Recursive Even Mirror Fourier Nonlinear Filters and Simplified Structures

In this paper, a novel class of recursive nonlinear filters is presented as an extension of finite-memory even mirror Fourier nonlinear filters. These filters are characterized by two relevant properties: i) they are able to arbitrarily well approximate any discrete-time, time-invariant, causal, infinite-memory, continuous, nonlinear system and ii) they are always stable according to the bounded-input-bounded-output criterion. Even though recursive models can represent many systems with fewer coefficients than their finite-memory counterparts, it is still possible to further reduce their computational complexity. In fact, while in general simplified structures lead to a loss of performance, it is pointed out in the paper that in various common real-world situations, they are able of giving remarkable complexity reductions without negatively affecting the modeling capabilities.