Abstract
We propose a new design method of a class of FIR low-pass filters having steep cut-off with small number of taps. This is a significant improvement of our precedent result where desired frequency characteristics are realized by a set of frequency scalings of basic filters and their series connection. Though the method can realize an FIR filter with much smaller number of taps than conventional Remez method, the resulting characteristics can be such that their cut-off edges are not steep due to just the simple series connection of scaled filters. In this paper, we consider the series connection with each module consisting of a function of the basic filters. It turns out that the function can be written as a recursion with the basic filters, called mean operation. The mean operation is performed in such a way that the skirts of the transition region is subtracted recursively one by another to cancel the gradual slope, so that the resulting characteristics become steep. In a design example, the proposed method is compared with conventional ones and is shown to approximate a desired characteristics with smaller number of multiplies.
