Abstract: The paper presents a methodology of regressive differentiating filters design. Elaborated differential filters ensure determining of appropriate derivatives of signal with errors far more less than simple differentiation methods, what plays particularly important role in the identification process. The advantage of the regressive differentiation filters if the possibility of obtaining the filtered signal of the same length as before the filtration. The designed algorithm enables to obtain a series of differential filters of orders up to n-th, where n is the order of the approximating polynomial.
B I B L I O G R A F I A[1] Zieliński T. P., Cyfrowe przetwarzanie sygnałów. Od teorii do zastosowań, W.K.Ł., ISBN: 83-206-1640-8, (2005)
[2] Rabiner L. R., Gold B., Theory and Application of Digital Signal Processing, Prentice-Hall, Inc.: Englewood Cliffs, NJ, (1975)
[3] Mocak J., Janiga I., Rievaj M., Bustin D., The Use of Fractional Differentiation or Integration for Signal Improvement, Measurement Science Review, Volume 7, (2007), Section 1, No. 5
[4] Söderström, T., Carlsson, B., & Bigi, S., Least squares parameter estimation of continuous-time ARX models from discrete-time data, IEEE Transactions on Automatic Control, 42(5), (1997), 659-672
[5] Jun-Sheng Y., Zu-Xun Z., Differentiation, semidifferentiation and semiintegration of a digital signals based on Fourier transformations, J. Electroanal. Chem., (1996), 403: 1-9
[6] Pintelon R., Schoukens J., Real-Time Integration and Differentiation of Analog Signals by Means of Digital Filtering, IEEE Transactions On Instrumentation And Measurement. VOL. 39, December (1990), NO. 6
[7] Cedro L., Janecki D., Filtry różniczkujące do identyfikacji układów mechanicznych za pomocą programu Mathematica, IV Sympozjum Modelowanie i Symulacja Komputerowa w Technice, Łódź (2005)
[8] Janecki D., Cedro L., Differential Filters With Application To System Identification, 7th European Conference of Young Research and Science Workers in Transport and Telecommunications TRANSCOM 2007, Żilina, Słowacja (2007), 115
[9] Janecki D., Rola sygnałów jednostajnie pobudzających w adaptacyjnych układach sterowania, IPPT PAN 27, (1995)
[10] Söderström T., Stoica P., System Identification, PHI (UK), (1994)
[11] Anderson T.W., The Statistical Analysis of Time Series, Wiley (1971)
[12] Cleveland W.S. and Loader C.L., Smoothing by Local Regression: Principles and Methods, In W. Hardle and M. G. Schimek, editors, Statistical Theory and Computational Aspects of Smoothing, 1049. Springer, New York (1996)
[13] Brinkmam S., Bodschwinna H., Lemke H.W., Accessing roughness in three-dimensions using Gaussian regression filtering, International Journal of Tools Manufacture, vol. 41, (2001), pp. 2153-2161
[14] Hoeks A.P.G, Van de Vorst J.J.W, Dabekaussen A., Brands P.J., Reneman R.S., An efficient algorithm to remove low frequency Doppler signals in digital Doppler systems, Ultrasonic Imaging, vol. 13, (1991), pp. 135-144
[15] Lyons R. G., An introduction to digital signal processing (in Polish), WKiŁ, Warsow (1999) 
Web of Science 
YADDA/CEON