Mth-band linear-phase FIR filter interpolators and decimators utilizing the Farrow structure

This paper introduces Mth-band linear-phase FIR filter interpolators and decimators utilizing the Farrow structure. In these new overall structures, each polyphase component (except for the pure delay term) is a Farrow structure with a distinct fractional delay. The overall 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. Many of these multiplier coefficients are trivial and it is possible to further reduce the complexity by utilizing symmetries. The proposed converter structures are more efficient than conventional single-stage converters structures are more efficient than conventional single-stage converters but less efficient than multistage converters in terms of arithmetic operations required per sample. However, the main advantages of the proposed structures are that they can be used also for conversions with prime number and that they are flexible as to the conversion factors. In particular, they can simultaneously implement several converters at a low cost. The multistage converters are not fully flexible since they can be designed using linear programming which generates optimum filters in the minimax sense. Design examples are included.