Józef Borkowski

Interpolated-DFT-Based Fast and Accurate Frequency Estimation for the Control of Power

The energy produced by renewable energy systems must fulfill quality requirements as defined in the respective standards and directives. Improvement of the quality could be achieved through a more accurate estimation of the frequency of the grids signal that is used to control an inverter. This paper presents an overview of a method for spectrum interpolation and frequency estimation, and a generalized method for very accurate frequency grid estimation using the fast Fourier transform procedure coupled with maximum decay sidelobe windows. An important feature of this algorithm is the elimination of the impact associated with the conjugates component on the estimations outcome (i.e, the possibility of designating the frequency even if the signals measurement time is on the order of 2.5 periods), and the implementation of the algorithm is straightforward. The results of the simulation show that the algorithm could be successfully used for a fast and accurate estimation of the grid signal frequency. The systematic frequency estimation error is approximately 5·10-11 Hz for a 5-ms measurement window. The algorithm could be used not only for a single sinusoidal signal, but also for a multifrequency signal. This is assuming that the appropriate spectrum leakage reduction (by a time window) will be performed.

Metrological analysis of the LIDFT method

The estimation error components in the DFT linear interpolation (LIDFT) method have been presented in the paper. The equations for random errors, total error, the minimum and optimal parameter value of data window for the case of one complex oscillation, and also the metrological analysis of the multifrequency signal case are presented. This analysis allows us to estimate final method accuracy and obtain the relation for the optimal data window parameter.

LIDFT-the DFT linear interpolation method

The method of linear interpolation of the discrete Fourier transform (LIDFT) to estimate parameters of a signal consisting of many sinusoidal oscillations, has been presented in the paper. The LIDFT method combines beneficial properties from known procedures of nonlinear interpolation of a spectrum, obtained as a result of DFT and from parametric methods based on the Prony method. The LIDFT algorithm with beneficial numerical properties has been obtained after formulating the assumptions of the LIDFT method, providing a linear matrix equation and following symbolic transformations of this equation. The basic operations involved are the FFT algorithm and linear matrix equation solving procedure. The parametric, linearizing data window together with the method-developed to choose the window parameter allow for effective application of the LIDFT method depending on the examined signal character.

Geometric matching of circular features by least squares fitting

Based on the hypothesis that a set of circular arcs is related to a set of circles by translation, rotation and scaling, the paper presents the design of a misalignment cost function, the derivation of an optimal geometric transformation based on least squares fitting to align circular arcs to circles, and computer simulation results to demonstrate the effectiveness of the proposed method.

Influence of noise on the estimation method to reject damped sinusoidal vibrations in adaptive optics systems

Damped sinusoidal signals occur in many fields of science and practical issues. One of them are adaptive optics systems where such signals are undesirable and often diminish the system performance. One of solutions to reject these signals is a method called AVC which is based on the estimation of vibrations parameters. In recent years, an universal, fast and accurate estimation method has been presented. It can be used to estimate multifrequency signals and can be useful in many various cases where the estimation method plays a crucial role. The main idea of this paper is using it in the AVC method to increase the system performance. There can be distinguished several measurement parameters that affect the accuracy and the speed of the estimation method: CiR (number of signal cycles in the estimation process), N (number of signal samples in a measurement window), H (time window order). There are also parameters that are especially important in practical situations (damped signals with noise and harmonics): SNR, THD, γ (changed in time a damping ratio). Total estimation errors consist of systematic errors and random errors. This paper is focusing on the second component, i.e. when the signal with γ ≠ 0 is distorted by noise. Results can be very useful from a practical point of view because they give information about the estimation accuracy in dependence of noise power for various damping ratio values. The value of the empirical MSE of the frequency estimator is approximately 10Λ-3 Hz for SNR = 30 dB H = 2 and γ = 0.01%.

The rejection of vibrations in adaptive optics systems using a DFT-based estimation method

Adaptive optics systems are commonly used in many optical structures to reduce perturbations and to increase the system performance. The problem in such systems is undesirable vibrations due to some effects as shaking of the whole structure or the tracking process. This paper presents a frequency, amplitude and phase estimation method of a multifrequency signal that can be used to reject these vibrations in an adaptive method. The estimation method is based on using the FFT procedure. The undesirable signals are usually exponentially damped harmonic oscillations. The estimation error depends on several parameters and consists of a systematic component and a random component. The systematic error depends on the signal phase, the number of samples N in a measurement window, the value of CiR (number of signal periods in a measurement window), the THD value and the time window order H. The random error depends mainly on the variance of noise and the SNR value. This paper shows research on the sinusoidal signal phase and the estimation of exponentially damped sinusoids parameters. The shape of errors signals is periodical and it is associated with the signal period and with the sliding measurement window. For CiR=1.6 and the damping ratio 0.1% the error was in the order of 10-5 Hz/Hz, 10-4 V/V and 10-4 rad for the frequency, the amplitude and the phase estimation respectively. The information provided in this paper can be used to determine the approximate level of the efficiency of the vibrations elimination process before starting it.