Fixed-point digital IIR filter design using two-stage ensemble evolutionary algorithm

The research on optimal design of infinite-impulse response (IIR) filter design based on various optimization techniques, including evolutionary algorithms (EAs), has gained much attention in recent years. Previously, the parameters of digital IIR filters are encoded with floating-point representations. It is known that a fixed-point representation can effectively save computational resources and is more convenient for direct realization on hardware. Inherently, compared with the floating-point representation, the fixed-point representation would make the search space miss much useful gradient information and therefore, surely rises new challenges for continuous EAs. In this paper, we first analyze the fitness landscape properties of optimal digital IIR filter design. Based on the fitness landscape investigation, a two-stage ensemble evolutionary algorithm (TEEA) is applied to digital IIR filter design with fixed-point representation. In order to fully evaluate the performance of TEEA, we experimentally compare it with five state-of-the-art EAs on four types of digital IIR filters with different settings. Based on the experimental results, we can conclude that TEEA has higher convergence speed, better exploration, and higher success rate. In order to benchmark TEEA further, we apply it to some more difficult problems with shorter word length or higher order. We can find that TEEA can provide satisfying performance on these hard tasks as well.