Design of high order and wide coefficient wordlength multiplierless FIR filters with low hardware cost using genetic algorithm

In this work, a novel genetic algorithm (GA) is proposed for the design of multiplierless finite impulse response (FIR) filters with high filter order and wide coefficient wordlength. GA mimics the nature evolution to optimize complicated problems and in theory optimum solutions can be obtained with infinite computation time. However, in practical filter design problem, when the filter specification is stringent, requiring high filter order and wide coefficient wordlength, GA often fails to find feasible solutions, because the discrete search space thus constructed is huge and majority of the solution candidates therein can not meet the specification. In the proposed GA, the discrete search space is partitioned into smaller ones. Each of the small space is constructed surrounding an optimum continuous solution with a floating passband gain. This increases the chances for the GA to find feasible solutions, but not sacrificing the coverage of the search space. In addition, the search in the multiple spaces can run in parallel, and thus the computation time for the design of filters under consideration reduces significantly. Design examples show that the proposed GA outperforms existing algorithms dealing with the similar problems

Linear-Phase FIR Digital Filter Design with Reduced Hardware Complexity using Extremal Optimization

Extremal Optimization is a recent method for solving hard optimization problems. It has been successfully applied on many optimization problems. Extremal optimization does not share the disadvantage of most of the other evolutionary algorithms, which is the tendency to converge into local minima. Design of finite word length FIR filters using deterministic techniques can guarantee optimality at the expense of exponential increase in computational complexity. Alternatively, Evolutionary Algorithms are capable of converging very fast to a minimum, but have higher chances of failure if the ratio of feasible solutions is very less in the search space. In this thesis, a set of feasible solutions are determined by linear programming. In the second step, Extremal Optimization is used to further refine these results. This strategy helps by reducing the search space for the EO algorithm and is able to find good solutions in much shorter time than the existing methods