Efficient Multirate Filter Bank Generation with Full Spectral Utilization

An engine for generating FIR filters of bandwidths that are arbitrary multiplications of a particular quantity are proposed. The design is based on first replacing z by z^L, where L is an integer, in a low pass filter to result in a multiband filter with arbitrarily sharp transition band. The complement of this multiband filter is also generated. The important step in the proposed design is to feed this into a polyphase filter bank structure to isolate each band. The same is done to the complement of the multiband filter using a second polyphase filter bank structure. This way we have separate bands that could be combined with perfectly flat magnitude response and linear phase. It is shown that all combinations of individual bands could be computed in minimum possible logarithmic time while using the minimum number of additions. In this way, we have a structure to generate any filter response within the smallest band in the multiband structure using few additions. The filters could be left as complex i.e. single band or could be made real with addition to their corresponding conjugates at the cost of losing half the filter bands. The proposed dual filter bank structure could result in a multicarrier communications system that achieves full spectral utilization.