Linear-phase FIR interpolation, decimation, and mth-band filters utilizing the farrow structure

This paper introduces novel linear-phase finite-impulse response (FIR) interpolation, decimation, and Mth-band filters utilizing the Farrow structure. In these new overall filters, each polyphase component (except for one term) is realized using the Farrow structure with a distinct fractional delay. The corresponding interpolation/decimation structures can therefore be implemented using only one set of linear-phase FIR subfilters and one set of multipliers that correspond to the distinct fractional delays. The main advantage of the proposed structures is that they are flexible as to the conversion factors, and this also for an arbitrary set of integer factors, including prime numbers. In particular, they can simultaneously implement several converters at a low cost. The proposed filters can be used to generate both general filters and Mth-band filters for interpolation and decimation by the integer factor M. (In this paper, a general filter for interpolation and decimation by M means a filter having a bandwidth of approximately π/M without the restriction that π/M be included in the transition band. This is in contrast to an Mth-band filter whose transition band does include π/M.) In both cases, the overall filter design problem can be posed as a convex problem, the solution of which is globally optimum. Design examples are included in the paper illustrating the properties and potentials of the proposed filters.