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 Þlter is composed of a periodic model Þlter, its complementary periodic Þlter, and two masking Þlters. The model and complementary model Þlters consist of two allpass Þlters in parallel, whereas the masking Þlters are linear-phase FIR Þlters. In the Þnal interpolators and decimators, the Þltering takes place at the lower of the two sampling rates involved. The design of the overall Þlters concerns separate designs of a half-band IIR model Þlter and of a linear-phase FIR Þlter. One major advantage of the new Þlters is that the allpass Þlters are functions of z 2 M which results in an M -fold increase of the maximal sample frequency compared with conventional half-band IIR Þlters. 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.