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    Wyświetlanie 1-8 z 8
    Tytuł:
    Fast one-cycle frequency estimation of a single sinusoid in noise using downsampled linear prediction model
    Autorzy:
    Duda, Krzysztof
    Zieliński, Tomasz P.
    Powiązania:
    https://bibliotekanauki.pl/articles/2052172.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    frequency estimation
    linear prediction
    Prony method
    smart DFT
    Opis:
    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.
    Źródło:
    Metrology and Measurement Systems; 2021, 28, 4; 661-672
    0860-8229
    Pojawia się w:
    Metrology and Measurement Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Minimization of maximum errors in universal approximation of the unit circle by a polygon
    Autorzy:
    Borkowski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/221779.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    unit circle
    approximation by polygon
    LIDFT
    interpolated DFT
    zero padding
    Opis:
    This paper presents a universal approximation of the unit circle by a polygon that can be used in signal processing algorithms. Optimal choice of the values of three parameters of this approximation allows one to obtain a high accuracy of approximation. The approximation described in the paper has a universal character and can be used in many signal processing algorithms, such as DFT, that use the mathematical form of the unit circle. One of the applications of the described approximation is the DFT linear interpolation method (LIDFT). Applying the results of the presented paper to improve the LIDFT method allows one to significantly decrease the errors in estimating the amplitudes and frequencies of multifrequency signal components. The paper presents the derived formulas, an analysis of the approximation accuracy and the region of best values for the approximation parameters.
    Źródło:
    Metrology and Measurement Systems; 2011, 18, 3; 391-402
    0860-8229
    Pojawia się w:
    Metrology and Measurement Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Estimation of the amplitude square using the interpolated Discrete Fourier Transform
    Autorzy:
    Lušin, T.
    Agrež, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/220579.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    estimation
    amplitude square
    spectral data processing
    interpolated DFT
    Hann window
    Opis:
    To improve the estimation of active power, the possibility of estimating the amplitude square of a signal component using the interpolation of the squared amplitude discrete Fourier transform (DFT) coefficients is presented. As with an energy-based approach, the amplitude square can be estimated with the squared amplitude DFT coefficients around the component peak and a suitable interpolation algorithm. The use of the Hann window, for which the frequency spectrum is well known, and the three largest local amplitude DFT coefficients gives lower systematic errors in squared interpolated approach or in better interpolated squared approach than the energy-based approach, although the frequency has to be estimated in the first step. All investigated algorithms have almost the same noise propagation and the standard deviations are about two times larger than the Cramér-Rao lower bound.
    Źródło:
    Metrology and Measurement Systems; 2011, 18, 4; 583-596
    0860-8229
    Pojawia się w:
    Metrology and Measurement Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Continuous and discontinuous linear approximation of the window spectrum by least squares method
    Autorzy:
    Borkowski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/221777.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    data window
    spectrum approximation
    interpolated DFT
    LIDFT
    spectrum estimation
    zero padding
    Opis:
    This paper presents the general solution of the least-squares approximation of the frequency characteristic of the data window by linear functions combined with zero padding technique. The approximation characteristic can be discontinuous or continuous, what depends on the value of one approximation parameter. The approximation solution has an analytical form and therefore the results have universal character. The paper presents derived formulas, analysis of approximation accuracy, the exemplary characteristics and conclusions, which confirm high accuracy of the approximation. The presented solution is applicable to estimating methods, like the LIDFT method, visualizations, etc.
    Źródło:
    Metrology and Measurement Systems; 2011, 18, 3; 379-390
    0860-8229
    Pojawia się w:
    Metrology and Measurement Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Frequency and Damping Estimation Methods - An Overview
    Autorzy:
    Zieliński, T. P.
    Duda, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/220581.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    damped sinusoids
    frequency estimation
    damping estimation
    linear prediction
    subspace methods
    interpolated DFT
    Opis:
    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.
