An efficient local search method guided by gradient information for discrete coefficient FIR filter design

A new local search method for the design of linear phase FIR filters with discrete valued coefficients is introduced in this paper. Conventional minimax criterion and normalized peak ripple magnitude (NPRM) are taken as objective functions. The principle is to search along low gradient routes with priority and to direct the search toward steeper sides as improved solutions cease to appear. The characteristics of the objective functions have been explained and used to devise the method. The method is novel in the way it generates the gradient information and makes use of it. At each step, a number of filter coefficients are picked according to the gradient information and perturbed to look for improved solutions. A specific neighborhood definition is proposed and used in perturbing the coefficients. The method has very low computational demand and is suitable for the design of long filters. The results of design examples demonstrate that the performance of the method can compete with those of optimal methods. Along the way, a closed form expression for the "filter gain" that minimizes NPRM is also given. Furthermore, it is shown that a previously proposed local search method unintentionally implements the ideas of this paper in an opposite order

Efficient and Accurate Optimal Linear Phase FIR Filter Design Using Opposition-Based Harmony Search Algorithm

In this paper, opposition-based harmony search has been applied for the optimal design of linear phase FIR filters. RGA, PSO, and DE have also been adopted for the sake of comparison. The original harmony search algorithm is chosen as the parent one, and opposition-based approach is applied. During the initialization, randomly generated population of solutions is chosen, opposite solutions are also considered, and the fitter one is selected as a priori guess. In harmony memory, each such solution passes through memory consideration rule, pitch adjustment rule, and then opposition-based reinitialization generation jumping, which gives the optimum result corresponding to the least error fitness in multidimensional search space of FIR filter design. Incorporation of different control parameters in the basic HS algorithm results in the balancing of exploration and exploitation of search space. Low pass, high pass, band pass, and band stop FIR filters are designed with the proposed OHS and other aforementioned algorithms individually for comparative optimization performance. A comparison of simulation results reveals the optimization efficacy of the OHS over the other optimization techniques for the solution of the multimodal, nondifferentiable, nonlinear, and constrained FIR filter design 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

Using Bayesian Inference in Design Applications

This dissertation presents a new approach for solving engineering design problems such as the design of antenna arrays and finite impulse response (FIR) filters. In this approach, a design problem is cast as an inverse problem. The tools and methods previously developed for Bayesian inference are adapted and utilized to solve design problems. Given a desired design output, Bayesian parameter estimation and model comparison are employed to produce designs that meet the prescribed design specifications and requirements. In the Bayesian inference framework, the solution to a design problem is the posterior distribution, which is proportional to the product of the likelihood and priors. The likelihood is obtained via the assignment of a distribution to the error between the desired and achieved design output. The priors are assigned distributions which express constraints on the design parameters. Other design requirements are implemented by modifying the likelihood. The posterior --- which cannot be determined analytically --- is approximated by a Markov chain Monte Carlo method by drawing a reasonable number of samples from it. Each posterior sample represents a design candidate and a designer needs to select a single candidate as the final design based on additional design criteria. The Bayesian inference framework has been applied to design antenna arrays and FIR filters. The antenna array examples presented here use different types of array such as planar array, symmetric, asymmetric and reconfigurable linear arrays to realize various desired radiation patterns which include broadside, end-fire, shaped beam, and three-dimensional patterns. Various practical design requirements such as a minimum spacing between two adjacent elements, limitations in the dynamic range and accuracy of the current amplitudes and phases, the ability to maintain antenna performance over a frequency band, and the ability to sustain the loss of an arbitrary element, have been incorporated. For the filter design application, all presented examples employ a linear phase FIR filter to produce various desired frequency responses. In practice, the filter coefficients are limited in dynamic range and accuracy. This requirement has been incorporated into two examples where the filter coefficients are represented by a sum of signed power-of-two terms