Five numerical algorithms of fractional calculus applied in modern signal analyzing and processing

Sichuan Daxue Xuebao (Gongcheng Kexue Ban)/Journal of Sichuan University (Engineering Science Edition)

Volumn 37, Issue 5, 2005, Pages 118-124

  Pu, Yi Fei ^a   Yuan, Xiao ^a   Liao, Ke ^a   Chen, Zhong Lin ^a   Zhou, Ji Liu ^a  

^a SICHUAN UNIVERSITY   (China)

Author keywords

Analog fractance circuit; Best initialization sampling scale; Best wavelet scanning time; Fractional order neural network; Fractional wavelet transforms; Generalized Hilbert transforms

Indexed keywords

ALGORITHMS; CALCULATIONS; DIFFERENTIATION (CALCULUS); FOURIER TRANSFORMS; MATHEMATICAL TRANSFORMATIONS; NEURAL NETWORKS;

ANALOG FRACTANCE CIRCUIT; BEST INITIALIZATION SAMPLING-SCALE; BEST WAVELET SCANNING TIME; FRACTIONAL CALCULUS; FRACTIONAL ORDER NEURAL NETWORK; FRACTIONAL WAVELET TRANSFORMS; GENERALIZED HILBERT TRANSFORMS; NUMERICAL ALGORITHMS; SIGNAL ANALYZING;

SIGNAL PROCESSING;

EID: 27744438008     PISSN: 10093087     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. Lamber-Torres G. Application of rough sets in power system control center data mining[A]. Power Engineering Society Winter Meeting[C]. IEEE Press, 2002, 1: 627-631.
2. Chen Zunde, Chen Fugui, Filtering characteristic of non-integral-order calculus and its numerical algorithm[J]. Journal of Numerical Calculus and Computer Application, 1999, 3,(1): 62-69.
3. Planka L, Mrozek A. Rule-based stabilization of the inverted pendulum[J]. Computational Intelligence, 1995, 11(2): 348-356.
4. Czogala E. Idea of a rough fuzzy controller and its application to the stabilization of a pendulum-car system[J]. Fuzzy Sets and Systems, 1995, 72(1): 61-73.
5. Takagi T, Sugeno M. Fuzzy identification of systems and its applications to modeling and control[J]. IEEE trans Syst, Man, Cybern, 1985, 15: 116-132.
6. Yuan Xiao, Chen Xiangdong, Li Qiliang, et al. Differential operator and the construction of wavelet[J]. Acta Electronica Sinica, 2002, 5(5): 769-773.
7. Pu Yifei, Yuan Xiao, Liao Ke, et al. A recursive two-circuits series analog fractance circuit for any order fractional calculus[A]. Proceedings of ICO20[C]. SPIE, 2005. 818-828.
8. Oldham K B, Spanier J. The fractional calculus[M]. New York: Academic Press, 1974.
9. Podlubny I. Fractional differential equations[M]. New York: Academic Press, 1999.
10. Bai Yitong, Luo Yufang, Hu Yongxu. Fractional calculus and its order-expanding formula[J]. Journal of Wuhan Mapping Science University, 1993, (1): 66-75.
11. Zhao Yuanying, Yuan Xiao, Teng Xudong, et al. Fractional order differentiation of periodical signals[J]. Journal of Sichuan University (Engineering Science Edition), 2004, 36(2): 94-97.
12. Pu Yifei, Yuan Xiao, Liao Ke, et al. Determination of scale sample step for getting numerical result of the continuous wavelet transform[J]. Journal of Sichuan University (Engineering Science Edition), 2004, 36(6): 111-116.