Filter Structures Composed of All-Pass and FIR Filters for Interpolation and Decimation by a Factor of Two

This paper introduces filter structures for interpolation and decimation by a factor of two. The structures are derived by using the frequency-response masking approach, in which the overall filter makes use of a periodic model filter, its complementary filter, and two masking filters. The periodic model filters are obtained by replacing each delay element in a model filter with M delay elements in cascade. The model filter is a half-band infinite-impulse response (IIR) filter composed of two all-pass filter in parallel, whereas the masking filters are linear-phase finite-impulse response (FIR) filters. In the final interpolator and decimator structures, the filtering takes place at the lowest of the two sampling rates involved. The corresponding overall filter can be designed by separately optimizing a half-band IIR filter and a linear-phase FIR filter. Both nonlinear-phase and approximately linear-phase filters are considered. One advantage of the proposed filter structures over conventional half-band IIR filter structures is that their maximal sample frequency is M times higher, which may be utilized to increase the speed in an implementation and/or to reduce the power consumption via power supply voltage scaling techniques. In the case of approximately linear-phase filters, the computational complexity can be reduced as well. Several design examples are included demonstrating the properties and advantages of the proposed filter structures.