Approximation of fir by IIR filters using hybrid genetic algorithm

This paper presents a method for the least-squares (LS) approximation of a finite impulse response (FIR) filter by an infinite impulse response (IIR) filter. The real LS error is defined as the sum of squared absolute values of the differences between the complex frequency responses of the FIR and IIR filters. The approximation problem is solved by means of its transformation into equivalent nonlinear constrained optimization problem. A hybrid approach for solving the considered optimization problem is proposed. In the first step, a genetic algorithm is applied. The final point from the genetic algorithm is used as the starting point for a local optimization method. Using a local optimization method in the second step results in improving the speed of convergence. Two design examples are given to illustrate the proposed technique.