Dusan Agrez

Weighted multi-point interpolated DFTF to improve amplitude estimation of multi-frequency signal

The error reductions of frequency and amplitude estimations of periodic signals with multi-point interpolated discrete Fourier transform (DFT) are described. The properties of interpolations are studied for the rectangular and Hanning windows with respect to their ability for correction systematic effects of used windows and their noise sensitivity. The correction is improved with increasing the interpolation points of DFT. The use of a suitable interpolation algorithm depends on effective bits of A/D conversion, on the position of the frequency component of signal and on mutual components interspacing along the frequency axis. Using different algorithms, we change adaptively the apparent window shape for the particular component.

Improving phase estimation with leakage minimization

This paper presents possibilities of an error reduction of the phase estimation with an interpolated discrete Fourier transform (DFT). The properties of interpolations are studied for the rectangular and Hanning windows with respect to their ability for correction systematic effects. The correction is improved by considering the leakage effect of the component spectrum. Uncertainties of the phase estimations have been studied. The simulation and experimental results are presented, showing the effectiveness in estimating the phase of the signal component.

Nonparametric Estimation of Power Quantities in the Frequency Domain Using Rife-Vincent Windows

This paper presents algorithms for fast measurement and the nonparametric estimation of the unknown changing frequency, amplitude, and phase difference of the signals from two channels with the same frequency, as well as other power quantities, such as the apparent, the active, and the reactive power. The possibilities for systematic error reduction through use of the interpolated discrete Fourier transform using the Rife-Vincent windows class I (RV-I) are described. RV-I windows are designed for maximization of the window spectrum side-lobes fall-off and owing to their minimal leakage, minimal systematic bias curves can be evaluated as a function of the measurement interval duration expressed in signal cycles. Parameters are calculated from the discrete Fourier transform coefficients around the component peaks by summation to reduce the leakage effects. The optimum for reducing the time of measurement and for reducing systematic errors under non-coherent conditions of sampling real noisy signals could be the estimation with the three cycles window using the three-point interpolation and the RV-I window order 3.

Comparison of nonparametric frequency estimators

This paper deals with the performance of several up-to-date nonparametric frequency estimators. The algorithms of frequency estimation are introduced and their bias, standard deviation and consumption time are compared with regard to the most common signal parameters.

Frequency estimation of the non-stationary signals using interpolated DFT

The measurement of a periodic signal with an unknown changing frequency can be well done with an interpolation of DFT (discrete Fourier transformation). This paper presents first an analysis of errors of the DFT coefficients caused by frequency variation. The relations between the stationary case errors and the non-stationary ones are carried out. The bias removal of the interpolation algorithms are studied for rectangular and Hanning windows. Finally, a new interpolation technique that allows very accurate measurements of the instantaneous frequency is proposed Interpolations with longer time of measurement and with larger number of points decrease the systematic errors. The proposed algorithm presents: very fast recovery time (3/4 of a new period), robustness to the amplitude variation, and very high accuracy (the maximal relative error is under one thousandth at slower frequency changes).

Active power estimation by averaging of the DFT coefficients

The paper proposes and discusses an algorithm to improve the estimation of the active power of electrical systems under incoherent sampling. It is based on smoothing sampled data by windowing, prior to their numeric integration, and then averaging the DFT (discrete Fourier transform) coefficients in the frequency domain to reduce the leakage effects. The simulation and experimental results are presented showing that averaging of DFT coefficients provides better estimation of the active power than by windowing. The spectrum of the used window must have a sine function in the kernel. The use of a suitable algorithm depends on a number of observed periods, on positions of the frequency components, and on signal to noise ratio.

Spectrum Analysis of Waveform Digitizers by IDFT and Leakage Minimization

The paper presents possibility of the spectrum estimation of a uniform sampled signal, which is obtained by the dynamic testing of the measurement channel of a waveform digitizer. The advantages of the weighted DFT interpolations for the frequency, amplitude, and phase estimations in order to reduce the leakage effect of the fundamental component in the investigation of the residual spectrum is described. The proposed non-parametric algorithms retain all benefits of DFT approaches and improve the estimation accuracy as a function of a number of the signal cycles in the estimation interval. The spectrum of the window used must be formally well known (like the Manning window) for better analytical expression of the parameter estimation

Active Power Estimation in the Non-coherent Sampling: A Comparative Study

The paper presents and compares three basic approaches of the active power estimation of electrical systems under noncoherent sampling conditions when the leakage effect arises. The properties of the normal time domain approach with smoothing and summation and two frequency domain approaches with improved interpolated DFT estimations of the parameters are studied with respect to their systematic errors and effectiveness in leakage suppression. The simulations are presented showing advantages and weaknesses of compared methods in the shortening measurement time: between one and six cycles in the measurement interval. From analysis and experiments, it can be deduced that averaging of DFT coefficients around zero component provides the best estimation of the active power when the DC offset component is small enough

Propagation of uncertainty in the interpolated DFT

In the paper, we have pointed out the problem of the uncertainty propagation in the interpolated DFT when we have the noncoherent sampling. A possibility of the systematic error reduction of the frequency and the amplitude estimation by the multipoint interpolation for Hanning window is presented. Analyses of the uncertainty propagation for different estimations have been made. The overall uncertainty is obtained as combination of the uncertainty of the amplitude DFT coefficients and the uncertainty introduced by the interpolation algorithm itself. Interpolations with the larger number of points decrease the systematic errors and increase the noise distortion of results. The standard deviations are not constant. They vary periodically with displacement term.

Power system frequency estimation in the shortened measurement time

An algorithm for fast measurement and estimation of power system frequency is presented. The frequency is calculated by an interpolation of the amplitude coefficients of the discrete Fourier transform. An analysis is made to study the influence of leakage effect and a number of sampling points when the rectangular window and the Hanning window are used. Algorithms are proposed for two cases: the measurement time is an integer multiple of the fundamental period of the power system, and it is below one period. Interpolations with longer time of measurement and with larger number of points decrease the systematic errors. When the time is shortened below the signal period, the DC coefficients are taken into account. If the sinusoidal signal is sampled at 64 samples per measurement interval, the proposed method achieves accuracy in measuring the frequency under a hundreth of Hz.