A fast algorithm for the design of narrow-band multirate digital filters

The design of multirate bandpass filters requires a search for the optimum multistage structure. The size of the search space grows exponentially as the filter bandwidth decreases, and excessive computer time is required to search it exhaustively. A fast branch-and-bound algorithm for searching this space is presented. In our tests, this algorithm decreases search time by an average factor which increases from 7.7 to 23.0 as the filter passband width decreases from 8 × 10^-4to 3.2 × 10^-6. It is also shown that when coefficient storage is the cost criterion, the actual filter structure resembles an unrealizable optimum filter structure for small bandwidth filters.