Frequency-Domain Design of Fractional-Order FIR Differentiators
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.
[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.
[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.
@article{"International Journal of Information, Control and Computer Sciences:58117", author = "Wei-Der Chang and Dai-Ming Chang and Eri-Wei Chiang and Chia-Hung Lin and Jian-Liung Chen", title = "Frequency-Domain Design of Fractional-Order FIR Differentiators", 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.", volume = "4", number = "5", pages = "963-4", }
