Estimation of $n$ Frequencies Using Adaptive Notch Filter

This paper introduces an adaptive structure composed of n coupled paralleled subfilters that directly estimates frequencies of multiple sinusoids. The order of differential equations governing this algorithm is 3n, where n is the number of sinusoids. Stability analysis of this algorithm is carried out based on the application of the averaging theory under the assumption of the slow adaptation. Simulation results verify the validity of the analytical issues

[1]  Romeo Ortega,et al.  A globally convergent frequency estimator , 1999, IEEE Trans. Autom. Control..

[2]  Thomas Kailath,et al.  Linear Systems , 1980 .

[3]  Gang Li,et al.  A stable and efficient adaptive notch filter for direct frequency estimation , 1997, IEEE Trans. Signal Process..

[4]  Y. Tadokoro,et al.  A new memoryless nonlinear gradient algorithm for a second-order adaptive IIR notch filter and its performance analysis , 1998 .

[5]  Alireza R. Bakhshai,et al.  An adaptive notch filter for frequency estimation of a periodic signal , 2004, IEEE Transactions on Automatic Control.

[6]  Miklós Farkas,et al.  Periodic Motions , 1994 .

[7]  François G. Meyer Decomposition of fMRI into Multiple Components , 2005 .

[8]  Scott C. Douglas,et al.  Adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequency , 1996, Autom..

[9]  Y. Xiao,et al.  Steady-state analysis of a plain gradient algorithm for a second-order adaptive IIR notch filter with constrained poles and zeros , 2001 .

[10]  Phillip A. Regalia,et al.  An improved lattice-based adaptive IIR notch filter , 1991, IEEE Trans. Signal Process..

[11]  Katsuhiko Ogata,et al.  Modern Control Engineering , 1970 .

[12]  Akira Ikuta,et al.  Statistical performance of the memoryless nonlinear gradient algorithm for the constrained adaptive IIR notch filter , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[14]  B. Farhang-Boroujeny,et al.  Adaptive Filters: Theory and Applications , 1999 .

[15]  Shuyuan Yang,et al.  Robust adaptive infinite impulse response notch filters: a novel state-space approach , 2006, 2006 IEEE International Symposium on Circuits and Systems.

[16]  Anssi Klapuri,et al.  Multiple fundamental frequency estimation based on harmonicity and spectral smoothness , 2003, IEEE Trans. Speech Audio Process..

[17]  K. Nonami,et al.  Adaptive unbalance vibration control of magnetic bearing system using frequency estimation for multiple periodic disturbances with noise , 1999, Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328).

[18]  Bor-Sen Chen,et al.  Adaptive notch filter by direct frequency estimation , 1992, Signal Process..

[19]  P. Kokotovic,et al.  Integral manifolds of slow adaptation , 1986 .

[20]  Chia-Hsiang Menq,et al.  Robust disturbance rejection for improved dynamic stiffness of a magnetic suspension stage , 2002 .