Optimization of stack filters based on mirrored threshold decomposition

In this paper, an adaptive optimization algorithm for the design of a new c lass of stack filters is presented. Unlike stack smoothers, this new class of stack Biters, based on mirrored threshold decomposition, has been empowe red not only with lowpass filtering characteristics but with bandpass and h ighpass filtering characteristics as well. Therefore, these filters can be effectively used in applications where frequency selection is critical. An adaptive optimization approach is introduced, where the positive Boolean fu nction (PBF) that characterizes the stack filter in the binary domain of mi rrored threshold decomposition is represented by a soft truth table where e ach possible binary input sequence is mapped to a real number in the interv al [-1, 1], At each iteration of the adaptive algorithm, the probability th at the PBF makes the correct decision when a given input sequence is presen ted is incremented by suitably changing the entries of the soft truth table . The proposed adaptive algorithm is simple to implement since it requires only increment, decrement, and local comparison operations. The performance of optimal stack filters is illustrated by several simulations.