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Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 913147, 9 pages
http://dx.doi.org/10.1155/2010/913147
Research Article

Signal Processing and Sampling Method for Obtaining Time Series Corresponding to Higher Order Derivatives

1Department of Physics, Politehnica University, 313 Spl. Independentei, 060042 Bucharest, Romania
2Department of Informatics, Titu Maiorescu University, 187 Cl. Vacaresti, 040051 Bucharest, Romania

Received 27 January 2010; Accepted 19 February 2010

Academic Editor: Ming Li

Copyright © 2010 Andreea Sterian and Alexandru Toma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For modeling and controlling dynamic phenomena it is important to establish with higher accuracy some significant quantities corresponding to the dynamic system. For fast phenomena, such significant quantities are represented by the derivatives of the received signals. In case of advanced computer modeling, the received signal should be filtered and converted into a time series corresponding to the estimated values for the dynamic system through a sampling procedure. This paper will show that present-day methods for computing in a robust manner the first derivative of a received signal (using an oscillating system working on a limited time interval and a supplementary differentiation method) can be extended to the robust computation of higher order derivatives of the received signal by using a specific set of second-order oscillating systems (working also on limited time intervals) so as estimative values for higher-order derivatives are to be directly generated (avoiding the necessity of additional differentiation or amplifying procedures, which represent a source of supplementary errors in present-day methods).