An optimum design of linear phase FIR filters by the generalized Brain-State-in-a-Box neural network model

In this paper, we used a neural network model to find, an optimum design for a linear phase FIR digital filters coefficients. We used GBSB neural network model. The GBSB can guarantee convergence to an equilibrium point of the Lyapunov energy function as well as the fast computational speed. We utilized WLS error function to formulate an energy function of GBSB neural network. When the dynamic equation achieves its stable configuration, the output of the GBSB yields the optimal filter coefficients.

[1]  V. Algazi,et al.  Design of almost minimax FIR filters in one and two dimensions by WLS techniques , 1986 .

[2]  James A. Anderson,et al.  An Introduction To Neural Networks , 1998 .

[3]  Fa-Long Luo,et al.  Applied neural networks for signal processing , 1997 .

[4]  Stephen A. Dyer,et al.  Digital signal processing , 2018, 8th International Multitopic Conference, 2004. Proceedings of INMIC 2004..

[5]  L. Rabiner Linear program design of finite impulse response (FIR) digital filters , 1972 .

[6]  S. Sunder An efficient weighted least-squares design of linear-phase nonrecursive filters , 1995 .

[7]  Graham A. Jullien,et al.  A linear programming approach to recursive digital filter design with linear phase , 1982 .

[8]  Stefen Hui,et al.  Dynamical analysis of the brain-state-in-a-box (BSB) neural models , 1992, IEEE Trans. Neural Networks.

[9]  Juebang Yu,et al.  A novel neural network-based approach for designing 2-D FIR filters , 1997 .

[10]  Andreas Antoniou,et al.  Design of equiripple FIR filters using a feedback neural network , 1998 .

[11]  Harvey J. Greenberg Equilibria of the brain-state-in-a-box (BSB) neural model , 1988, Neural Networks.

[12]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[13]  L. Rabiner,et al.  FIR digital filter design techniques using weighted Chebyshev approximation , 1975, Proceedings of the IEEE.

[14]  Yong Ching Lim,et al.  A weighted least squares algorithm for quasi-equiripple FIR and IIR digital filter design , 1992, IEEE Trans. Signal Process..

[15]  R. Golden The :20Brain-state-in-a-box Neural model is a gradient descent algorithm , 1986 .

[16]  L. Rabiner The design of finite impulse response digital filters using linear programming techniques , 1972 .

[17]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[18]  R. Golden Stability and optimization analyses of the generalized brain-state-in-a-box neural network model , 1993 .

[19]  Alan V. Oppenheim,et al.  Discrete-time Signal Processing. Vol.2 , 2001 .

[20]  Renzo Perfetti,et al.  A synthesis procedure for brain-state-in-a-box neural networks , 1995, IEEE Trans. Neural Networks.

[21]  A. Antoniou,et al.  Real-time design of FIR filters by feedback neural networks , 1996, IEEE Signal Processing Letters.

[22]  Yue-Dar Jou,et al.  Design of FIR Digital Filters Using Hopfield Neural Network , 2007, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[23]  Thomas W. Parks,et al.  Optimal design of FIR filters with the complex Chebyshev error criteria , 1995, IEEE Trans. Signal Process..

[24]  Stephen A. Ritz,et al.  Distinctive features, categorical perception, and probability learning: some applications of a neural model , 1977 .