Modular filters based on filter sharpening and optimal minimax design

A filter design algorithm is presented that can be viewed as a generalization of filter sharpening with guaranteed minimax optimality and that leads to an efficient modular topology. The structure consists of repetitive usage of a given sub-filter in a fashion similar to a traditional tapped-delay line. In cases where a sub-filter is not specified a priori, a low order sub-filter that approximates the given filter specifications can be used in this structure. The transfer functions of the overall modular filters obtained with this algorithm can be expressed mathematically as the functional composition of two transfer functions. This mathematical formulation creates a convenient framework to analyze and reduce sensitivity with respect to coefficients of the sub-filter or the tap coefficients without altering the characteristics of the overall design.