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Design of Computationally Efficient FIR Filters Using Periodic Subfilters as Building Blocks

For many digital signal processing applications, FIR filters are preferred over their IIR counterparts as the former can be designed with exactly linear phase and they are free of stability problems and limit cycle oscillations. The major drawback of FIR filters is that they require, especially in applications demanding narrow transition bands, considerably more arithmetic operations and hardware components than do comparable IIR filters. Ignoring the correction term for very low-order filters, the minimum order of an optimum linear-phase lowpass FIR filter can be approximated by [Herrmann, Rabiner, and Chan, 1973]