bits b, the phase shift of the grid signal relative to the time window, the width of the time window relative to the grid signal period (expressed as a cycle in range (CiR) parameter) and the number of N samples obtained in this window with the A/D converter on the developed estimation method results. An increase in the number b by 8 decreases the estimation error by approximately 256 times. The largest estimation error occurs when the signal module maximum is in the time window center (for small values of CiR) or when the signal value is zero in the time window center (for large values of CiR). In practical applications, the dominant component of the frequency estimation error is the error caused by the quantization noise, and its range is from approximately 8×10-10 to 6×10-4.
12
Content available remote Frequency Estimation Algorithms by Fusion Spectra of Multi-section Sinusoids
Xiao W., Tu Y., Liu L., Shen Y., Zhang L.
Przegląd Elektrotechniczny
|
2013
|
R. 89, nr 3b
246--253
EN
For achieving a more precise frequency estimation of a short sinusoid at low SNR, a algorithm based on fusion spectra of Multi-section Sinusoids(M-sinusoids) was proposed. In order to solve the discontinuous phases problem of M-sinusoids, the Optimization Weighted-Accumulation (OW-A) spectrum was gained through weighted-accumulation spectra of M-sinusoids by the designed weighted factor. The correlation spectrum, which could inherit the narrow and high main-lobe of the OW-A spectrum, and the good noise immunity of the accumulation spectrum of M-sinusoids, was constructed by correlation OW-A spectrum and the accumulation spectrum. Therefore, higher precision frequency estimation could be obtained through spectral peak searching of the correlation spectrum. Moreover, in order to meet the high real-time demand in some fields, a fast algorithm of the proposed algorithm was put forward. This fast algorithm could reduce most computational cost of the proposed algorithm by the following techniques: design a fast DTFT algorithm, reduction dimensions of the weighted fusion spectrum matrix, 1/3 main-lodes correlation of the OW-A spectrum and the accumulation spectrum. Simulations demonstrate the superior performance of the proposed algorithms; the fast algorithm could reduce most calculation of the proposed algorithm with lowering a little frequency estimation precision, and it works better in very low SNR (SNR≤-13dB).
PL
W artykule zaproponowano algorytm estymacji częstotliwości krótkich fal sinusoidalnych o niskim zaszumieniu (SNR). Rozwiązanie bazuje na widmie fuzji M-częstotliowości sinusoid (M-sinusoids). W celu rozwiązania problemu nieciągłości faz M-sinusoid zastosowano współczynniki wagowe zawartości częstotliwości, co pozwoliło na ich optymalizację (ang. Optimization Weighted-Accumulation). Zastosowanie algorytmu pozwala na zwiększenie precyzji estymacji przy jednoczesnym zwiększeniu szybkości wykonania. Wyniki badań symulacyjnych potwierdzają skuteczność działania.
13
Content available Power system frequency estimation algorithm for electric energy metering of nonlinear loads
Peng Z., Hong-Bin L.
Metrology and Measurement Systems
|
2012
|
Vol. 19, nr 2
307-320
EN
In this paper, a discrete wavelet transform (DWT) based approach is proposed for power system frequency estimation. Unlike the existing frequency estimators mainly used for power system monitoring and control, the proposed approach is developed for fundamental frequency estimation in the field of energy metering of nonlinear loads. The characteristics of a nonlinear load is that the power signal is heavily distorted, composed of harmonics, inter-harmonics and corrupted by noise. The main idea is to predetermine a series of frequency points, and the mean value of two frequency points nearest to the power system frequency is accepted as the approximate solution. Firstly the input signal is modulated with a series of modulating signals, whose frequencies are those frequency points. Then the modulated signals are decomposed into individual frequency bands using DWT, and differences between the maximum and minimum wavelet coefficients in the lowest frequency band are calculated. Similarities among power system frequency and those frequency points are judged by the differences. Simulation results have proven high immunity to noise, harmonic and inter-harmonic interferences. The proposed method is applicable for real-time power system frequency estimation for electric energy measurement of nonlinear loads.
14
Content available RADAR Signal Parameters Estimation in the MTD Tasks
Prokopenko I. G., Omelchuk I. P., Chyrka Y. D.
