A novel iterative design technique for linear-phase FIR half-band filters

This paper proposes a novel iterative design scheme for generating linear-phase, half-band FIR filters with considerably reduced arithmetic operations and narrow transition bandwidth. Starting from a short half-band subfilter, preferably a multiplier-free one, the scheme can evolve this subfilter to a better composite half-band filter by using simple algebraic composition transformation iteratively. Compared to the existing design methods, the proposed scheme is free of filter optimization processes and is much simpler. In implementation, the designed half-band filters can be realized as a multi-stage cascaded structure, composed of several short half-band subfilters and delay elements. Since its building elements have trivial coefficients with short wordlengths, the proposed structure for half-band filters has low complexity and low coefficient dynamic range. Thus it is suitable for finite-precision implementation. Furthermore, the structure is highly modular, repetitive in all stages, and suitable for VLSI implementation.