Signal processing and sampling method for obtaining time series corresponding to higher order derivatives. (English) Zbl 1191.94076

Summary: 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).


94A20 Sampling theory in information and communication theory
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Full Text: DOI EuDML


[1] G. Toma, “Practical test-functions generated by computer algorithms,” in Proceedings of International Conference on Computational Science and Its Applications (ICCSA /05), vol. 3482 of Lecture Notes in Computer Science, pp. 576-584, 2005.
[2] A. Sterian and G. Toma, “Possibilities for obtaining the derivative of a received signal using computer-driven second order oscillators,” in Proceedings of the International Conference on Computational Science and Its Applications (ICCSA /05), vol. 3482 of Lecture Notes in Computer Science, pp. 585-591, May 2005.
[3] W. R. Cawthorne and F. S. Jy-Jen, “Method of determining the derivative of an input signal,” US patent no. 7587442, Publication number: US 2005/0256919 A1, September 2009.
[4] M. Petrou and F. Faille, “An imaging architecture based on derivative estimation sensors,” in Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications, vol. 5856 of Lecture Notes in Computer Science, pp. 3-18, Springer, Berlin, Germany, 2009. · Zbl 05633962
[5] G. Toma, “Specific differential equations for generating pulse sequences,” Mathematical Problems in Engineering, vol. 2010, Article ID 324818, 11 pages, 2010. · Zbl 1191.37052
[6] J. J. Rushchitsky, C. Cattani, and E. V. Terletskaya, “Wavelet analysis of the evolution of a solitary wave in a composite material,” International Applied Mechanics, vol. 40, no. 3, pp. 311-318, 2004. · Zbl 1075.74048
[7] C. Cattani, “Harmonic wavelets towards the solution of nonlinear PDE,” Computers & Mathematics with Applications, vol. 50, no. 8-9, pp. 1191-1210, 2005. · Zbl 1118.65133
[8] E. G. Bakhoum and C. Toma, “Relativistic short range phenomena and space-time aspects of pulse measurements,” Mathematical Problems in Engineering, vol. 2008, Article ID 410156, 20 pages, 2008. · Zbl 1163.83319
[9] E. G. Bakhoum and C. Toma, “Mathematical transform of traveling-wave equations and phase aspects of quantum interaction,” Mathematical Problems in Engineering, vol. 2010, Article ID 695208, 15 pages, 2010. · Zbl 1191.35220
[10] M. Li, “Fractal time series-a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010. · Zbl 1191.37002
[11] M. Li and W. Zhao, “Representation of a stochastic traffic bound,” to appear in IEEE Transactions on Parallel and Distributed Systems.
[12] M. Li and S. C. Lim, “Modeling network traffic using generalized Cauchy process,” Physica A, vol. 387, no. 11, pp. 2584-2594, 2008.
[13] F. Leon, S. Curteanu, C. Lisa, and N. Hurduc, “Machine learning methods used to predict the liquid-crystalline behavior of some copolyethers,” Molecular Crystals and Liquid Crystals, vol. 469, no. 1, pp. 1-22, 2007.
[14] F. Leon, M. H. Zaharia, and D. Galea, “Emergent dynamic routing using intelligent agents in mobile computing,” Studies in Informatics and Control, vol. 17, no. 2, 2008.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.