A new fast running filtering algorithm of decompositional type for realizing stack filters that are based on a subclass of positive Boolean functions, namely cyclic positive Boolean functions, is proposed. Peculiar to the presented algorithm is the use of Fibonacci p-codes, which make it possible to have a unified approach to running filtering, containing as special cases the complete threshold decomposition (when p is greater than the maximal value of input data) and the binary-tree threshold decomposition (when p equals 0). The choice of optimal value of p depends on the statistics of input data and reduces the complexity of running stack filtering.