International Journal of Electronics and Telecommunications
|
2012
|
Vol. 58, No. 2
159-164
EN
The MTD method adaptive to current target speed, in which suboptimal iterative algorithms for the reflected signal parameters estimation are synthesized, is suggested. This method allows to detect a slowly moving targets with radial speed 3-4 times less, than for pulse-pair subtraction (PPS).
15
Content available remote Śledzenie parametrów cyfrowych sygnałów sinusoidalnych z zastosowaniem filtrów adaptacyjnych
Duda K.
Przegląd Elektrotechniczny
|
2011
|
R. 87, nr 1
140-143
PL
Niniejsza praca dotyczy zagadnienia estymacji chwilowej częstotliwości, amplitudy i fazy cyfrowych sygnałów sinusoidalnych. Sygnał sinusoidalny jest modelowany równaniem rekurencyjnym filtra cyfrowego ze sprzężonym biegunem zespolonym na okręgu jednostkowym. Równanie to umożliwia określenie, optymalnej w sensie najmniejszych kwadratów (LS), częstotliwości sygnału na podstawie próbek (pomiarów). Zastosowanie postaci analitycznej sygnału pomiarowego umożliwia wyznaczenie, optymalnych w sensie LS, estymat amplitudy i fazy sygnału. W referacie podano iteracyjne rozwiązanie problemu estymacji parametrów sygnałów sinusoidalnych w postaci filtrów adaptacyjnych RLS i LMS. Podano przykładową realizację algorytmu estymacji oraz określono jej błędy systematyczne, a także zilustrowano własność śledzenia częstotliwości i amplitudy chwilowej.
EN
The paper describes new method for estimation of instantaneous frequency, amplitude, and phase of sinusoidal signals. The sinusoidal signal is modeled by the difference equation of the digital filter with the complex conjugate pole placed on the unit circle. The difference equation is used for computing signal's frequency optimal in the least squares (LS) sense. Optimal LS solutions for the amplitude and phase are derived with the use of analytic signal. In the paper the problem of LS solution is next stated as the problem of adaptive filtering and the iterative solutions in the form of RLS and LMS filters are given. Those filters contain only one coefficient and the computational burden is significantly reduced as to compare to popular Kalman or extended Kalman filter. The specific implementation of the proposed method is given and discussed in the paper. We show the systematic errors of frequency, amplitude, and phase estimation. The tracking of instantaneous frequency and amplitude is illustrated with the test signal disturbed by Gaussian noise with simultaneous frequency and amplitude modulation. The compromise between tracking abilities and noise immunity is also shown by means of numerical simulations.
16
Content available remote Analysis of distorted waveforms in power converter systems
Rezmer J., Leonowicz Z., Gono R.
Przegląd Elektrotechniczny
|
2011
|
R. 87, nr 1
254-257
EN
We present a method of determining the frequency, developed and based on the Prony model. The method was derived for those cases in which the process contains two dominant harmonics and noise. Additionally, in order to improve the accuracy of the method, median filtering was applied. The presented methods can be useful for practical applications in power systems, like the control systems of frequency converters.
PL
W artykule przedstawiono metodę wyznaczania częstotliwości, opracowaną na podstawie modelu Prony'ego. Metoda została opracowana z założeniem, że analizowany proces zawiera dwie harmoniczne i szum. Dodatkowo, w celu poprawy dokładności metody, zastosowano filtrowanie medianowe. Zaprezentowana metoda może być wykorzystana w układach elektroenergetycznych, takich jak układy sterujące przekształtników.
17
Content available Phase-locked loop technique system with orthogonal signal generator for power electronics controllers
Wyszomirski M., Rosołowski E.
Present Problems of Power System Control
|
2011
|
Nr 1
61-74
EN
This paper presents a Phase-Locked Loop (PLL) scheme with Orthogonal Signal Generator (OSG). The proposed technique enables to eliminate the influence of distortions from the observed signal on proper determination of its parameters as a phase, magnitude or frequency. A simulation model of the system is developed and results of investigation are provided. Some recommendations on the scheme settings for elimination of harmonic and inter-harmonic components are also included. It was verified that the proposed PLL with OSG system can be considered as an useful and effective tool in implementations that require a great accuracy of the phase angle and frequency estimation. The system could be applied in three-phase power systems control units such as FACTS converters or doubly-fed induction generators control scheme. Simulation results demonstrate the effectiveness and robustness of the proposed solution.
