A generalized structural subband decomposition of FIR filters and its application in efficient FIR filter design and implementation

It is shown that any FIR (finite-impulse-response) transfer function can be realized as a parallel connection of interpolated FIR (IFIR) sections consisting of a cascade of a subfilter with a sparse impulse response and an FIR interpolator which fills in the missing samples of the corresponding subfilter. The set of interpolators can be realized as a subband filter bank, and as a result, each IFIR section contributes to the overall frequency response essentially within a given band of frequencies. The proposed decomposition can be considered as a generalization of the polyphase decomposition. It results in a computationally efficient structure in sampling rate alteration applications and also leads to faster FIR filter design algorithms. Examples are included to demonstrate the improvements in the speed of least-squares and minimax design algorithms based on the suggested structure