STATISTICAL-ANALYSIS AND OPTIMIZATION OF STACK FILTERS

This thesis considers new theoretical and practical aspects of an impo rtant class of nonlinear digital filters, namely stack filters. The fi rst main contribution of this thesis is the establishment of important connections between rank selection probabilities and other quantities of stack filters. In addition, new algorithms for the calculation of selection probabilities are presented. Breakdown points and breakdown probabilities of stack filters are defined and studied in this thesis. Their connections to rank selection probabilities and other quantitie s of stack filters axe established. Midpoint sensitivity curves are al so introduced and studied. A new expression for the moments about the origin of the output of stack filtered data is derived and studied in this thesis. The noise attenuation capability of any stack filter can now be calculated using this new expression. The second main contribut ion of this thesis is the development of an extension of the existing optimality theory for stack filters. This theory combines the noise at tenuation and different constraints on the filter's behavior. In this thesis various new constraints are introduced and used in optimization . A new approach based on breakdown probability as a measure of noise attenuation is also derived. For self-dual stack filters it is shown t hat an optimal stack filter which achieves the best noise attenuation subject to given constraints can usually be obtained in closed form. A n algorithm for finding this form is given and several design examples illustrating the possible use of this algorithm in practice as a filt er design method axe presented.