Design of two-dimensional recursive filters using genetic algorithms

Abstract

Abstract-In this paper, we examine a new design method for two-dimensional (2-D) recursive digital filters using genetic algorithms (GAs). The design of the 2-D filter is reduced to a constrained minimization problem the solution of which is achieved by the convergence of an appropriate GA. Theoretical results are illustrated by a numerical example. Also, comparison with the results of some previous design methods is attempted.Index Terms-Constrained optimization, genetic algorithm (GA), multidimensional systems, two-dimensional (2-D) recursive filters, 2-D systems.

Evolutionary design of 2-dimensional recursive filters via the computer language GENETICA

“…For design purposes, the function is equivalent to a class of nonsymmetric half-plane (NSHP) filters, whose 2-D transfer function is given by (1) This approximation can be achieved by minimizing [10], [11] (…”

“…Let the desired amplitude response be given by if if otherwise (9) IV. PROBLEM SOLUTION The aforementioned problem has been tackled by using neural networks [10] or a genetic algorithm [11]. The problem-solving application presented here is developed in the computer language GENETICA [12], [13], which is integrated in a programming environment that includes an evolutionary computational system.…”

“…In our case, the problem is to minimize by defining the values , which range in the real interval , as it is shown in [10], [11] Table I, under the constraints and . Consider the values defined on the axes respectively (Fig. 1).…”

“…Evolutionary Design of 2-Dimensional Recursive Filters via the Computer Language GENETICA "recipes" have been adopted in order to resolve all these instability problems, but the outcome is likely to be a system that has a very small stability margin and hence, not of much practical importance [10], [11].…”

“…Considering potential solutions outside the stability region reduces the effectiveness of the evolutionary search even if a hard fitness-penalty is used for such solutions [11]. However, a conventional genetic algorithm cannot restrict the search within the stability region, because this region cannot be defined to be closed with respect to the genetic operations.…”