Nonlinear system characterization and optimization

Characterization and optimization of nonlinear systems is considered from the function space point of view, and implications of this point of view are discussed. Optimization of nonlinear systems is regarded as the problem of mapping the function space of the past of the input onto a line that corresponds to the amplitude of the filter output. It is shown that a system representation that is orthogonal for all possible inputs results from any mapping that partitions this space into nonoverlapping cells. The complication of solving for optimum systems in terms of measured higher-order statistics is circumvented by formulating the problem so that particular statistical measurements directly yield the optimum systems.