Time-varying recursive filters for decimation and interpolation

Decimation and interpolation require filtering. In order to reduce the hardware effort, FIR filters with linear phase are implemented as polyphase filters often. Still, the number of coefficients cannot be reduced by this method. Comb filters implemented as cascaded-integrator-comb filters are hardware-efficient filters. Due to the periodicity of the comb section the number of registers (i.e., the state space) can be reduced, while the separation of poles and zeros provides a means to avoid coefficient multipliers at all. However, due to the necessarily perfect pole-zero cancellation these filters can only realize zeros at integer multiples of the lower sample rate. The presented time-varying recursive filter structures exploit the advantage of CIC-filters of implementing the transfer-zeros for only one period of a periodic comb section and thus, reduce complexity considerably. Moreover, they provide perfect pole-zero cancellation for arbitrary zero placement.