Design of FIR Hilbert transformers using prescribed subfilters and nested FT technique

In this article, a transformation (subfilter) for designing finite impulse response (FIR) Hilbert transformers (HTs) is proposed. With our approach, except simple search procedures, neither optimisation nor any filter design algorithm is needed to obtain the transformation. The proposed subfilter requires only two multipliers regardless of the subfilter order. For the frequency transformation design, the purpose of the subfilter is to provide a "rough" shape of the desired HT; the two coefficients of the subfilter can be implemented as the form of sum of power of two (SOPOT) with only a few bits, thus leading to a multiplierless realisation. Moreover, by applying the transformation on the subfilter again, a technique named as nested frequency transformation (nested FT) is introduced. This technique can further reduce the number of multipliers needed in the overall HT.