A GENERALIZED STRUCTURAL SUBBAND DECOMPOSITION OF FIR FILTERS AND ITS APPLICATION IN EFFICIENT FIR FILTER DESIGN AND IMPLEMENTATION

It is shown that any FIR transfer function can be realized as a parallel connection of 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 resulting in a computationally efficient structure in sampling rate alteration applications. The proposed structural decomposition 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.