Second order approximation of the fractional laplacian operator for equal-ripple response

作者: Todd J. Freeborn , Brent Maundy , Ahmed Elwakil

DOI: 10.1109/MWSCAS.2010.5548870

关键词:

摘要: In this paper we propose a modification to second order approximation of the fractional-order Laplacian operator, sα, where 0 < α 1. We show how proposed can be used change ripple error both magnitude and phase responses when compared ideal case. Equal-ripple that have less cumulative maximum deviation are presented using modification. A 1st lowpass filter with fractional step 0.8, is 1.8, implemented approximation. Experimental results verify operation in realization filter.

参考文章(10)
Igor Podlubny, I Petras, Blas M Vinagre, P O'Leary, L Dorcak, Analogue Realizations of Fractional-Order Controllers Nonlinear Dynamics. ,vol. 29, pp. 281- 296 ,(2002) , 10.1023/A:1016556604320
Ahmed G Radwan, Ahmed S Elwakil, Ahmed M Soliman, None, ON THE GENERALIZATION OF SECOND-ORDER FILTERS TO THE FRACTIONAL-ORDER DOMAIN Journal of Circuits, Systems, and Computers. ,vol. 18, pp. 361- 386 ,(2009) , 10.1142/S0218126609005125
José V. Valverde, Raquel Pérez-Aloe, Blas M. Vinagre, Guillermo E. Santamaría, Microelectronic Implementations of Fractional-Order Integrodifferential Operators Journal of Computational and Nonlinear Dynamics. ,vol. 3, pp. 1267- 1274 ,(2007) , 10.1115/1.2833907
Concepción A Monje, YangQuan Chen, Blas M Vinagre, Dingyü Xue, Vicente Feliu, None, Fractional order control strategies for power electronic buck converters Signal Processing. ,vol. 86, pp. 2803- 2819 ,(2006) , 10.1016/J.SIGPRO.2006.02.022
Todd J. Freeborn, Brent Maundy, Ahmed Elwakil, Towards the realization of fractional step filters international symposium on circuits and systems. pp. 1037- 1040 ,(2010) , 10.1109/ISCAS.2010.5537360
B. T. Krishna, K. V. V. S. Reddy, Active and Passive Realization of Fractance Device of Order 1/2 Active and Passive Electronic Components. ,vol. 2008, pp. 1- 5 ,(2008) , 10.1155/2008/369421
Brent Maundy, Ahmed Elwakil, Stephan Gift, On a multivibrator that employs a fractional capacitor Analog Integrated Circuits and Signal Processing. ,vol. 62, pp. 99- 103 ,(2010) , 10.1007/S10470-009-9329-3
Manuel Ortigueira, An introduction to the fractional continuous-time linear systems: the 21st century systems IEEE Circuits and Systems Magazine. ,vol. 8, pp. 19- 26 ,(2008) , 10.1109/MCAS.2008.928419
Ahmed G Radwan, Ahmed M Soliman, Ahmed S Elwakil, None, FIRST-ORDER FILTERS GENERALIZED TO THE FRACTIONAL DOMAIN Journal of Circuits, Systems, and Computers. ,vol. 17, pp. 55- 66 ,(2008) , 10.1142/S0218126608004162
K. Biswas, S. Sen, P.K. Dutta, Realization of a Constant Phase Element and Its Performance Study in a Differentiator Circuit IEEE Transactions on Circuits and Systems Ii-express Briefs. ,vol. 53, pp. 802- 806 ,(2006) , 10.1109/TCSII.2006.879102