Novel decimators and interpolators using computationally efficient halfband subfilters

Digital decimators and interpolators are considered that makes use of a novel linear-phase halfband FIR (finite-impulse response) filter structure which has a highly reduced number of general multiplications per sample compared to conventional halfband FIR filters. The novel filter is based on subfilters whose filter coefficients are related to each other recursively. The structure allows also convenient means for adjusting the passband and stopband ripples in a wide range. It is shown that the novel subfilters can be used to implement computationally efficient multistage polyphase decimators and interpolators. Since the novel filter structure has a highly reduced number of general multipliers, it is ideal for the sharpening techniques of J.F. Kaiser and R.W. Hamming (1977) and for the variable cutoff filter constructs of A.V. Oppenheim et al. (1976). The composite halfband FIR filter obtained from the sharpening or frequency transformation methods can be implemented as a polyphase filter in the lower sampling rate, resulting in savings of the data storage