PL
W artykule przedstawiono układ pętli synchronizacji fazowej (PSF) z generatorem sygnałów ortogonalnych (GSO). Proponowana technika umożliwia wyeliminowanie wpływu zakłóceń zanalizowanego sygnału na określenie jego parametrów takich jak faza, amplituda czy częstotliwość. Przedstawiono model symulacyjny proponowanego układu i zaprezentowano wyniki doświadczeń. Zawarto także niektóre z zalecanych konfiguracji schematu w celu eliminacji składowych harmonicznych i interharmonicznych sygnału. Dowiedziono, że proponowany system PSF z GSO może być rozpatrywany jako użyteczne i efektywne narzędzie w implementacjach wymagających dużej dokładności estymacji fazy i częstotliwości. Proponowany system może być stosowany w układach sterowania trójfazowych systemów takich jak FACTS lub w układach sterowania generatorów indukcyjnych dwustronnie zasilanych (DFIG). Wyniki symulacji wskazują na skuteczność i poprawność działania zaproponowanego rozwiązania.
18
Content available Frequency and Damping Estimation Methods - An Overview
Zieliński T. P., Duda K.
Metrology and Measurement Systems
|
2011
|
Vol. 18, nr 4
505-528
EN
This overview paper presents and compares different methods traditionally used for estimating damped sinusoid parameters. Firstly, direct nonlinear least squares fitting the signal model in the time and frequency domains are described. Next, possible applications of the Hilbert transform for signal demodulation are presented. Then, a wide range of autoregressive modelling methods, valid for damped sinusoids, are discussed, in which frequency and damping are estimated from calculated signal linear self-prediction coefficients. These methods aim at solving, directly or using least squares, a matrix linear equation in which signal or its autocorrelation function samples are used. The Prony, Steiglitz-McBride, Kumaresan-Tufts, Total Least Squares, Matrix Pencil, Yule-Walker and Pisarenko methods are taken into account. Finally, the interpolated discrete Fourier transform is presented with examples of Bertocco, Yoshida, and Agrež algorithms. The Matlab codes of all the discussed methods are given. The second part of the paper presents simulation results, compared with the Cramér-Rao lower bound and commented. All tested methods are compared with respect to their accuracy (systematic errors), noise robustness, required signal length, and computational complexity.
19
Zastosowanie modelu AR do analizy sygnału dopplerowskiego radaru z modulowaną falą ciągłą
Rytel-Adrianik R.
Elektronika : konstrukcje, technologie, zastosowania
|
2009
|
Vol. 50, nr 8
48-52
PL
W artykule przedstawiono analizę sygnałów echa radarowego od samochodu i od poruszającego się pieszego, przeprowadzoną z zastosowaniem modelu autoregresji (AR). W przypadku echa gwałtownie hamującego samochodu estymowano jego prędkość chwilową, do czego wykorzystano względną odporność modelu AR na odstępstwa od sinusoidalnego modelu sygnału użytecznego. W przypadku echa pieszego przeprowadzono dodatkowo analizę złożonej prędkościowej struktury echa, do czego wykorzystano wysoką rozdzielczość częstotliwościową modelu AR. Rejestracje wykonano przy wykorzystaniu radaru z falą ciągłą zmodulowaną częstotliwościowo (radaru FMCW).
EN
The paper deals with an analysis of recorded FMCW radar Doppler signals of a braking car and a running man. In the analysis the autoregresive (AR) signal model was used what allowed for the robust estimation of an instantaneous velocity of the braking car and characterization of a velocity structure of the running man whose both trunk and arms and/or legs were visible.
20
Content available A highly accurate DFT-based parameter estimator for complex exponentials
Tsui J., Reisenfeld S.
Journal of Telecommunications and Information Technology
|
2006
|
nr 1
76-82
EN
A highly accurate DFT-based complex exponential parameter estimation algorithm is presented in this paper. It will be shown that for large number of samples and high signal to noise ratio (SNR), the phase estimation error variance performance is only 0.0475 dB above the Cramer-Rao lower bound (CRLB) for phase estimation with unknown frequency and phase. The amplitude estimation error variance performance was found to lay on the CRLB for amplitude estimation. Exact phase and amplitude estimation can be achieved in the noiseless case with this algorithm. The algorithm has low implementation computational complexity and is suitable for numerous real time digital signal processing applications.
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