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 novelhybrid descent method, consisting of a simulated annealing algorithm and a gradient-based method, isproposed. The simulated annealing algorithm operates on the space of orthogonal matrices and is used tolocate descent points for previously converged local minima. The gradient-based method is derived fromconverting the discrete problem to a continuous problem via the Stiefel manifold, where convergence canbe guaranteed. To demonstrate the effectiveness of the proposed hybrid descent method, several numericalexamples show that better discrete filter designs can be sought via this hybrid descent method

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