Design of optimal digital lattice filter structures based on genetic algorithm

In this paper, a new class of lattice-based digital filter structures is derived. The optimum structure problem is formulated in terms of minimizing the signal power ratio with respect to the two sets of free parameters in the proposed structures. An efficient genetic algorithm is proposed to solve the optimum structure problem with the constraint on the structure parameters to be represented in signed power-of-two format. Two design examples are given, in which the optimized structures show excellent finite wordlength properties such as very low parameter sensitivity and very uniform signal powers across signal nodes and outperform the classical lattice structures.

[1]  M. Gevers,et al.  Parametrizations in Control, Estimation and Filtering Problems: Accuracy Aspects , 1993 .

[2]  Tao Wu,et al.  On normal realizations of digital filters with minimum roundoff noise gain , 2009, Signal Process..

[3]  Robert T. Wirski.  On the realization of 2-D orthogonal state-space systems , 2008, Signal Process..

[4]  Hung-Ching Lu,et al.  Genetic algorithm approach for designing higher-order digital differentiators , 1999, Signal Process..

[5]  Y. Lim.  Design of discrete-coefficient-value linear phase FIR filters with optimum normalized peak ripple magnitude , 1990 .

[6]  Jingyu Hua,et al.  An improved orthogonal digital filter structure , 2010, Signal Process..

[7]  P. P. Vaidyanathan,et al.  An improved sufficient condition for absence of limit cycles in digital filters , 1987 .

[8]  Colin R. Reeves,et al.  Genetic Algorithms: Principles and Perspectives: A Guide to Ga Theory , 2002 .

[9]  Ying-Yi Hong,et al.  Optimal VAR Control Considering Wind Farms Using Probabilistic Load-Flow and Gray-Based Genetic Algorithms , 2009, IEEE Transactions on Power Delivery.

[10]  Yong Ching Lim,et al.  Design of Linear Phase FIR Filters in Subexpression Space Using Mixed Integer Linear Programming , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  Truong Q. Nguyen,et al.  A Lattice Structure of Biorthogonal Linear-Phase Filter Banks With Higher Order Feasible Building Blocks , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[12]  S. Hwang.  Minimum uncorrelated unit noise in state-space digital filtering , 1977 .

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

[14]  A. Gray,et al.  Fixed-point implementation algorithms for a class of orthogonal polynominal filter structures , 1975 .

[15]  Gang Li,et al.  Very Robust Low Complexity Lattice Filters , 2010, IEEE Transactions on Signal Processing.

[16]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[17]  Yong Lim.  On the synthesis of IIR digital filters derived from single channel AR lattice network , 1984 .

[18]  Thibault Hilaire.  Low-Parametric-Sensitivity Realizations With Relaxed $L_{2}$-Dynamic-Range-Scaling Constraints , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[19]  Elizabeth Elias,et al.  Design of multiplier-less nonuniform filter bank transmultiplexer using genetic algorithm , 2009, Signal Process..

[20]  Yong Ching Lim,et al.  Signed power-of-two term allocation scheme for the design of digital filters , 1999 .

[21]  A. Gray,et al.  Digital lattice and ladder filter synthesis , 1973 .

[22]  Clifford T. Mullis,et al.  Synthesis of minimum roundoff noise fixed point digital filters , 1976 .

[23]  Ling Cen,et al.  A hybrid genetic algorithm for the design of FIR filters with SPoT coefficients , 2007, Signal Process..