Computation of fractional derivatives using Fourier transform and digital FIR differentiator

Signal Processing

Volumn 80, Issue 1, 2000, Pages 151-159

  Tseng, Chien Cheng ^a   Pei, Soo Chang ^b   Hsia, Shih Chang ^a  

^a NATIONAL KAOHSIUNG UNIVERSITY OF APPLIED SCIENCES   (Taiwan)

^b NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIATING CIRCUITS; FIR FILTERS; FOURIER TRANSFORMS;

FRACTIONAL DERIVATIVES;

DIGITAL SIGNAL PROCESSING;

EID: 0033881047     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-1684(99)00118-8     Document Type: Article

References (24)

1. L.B. Almeida, The fractional Fourier transform and time frequency representation, IEEE Trans. Signal Process. 42 (November 1994) 3084-3091.
2. M.F. Barnsley, Fractal Everywhere, Academic, Boston, 1988.
3. M. Deriche, A.H. Tewfik, Signal modeling with filtered fractional noise processes, IEEE Trans. Signal Process. 41 (9) (September 1993) 2839-2849.
4. S.C. Dutta Roy, B. Kumar, Digital differentiators, in: N.K. Bose, C.R. Rao (Eds.), Handbook of Statistics, Vol. 10, Elsevier Science Publishers, Amsterdam, 1993, pp. 159-205.
5. N. Engheta, On the role of fractional calculus in electro-magnetic theory, IEEE Antennas Propagation Mag. 39 (4) (August 1997) 35-46.
6. A. Fenander, A fractional derivative railpad model included in a railway track model, J. Sound Vib. 212 (5) (1998) pp. 889-903.
7. J. Lancis, T. Saoplik, E. Tajahuerce, V. Climent, M. Fernandez-Alonso, Fractional derivative Fourier plane filter for phase-change visualization, Appl. Opt. 36 (29) (October 1997) 7461-7464.
8. B. Mbodje, G. Montseny, Boundary fractional derivative control of the wave equation, IEEE Trans. Automat. Control 40 (2) (February 1995) 378-382.
9. K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
10. V. Namias, The fractional order Fourier transform and its application to quantum mechanics, J. Inst. Maths Appl. 25 (1980) 241-265.
11. K. Nishimoto, Nishimoto's fractional calculus of elementary functions, Proceedings of the International Conference of Fractonal Calculus and its Applications, College of Engineering, Nihon University, Tokyo, May-June, 1989, pp. 112-122.
12. K.B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.
13. A.V. Oppenheim, R.W. Schafer, Discrete-Time Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1989.
14. T.W. Parks, J.H. McClellan, Chebyshev approximation for non recursive digital filters with linear phase, IEEE Trans. Circuit Theory 19 (March 1972) 189-194.
15. S.C. Pei, J.J. Shyu, Design of FIR Hubert transformers and differentiators by eigenfilters, IEEE Trans. Circuits Systems 35 (November 1988) 1457-1461.
16. S.C. Pei, J.J. Shyu, Eigenfilter design of higher-order digital differentiators, IEEE Trans. Acoust. Speech Signal Process. 37(1989) 505-511.
17. S.C. Pei, M.H. Yeh, C.C. Tseng, Discrete fractional Fourier transform based on othogonal projections, IEEE Trans. Signal Process. 47 (May 1999) 1335-1348.
18. L.A. Rubenfeld, A First Course in Applied Complex Variables, Wiley, New York, 1985.
19. M. Shao, C.L. Nikias, Signal processing with fractional lower order moment: stable processes and their applications, Proc. IEEE 81 (July 1993) 986-1010.
20. H. Shekarforous, J. Zerubia, M. Berthod, Denoising by extracting fractional order singularities, ICASSP 98, pp. 2889-2892.
21. M.I. Skolnik, Introduction to Radar Systems, McGraw-Hill, New York, 1980.
22. S. Sunder, W.S. Lu, A. Antoniou, Y. Su, Design of digital differentiators satisfying prescribed specifications using optimization techniques, Proc. Inst. Elect. Eng. Pt. G 138 (June 1991) 315-320.
23. S. Sunder, V. Ramachandra, Design of equiripple non-recursive digital differentiators and Hubert transformers using a weighted least-squares technique, IEEE Trans. Signal Processing 42 (9) (September 1994) 2504-2509.
24. S. Usui, I. Amidror, Digital lowpass differentiation for biological signal processing, IEEE Trans. Biomedical Eng. 29 (1982) 686-693.