Design of variable and adaptive fractional order FIR differentiators

Signal Processing

Volumn 86, Issue 10, 2006, Pages 2554-2566

  Tseng, Chien Cheng ^a  

^a NATIONAL KAOHSIUNG UNIVERSITY OF APPLIED SCIENCES   (Taiwan)

Author keywords

1 f noise; Adaptive filter; Farrow structure; Fractional calculus; Fractional derivative; Fractional order differentiator; Signature verification; Variable filter

Indexed keywords

ALGORITHMS; DATA ACQUISITION; ERRORS; PARAMETER ESTIMATION; PROBLEM SOLVING; SIGNAL PROCESSING;

1/F NOISE; ADAPTIVE FILTER; FARROW STRUCTURE; FRACTIONAL CALCULUS; FRACTIONAL DERIVATIVE; FRACTIONAL ORDER DIFFERENTIATOR; SIGNATURE VERIFICATION; VARIABLE FILTER;

FIR FILTERS;

EID: 33745698055     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2006.02.004     Document Type: Article

References (31)

1. Oldham K.B., and Spanier J. Ther Fractional Calculus (1974), Academic Press, New York
2. Miller K.S., and Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), Wiley, New York
3. Podlubny I. Fractional Differential Equations (1999), Academic Press, San Diego
4. Machado J.A.T. Discrete-time fractional-order controllers. Fractional Calculus Appl. Anal. 4 (2001) 47-66
5. Engheta N. On the role of fractional calculus in electromagnetic theory. IEEE Antennas Propagation Mag. 39 8 (August 1997) 35-46
6. Mathieu B., Melchior P., Oustaloup A., and Ceyral C. Fractional differentiation for edge detection. Signal Process. 83 (2003) 2421-2432
7. Vinagre B.M., Podlubny I., Hernandez A., and Feliu V. Some approximations of fractional order operators used in control theory and applications. Fractional Calculus Appl. Anal. 4 (2001) 47-66
8. 1/n by a regular Newton process. IRE Trans. Circuit Theory 11 (1964) 210-213
9. Roy S.C.D. On the realization of a constant-argument immitance of fractional operator. IRE Trans. Circuit Theory 14 (1967) 264-274
10. Chareff A., Sun H.H., Tsao Y.Y., and Onaral B. Fractal system as represented by singularity function. IEEE Trans. Automat Control 37 (1992) 1465-1470
11. Oustaloup A., Levron F., Mathieu B., and Nanot F.M. Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Trans. Circuits Systems-I 47 (2000) 25-39
12. Hosking J.R.M. Fractional differencing. Biometrika 68 (1981) 165-176
13. Chen Y.Q., and Moore K.L. Discrete schemes for fractional-order differentiators and integrators. IEEE Trans. Circuits Systems-I 49 (2002) 363-367
14. Chen Y.Q., and Vinagre B.M. A new IIR-type digital fractional order differentiator. Signal Process. 83 (2003) 2359-2365
15. Tseng C.C., Pei S.C., and Hsia S.C. Computation of fractional derivatives using Fourier transform and digital FIR differentiator. Signal Process. 80 (2000) 151-159
16. Tseng C.C. Design of fractional order digital FIR differentiators. IEEE Signal Process. Lett. 8 3 (March 2001) 77-79
17. Y. Ferdi, B. Boucheham, Recursive filter approximation of digital fractional differentiator and integrator based on Prony's method, In: First IFAC Workshop on Fractional Differentiation and its Applications, July 2004, pp. 428-433.
18. Deng T.B. Design of recursive 1-D variable filters with guaranteed stability. IEEE Trans. Circuits Systems-II 44 9 (September 1997) 689-695
19. D.B.H. Tay, S.S. Abesekera, A.P. Balasuriya, Audio signal processing via harmonic separation using variable Laguerre filters, in Proceedings of the International Symposium on Circuits and Systems, vol. 3, May 2003, pp. 558-561.
20. T. Shinbo, Y. Sugita, N. Aikawa, T. Kimura, T. Moriti, Y. Wakasa, A design of the stopband variable FIR digital filters using spectral parameter, in: Proceedings IEEE PacRim, vol. 1, August 2003, pp. 90-93.
21. Laakso T.I., Valimaki V., Karjalainen M., and Laine U.K. Splitting the unit delay: tool for fractional delay filter design. IEEE Signal Process. Mag. 1 (1996) 30-60
22. C.W. Farrow, A continuously variable digital delay element, in: Proceedings of the International Symposium on Circuits and Systems, May 1988, pp. 2641-2645.
23. Lu W.S., and Deng T.B. An improved weighted least-squares design for variable fractional delay FIR filters. IEEE Trans. Circuits Systems-II 46 8 (August 1999) 1035-1040
24. Deng T.B., and Lu W.S. Weighted least-squares method for designing variable fractional delay 2-D FIR filters. IEEE Trans. Circuits Systems-II 47 2 (February 2000) 114-124
25. Tseng C.C. Design of 1-D and 2-D variable fractional delay allpass filters using weighted least-squares method. IEEE Trans. Circuits Systems-I 49 10 (October 2002) 1413-1422
26. C.C. Tseng, Design of variable fractional delay FIR filter using differentiator bank, in: Proceedings of the International Symposium on Circuits and Systems, vol. 4, May 2002, pp. 421-424.
27. Deng T.B. Closed-form design and efficient implementation of variable digital filters with simultaneously tunable magnitude and fractional delay. IEEE Trans. Signal Process. 52 6 (June 2004) 1668-1681
28. Lorenzo C.F., and Hartley T.T. Variable order and distributed order fractional operators. J. Nonlinear Dyn. 29 (July 2002) 57-98
29. Haykin S. Adaptive Filter Theory. fourth ed. (2002), Prentice-Hall, New Jersey
30. Jain A., Bolle R., and Pankanti S. Biometrics: Personal Identification in Network Society (1999), Kluwer Academic Publishers, Dordrecht
31. N.J. Cheng, K. Liu, K.C. Cheng, C.C. Tseng, B.S. Jeng, Online Chinese signature verification using voting scheme, in: Proceedings of the IEEE International Carnahan Conference on Security Technology, October 1997, pp. 123-126.