Efficient multirate realization for narrow transition-band FIR filters

A filtering technique for reducing the computational complexity in FIR (finite-impulse-response) filters at any bandwidth is described. This technique uses a combination of multirate and complementary filters. It is shown that the resulting computational complexity is almost independent of the transition bandwidth of the filter, but depends somewhat on the cutoff frequency. It is concluded that any reasonable filter specification can be met by using about 45 multiplications per sample.<>