Optimization of stack filters based on mirrored threshold decomposition

An adaptive optimization algorithm for the design of a new class of stack filters is presented. Unlike stack smoothers, this new class of stack filters, based on mirrored threshold decomposition, has been empowered not only with lowpass filtering characteristics but with bandpass and highpass 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 function (PBF) that characterizes the stack filter in the binary domain of mirrored threshold decomposition is represented by a soft truth table where each possible binary input sequence is mapped to a real number in the interval [-1, 1]. At each iteration of the adaptive algorithm, the probability that the PBF makes the correct decision when a given input sequence is presented 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