A new hybrid descent method with application to the optimal design of finite precision FIR filters

In this paper, the problem of the optimal design of discrete coefficient FIR filters is considered. A novel hybrid descent method, consisting of a simulated annealing algorithm and a gradient-based method, is proposed. The simulated annealing algorithm operates on the space of orthogonal matrices and is used to locate descent points for previously converged local minima. The gradient-based method is derived from converting the discrete problem to a continuous problem via the Stiefel manifold, where convergence can be guaranteed. To demonstrate the effectiveness of the proposed hybrid descent method, several numerical examples show that better discrete filter designs can be sought via this hybrid descent method.

[1]  Sathyanarayan S. Rao,et al.  Design of discrete coefficient FIR filters by simulated evolution , 1996, IEEE Signal Processing Letters.

[2]  Kok Lay Teo,et al.  A new design method for broadband microphone arrays for speech input in automobiles , 2002, IEEE Signal Processing Letters.

[3]  Kok Lay Teo,et al.  Multicriteria design of oversampled uniform DFT filter banks , 2004, IEEE Signal Processing Letters.

[4]  Kok Lay Teo,et al.  A robust transform domain echo canceller employing a parallel filter structure , 2006, Signal Process..

[5]  Y. Lim,et al.  FIR filter design over a discrete powers-of-two coefficient space , 1983 .

[6]  Yong Hoon Lee,et al.  Design of nonuniformly spaced linear-phase FIR filters using mixed integer linear programming , 1996, IEEE Trans. Signal Process..

[7]  D. Kodek.  Design of optimal finite wordlength FIR digital filters using integer programming techniques , 1980 .

[8]  Sven Nordholm,et al.  Adaptive microphone array employing calibration signals: an analytical evaluation , 1999, IEEE Trans. Speech Audio Process..

[9]  A. Cantoni,et al.  FIR filter design over discrete coefficients and least square error , 2000 .

[10]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[11]  Kok Lay Teo,et al.  A hybrid method for the design of oversampled uniform DFT filter banks , 2006, Signal Process..

[12]  U. Helmke,et al.  Optimization and Dynamical Systems , 1994, Proceedings of the IEEE.

[13]  Nam Ik Cho,et al.  Optimal design of finite precision FIR filters using linear programming with reduced constraints , 1998, IEEE Trans. Signal Process..

[14]  A. Uncini,et al.  Power-of-two adaptive filters using tabu search , 2000 .

[15]  Wei-Yong Yan,et al.  Optimal finite-precision approximation of FIR filters , 2002, Signal Process..

[16]  Kok Lay Teo,et al.  Near-field broadband beamformer design via multidimensional semi-infinite-linear programming techniques , 2003, IEEE Trans. Speech Audio Process..

[17]  S. Dreyfus,et al.  Thermodynamical Approach to the Traveling Salesman Problem : An Efficient Simulation Algorithm , 2004 .

[18]  Michele Marchesi,et al.  Digital filters design by simulated annealing , 1989 .

[19]  Nevio Benvenuto,et al.  On the Design of FIR Filters with Powers-of-Two Coefficients , 1984, IEEE Trans. Commun..

[20]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[21]  Yoshiaki Tadokoro,et al.  A simple design of FIR filters with powers-of-two coefficients , 1988 .