A pipelined recursive residue number system digital filter

The well-known advantages of pipelining as applied to Finite Impulse Response (FIR) Residue Number System (RNS) arithmetic digital filters is extended to the important area of Infinite Impulse Response (IIR) digital filters through a new technique based on augmentation of the IIR transfer function. Through this technique, pipelined IIR filters based on RNS Read-Only-Memory (ROM) table look-up techniques can be designed which offer throughput rates equal to the table look-up time of the ROM's. This high-speed realization can be achieved even though the recursive filter algorithm requires multiple delays in realizing the output of the filter. For the example of a typical second-order IIR filter, the pipelined structure represents a five-fold increase in speed over standard techniques. Higher order realizations will yield proportionately higher speed improvements. Although the new technique does increase somewhat the hardware complexity of the filter, the increase in speed will often justify the additional hardware. The paper discusses the basic technique, stability considerations, and hardware realizations.