Parametric design of nonlinear optimal filters

The design of optimal nonlinear filters for signal processing has involved mostly nonparametric estimation. This paper discusses the elements of parametric design for analog signal processing. It provides details for the class of conjunctive homothetic granulometric bandpass filters. These are nonlinear and their optimization in the signal-union-noise model for random sets can be completely characterized in terms of the granulometric size density induced by the granulometry from which the optimal filter is to be selected.