Filter structures composed of allpass and FIR filters for interpolation and decimation with factors of two

Filter structures for interpolation and decimation with factors of two are introduced. The structures are derived by using the frequency-response masking approach, in which the overall filter is composed of a periodic model filter, its complementary periodic filter, and two masking filters. The model and complementary model filters consist of two allpass filters in parallel, whereas the masking filters are linear-phase FIR filters. In the final interpolators and decimators, the filtering takes place at the lower of the two sampling rates involved. The design of the overall filters concerns separate designs of a half-band IIR model filter and of a linear-phase FIR filter. One major advantage of the new filters is that the allpass filters are functions of z^2M which results in an M-fold increase of the maximal sample frequency compared with conventional half-band IIR filters. In the case where one of the allpass branches is a pure delay, resulting in approximately linear phase, the arithmetic complexity can also be reduced. Examples are included that demonstrate this