    Źródło:
    Metrology and Measurement Systems; 2011, 18, 4; 505-528
    0860-8229
    Pojawia się w:
    Metrology and Measurement Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Comparison of sine-wave frequency estimation methods in respect of speed and accuracy for a few observed cycles distorted by noise and harmonics
    Autorzy:
    Borkowski, J.
    Kania, D.
    Mroczka, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/220583.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    DFT spectrum interpolation
    short-time frequency estimation
    statistical analysis
    Prony LS
    TLS
    ESPRIT
    Opis:
    The paper deals with frequency estimation methods of sine-wave signals for a few signal cycles and consists of two parts. The first part contains a short overview where analytical error formulae for a signal distorted by noise and harmonics are presented. These formulae are compared with other accurate equations presented previously by the authors which are even more accurate below one cycle in the measurement window. The second part contains a comparison of eight estimation methods (ESPRIT, TLS, Prony LS, a newly developed IpDFT method and four other 3-point IpDFT methods) in respect of calculation time and accuracy for an ideal sine-wave signal, signal distorted by AWGN noise and a signal distorted by harmonics. The number of signal cycles is limited from 0.1 to 3 or 5. The results enable to select the most accurate/fastest estimation method in various measurement conditions. Parametric methods are more accurate but also much slower than IpDFT methods (up to 3000 times for the number of samples equal to 5000). The presented method is more accurate than other IpDFT methods and much faster than parametric methods, which makes it possible to use it as an alternative, especially in real-time applications.
    Źródło:
    Metrology and Measurement Systems; 2018, 25, 2; 283-302
    0860-8229
    Pojawia się w:
    Metrology and Measurement Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Systematic errors of the LIDFT method: analytical form and verification by a Monte Carlo method
    Autorzy:
    Borkowski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/221176.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    LIDFT
    multifrequency signal
    interpolated DFT
    spectrum estimation
    zero padding
    unit circle
    approximation by polygon
    Opis:
    This paper derives analytical formulas for the systematic errors of the linear interpolated DFT (LIDFT) method when used to estimating multifrequency signal parameters and verifies this analysis using Monte-Carlo simulations. The analysis is performed on the version of the LIDFT method based on optimal approximation of the unit circle by a polygon using a pair of windows. The analytical formulas derived here take the systematic errors in the estimation of amplitude and frequency of component oscillations in the multifrequency signal as the sum of basic errors and the errors caused by each of the component oscillations. Additional formulas are also included to analyze particular quantities such as a signal consisting of two complex oscillations, and the analyses are verified using Monte-Carlo simulations.
    Źródło:
    Metrology and Measurement Systems; 2012, 19, 4; 673-684
    0860-8229
    Pojawia się w:
    Metrology and Measurement Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Interpolated-DFT-Based Fast and Accurate Amplitude and Phase Estimation for the Control of Power
    Autorzy:
    Borkowski, J.
    Kania, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/221570.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    control of power
    grid signal
    amplitude and phase estimation
    renewable energy
    interpolated DFT
    maximum decay side-lobes windows
    Opis:
    Quality of energy produced in renewable energy systems has to be at the high level specified by respective standards and directives. One of the most important factors affecting quality is the estimation accuracy of grid signal parameters. This paper presents a method of a very fast and accurate amplitude and phase grid signal estimation using the Fast Fourier Transform procedure and maximum decay side-lobes windows. The most important features of the method are elimination of the impact associated with the conjugate’s component on the results and its straightforward implementation. Moreover, the measurement time is very short ‒ even far less than one period of the grid signal. The influence of harmonics on the results is reduced by using a bandpass pre-filter. Even using a 40 dB FIR pre-filter for the grid signal with THD ≈ 38%, SNR ≈ 53 dB and a 20‒30% slow decay exponential drift the maximum estimation errors in a real-time DSP system for 512 samples are approximately 1% for the amplitude and approximately 8.5・10‒2 rad for the phase, respectively. The errors are smaller by several orders of magnitude with using more accurate pre-filters.
    Źródło:
    Metrology and Measurement Systems; 2016, 23, 1; 13-26
    0860-8229
    Pojawia się w:
    Metrology and Measurement Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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