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Lin, Z. Yanhong, T. Ran, and W. Yue, “Adaptive filtering in fractional Fourier domain,” IEEE Int. Symp. , 2005), 1033-1036. [31] B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal - Part II : Algorithms and applications,” Proc. IEEE, vol. 80, no. , 1992), 549-568. [32] H. K. C. Kwok and D. L. Jones, “Improved instantaneous frequency estimation using an adaptive short-time Fourier transform,” IEEE Trans. , vol. 10, no. , 2000) 2964-2972. [33] L. Durak and S. Aldırmaz, “Adaptive fractional Fourier domain filtering,” Signal Processing, vol.
2. 1 Fractional Fourier transform FrFT is a generalization of the ordinary Fourier transform with a fractional order parameter a, which corresponds to the ath fractional power of the Fourier transform operator, F. The ath -order FrFT of x (t) is defined as x a = F a { x (t)} = K a (t, t ) x (t )dt (2) 313 Adaptive Fractional Fourier Filtering in Active Noise Control Adaptive Fractional Fourier Domain Filtering in Domain Active Noise Control where 0 < | a| < 2, and the transformation kernel K a (t, t ) is K a (t, t ) = A ϕ e− jπ ( t2 cot( ϕ)−2tt Aϕ = e csc( ϕ )+ t 2 cot( ϕ ) − jπsgn(sin( ϕ)) /4+ j ( ϕ)/2 /| sin( ϕ)| (3) 1/2 with the transform angle ϕ = aπ/2 (25).
54, no. 3, (Sep. 2007), 1891-1899. [11] A. Goel, A. Vetteth, K. R. Rao, and V. Sridhar, “Active cancellation of acoustic noise using a self-tuned filter,” IEEE Trans. on Circuits and Systems I, vol. 51, no. , 2004),2148-2156. C. S. Peña, “ Active Noise Hybrid Time-Varying Control for Motorcycle Helmets,” IEEE Trans. on Control Systems Technology, vol. 18, no. 3, (May, 2010), 474-480. [13] Z. Yuexian, C. Shing-Chow, and N. Tung-Sang, “Least mean M-estimate algorithms for robust adaptive filtering in impulse noise,” IEEE Trans.