A Study of Filters Selectivity with Maximally Flat Responses with Respect to Hausdorff Distance

This article examines the approximations of the ideal transfer function of a low pass filter with sigmoidal functions using Hausdorff distance. A relation between the filter selectivity and the Hausdorff distance is established. The approximation parameters are defined. Analytical dependencies of transfer functions and their respective Hausdorff distances are derived. An analysis of the results is made.