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

Abstract

Abstract-In this paper, we present a new design method for a class of two-dimensional (2-D) recursive digital filters using an evolutionary computational system. 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 evolutionary algorithm. In our approach, the genotypes of potential solutions have a uniform probability within the region of the search space specified by the constraints and zero probability outside this region. This approach is particularly effective as the evolutionary search considers only those potential solutions that respect the constraints. We use the computer language GENETICA, which provides the expressive power necessary to get an accurate problem formulation and supports an adjustable evolutionary computational system. Results of this procedure are illustrated by a numerical example, and compared with those of some previous designs.

Genetic-Algorithm-Based Method for Optimal Analog Test Points Selection

“…This evolutionary method cannot be classified into inclusion or exclusion group, i.e., the set of test points can be modified in any way during each evolutionary cycle (not only by one point exclusion or inclusion). Evolutionary techniques have been successfully applied in many difficult tasks [11]- [20]. This group of soft computation consists of genetic algorithm (GA) [11]- [13], genetic programming [15]- [17], differential evolution [18], evolution strategy (ES), and evolutionary programming [21].…”

A Quantum-Behaved Particle Swarm Optimization With Diversity-Guided Mutation for the Design of Two-Dimensional IIR Digital Filters

“…The design task of 2-D filters amounts to finding a transfer function H(z 1 , z 2 ) as in (1) such that the function M (ω 1 , ω 2 ) = H(e −jω 1 , e −jω 2 ) approximates the desired amplitude response of the 2-D filters M d (ω 1 , ω 2 ). The approximation can be achieved by minimizing [4]- [7] J = J(a ij , q k , r k , s k , H 0 )…”

“…Since the denominator only contains first-degree factors, we can assert the stability conditions as the constraints (3b) [4]- [7].…”

“…To test QPSO-DGM, we use the same example of the design problem as in [4]- [7], where M d (ω 1 , ω 2 ) is given by…”

“…Modern heuristic methods have also been employed for 2-D IIR filter design problems, such as genetic algorithm (GA) [4], neural network (NN) [5], particle swarm optimization (PSO) [6], and the computer language GENETICA [7]. These techniques were able to find out better solutions than those mentioned in the previous paragraph.…”