Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33093
Frequency-Domain Design of Fractional-Order FIR Differentiators
Authors: Wei-Der Chang, Dai-Ming Chang, Eri-Wei Chiang, Chia-Hung Lin, Jian-Liung Chen
Abstract:
In this paper, a fractional-order FIR differentiator design method using the differential evolution (DE) algorithm is presented. In the proposed method, the FIR digital filter is designed to meet the frequency response of a desired fractal-order differentiator, which is evaluated in the frequency domain. To verify the design performance, another design method considered in the time-domain is also provided. Simulation results reveal the efficiency of the proposed method.Keywords: Fractional-order differentiator, FIR digital filter, Differential evolution algorithm.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1072028
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2250References:
[1] K. B. Oldham and J. Spanier, The fractional Calculus. New York: Academic, 1974.
[2] C. Hwang, J. F. Leu, and S. Y. Tsay, "A note on time-domain simulation of feedback fractional-order systems," IEEE Trans. on Automatic Control, vol. 47, pp. 625-631, 2002.
[3] Z. M. Ge and M. Y. Hsu, "Chaos in a generalized van der Pol system and in its fractional order system," Chaos, Solitons and Fractals, vol. 33, pp. 1711-1745, 2007.
[4] M. Nakagava and K. Sorimachi, "Basic characteristics of a fractance device," IEICE Trans. Fundamentals, vol. E75-A, pp. 1814-1818, 1992.
[5] H. Samavati, A. Hajimiri, A. Shahani, G. Nasserbakht, and T. Lee, "Fractal capacitors," IEEE J Solid-State Circ., vol. 33, pp. 2035-2041, 1998.
[6] I. Podlubny, "Fractiona-order systems and PI λ D╬╝ -controllers," IEEE Trans. on Automatic Control, vol. 44, pp. 208-214, 1999.
[7] C. C. Tseng, "Design of fractional order digital FIR differentiators," IEEE Signal Processing Letters, vol. 8, pp. 77-79, 2001.
[8] S. Samadi, M. Omair Ahmad, and M. N. S. Swamy, "Exact fractional-order differentiators for polynomial signals," IEEE Signal Processing Letters, vol. 11, pp. 529-523, 2004.
[9] R. S. Barbosa, J. A. Tenreiro Machado, and M. F. Silva, "Time domain design of fractional differintegrators using least-squares," Signal Processing, vol. 86, pp. 2567-2581, 2006.
[10] R. Storn and K. Price, "Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces," Journal of Global Optimization, vol. 11, pp. 341-359, 1997.
[11] R. Storn, "System design by constraint adaptation and differential evolution," IEEE Transactions on Evolutionary Computation, vol. 3, pp. 95-99, 1999.
[12] S. L. Cheng and C. Hwang, "Optimal approximation of linear systems by a differential algorithm," IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, vol. 31, pp. 698-707, 2001.
[13] W. D. Chang, "Parameter identification of Chen and L├╝ systems: a differential evolution approach," Chaos, Solitons & Fractals, vol. 32, pp. 1464-1471, 2007.