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).
Highlights
For modeling and controlling dynamic phenomena it is important to establish with higher accuracy some physical quantities corresponding to the dynamic system
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 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
This paper has presented a possibility of obtaining the derivatives of the received electrical signal using a filtering device consisting of a sequence of certain oscillating second-order systems and an integrator
Summary
For modeling and controlling dynamic phenomena it is important to establish with higher accuracy some physical quantities corresponding to the dynamic system This procedure is based on signal processing method applied upon the signal received from the dynamic system, implying some filtering methods for noise rejection. For avoiding significant errors the difference z tk −z tk−1 should be estimated with higher accuracy This implies that the filtered values u tk should be close to the values of the useful part of the received signal z tk. The filtering device should reject the noise supposed to present fast variation as compared to the variations of the useful part z t in a significant manner For this purpose, the filtering and sampling devices based on asymptotically stable systems can be improved.
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