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1

On the statistical analysis of the harmonic signal autocorrelation function

Sienkowski Sergiusz, Krajewski Mariusz

International Journal of Applied Mathematics and Computer Science

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2021

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Vol. 31, no. 4

729--744

EN

The article presents new tools for investigating the statistical properties of the harmonic signal autocorrelation function (ACF). These tools enable identification of the ACF estimator errors in measurements in which the triggering of the measurements is non-synchronized. This is important because in many measurement situations the initial phase of the measured signal is random. The developed tools enable testing the ACF estimator of a harmonic signal in the presence of Gaussian noise. These are the formulas on the basis of which the statistical properties of the estimator can be determined, including the bias, the variance and the mean squared error (MSE). For comparison, the article also presents the ACF statistical analysis tools used in the conditions of synchronized measurement triggering, known from the literature. Operation of the new tools is verified by simulation and experimental studies. The conducted research shows that differences between the MSE results obtained with the use of the developed formulas and those attained from simulations and experimental tests are not greater than 1 dB.

2

Ortogonalne i nieortogonalne-zaburzone próbkowanie sygnałów harmonicznych

Siwczyński Maciej, Jaraczewski Marcin

Przegląd Elektrotechniczny

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2019

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R. 95, nr 1

219--222

PL

Praca dotyczy próbkowania sygnałów harmonicznych za pomocą dwóch próbek, które wystarczają do pełnego zidentyfikowania sygnału. Rozpatruje się dwa rodzaje próbkowania. Próbkowanie ortogonalne, które nie zniekształca operatorów przejścia przetworników liniowych czasowo-niezmienniczych i tzw. próbkowanie nieortogonalne, zniekształcające operatory przejścia i relacje mocowe.

EN

The work is on sampling a harmonic signals using two samples that is sufficient to fully identify the signal. Two types of sampling are considered. Orthogonal sampling, which does not distort the transient time-invariant linear transducer operators and so called non-orthogonal sampling that distorts these operators, and power relations.

3

Fast estimation of the non-stationary amplitude of a harmonically distorted signal using a Kalman filter

Kovač U., Košir A.

Metrology and Measurement Systems

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2013

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Vol. 20, nr 1

27-42

EN

In this paper we introduce a self-tuning Kalman filter for fast time-domain amplitude estimation of noisy harmonic signals with non-stationary amplitude and harmonic distortion, which is the problem of a contactvoltage measurement to which we apply the proposed method. The research method is based on the self-tuning of the Kalman filter's dropping-off behavior. The optimal performance (in terms of accuracy and fast response) is achieved by detecting the jump of the amplitude based on statistical tests of the innovation vector of the Kalman filter and reacting to this jump by adjusting the values of the covariance matrix of the state vector. The method's optimal configuration of the parameters was chosen using a statistical power analysis. Experimental results show that the proposed method outperforms competing methods in terms of speed and accuracy of the jump detection and amplitude estimation.