Abstract: The properties of some algorithms based on digital signal processing for the impedance components determination in circuits with sampling sensor have been analysed. It is supposed that the voltage and current are sampled in a synchronous way with a fundamental frequency of the generated sinusoidal signal. Two groups of fitting sine wave algorithms, which are based on the least mean square (LMS) technique, have been described. The first group of algorithms implements an indirect measurement method. The algorithms of the second group estimate the unknown impedance components using a direct measurement method. In order to simplify the calculations in all of these algorithms, different forms of input matrix have been used. The propagation of the uncertainty in the described algorithms can be analysed by means of a covariance matrix. In order to verify the performance of the considered algorithms (e.g., accuracy, estimator bias and convergence) the Monte Carlo simulations have been performed in MATLAB environment. It has been shown that these algorithms provide the minimisation of the uncertainty for selected numbers of samples and phase angles.
B I B L I O G R A F I A1. Angrasani, L.& Baccigalupi, A.& Pietrosanto, A., "A digital signal-processing instrument for impedance measurement", IEEE Trans. Instrum. Meas., vol. 45, 6, 1996, p.930-934
2. Ramos, P.M.& Fonseca da Silva, M.& Cruz Serra, A., "Low frequency impedance measurement using sine-fitting", Measurement, vol. 35, 2004, p.89-96
3. Soliman, S.A.& El-Hawary, M.E., "A digital estimation algorithm for impedance measurements", Elect. Mach. Power Syst., vol. 27, 12, 1999, p.1279-1288
4. Dutta, M.& Rakshit, A.& Bhattacharyya, S.N., "Development and study of an automatic AC bridge for impedance measurement", IEEE Trans. Instrum. Meas., vol. 50, 5, 2001, p.1048-1052
5. Angrasani, L.& Ferrigno, L., "Reducing the uncertainty in real-time impedance measurements", Measurement, vol. 30, 2001, p.307-315
6. J. Augustyn, Uncertainty analysis of impedance measurements in the sampling sensor instrument, in: Proceedings of the IMEKO-TC7 Symposium, Cracow, Poland, June 25-27, 2002, pp. 66-69.
7. Brandt, S., "Statistical and Computational Methods in Data Analysis", 1997, third ed.
8. Söderström, T.& Stoica, P., "System Identification", 1994
9. Hamilton, J.D., "Time Series Analysis", 1994
10. Handbook of Measurement Science, Theoretical Fundamentals. A Wiley-Interscience Publication, vol. I, 1982.
11. D'Antona, G., "Measurement data processing using random matrices: a generalized formula for the propagation of uncertainty", IEEE Trans. Instrum. Meas., vol. 53, 2, 2004, p.537-545
12. J. Augustyn, A comparative evaluation of some LMS-based algorithms for calculating of impedance components in the sampling sensor instrument, in: Proceedings of the XVIIth IMEKO World Congress, Dubrovnik, Croatia, vol. TC4, June 22-27, 2003, pp. 778-782. 
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