ρ-Direct Form transposed and Residue Number Systems for Filter implementations
Jean-Claude Bajard, Laurent-Stéphane Didier, Thibault Hilaire · 2011
This paper deals with a new approach for Infinite Impulse Response (IIR) Filter based on specific structure and arithmetic. The ρ-Direct Form II transposed, introduced by G. Li [1], is an numerically efficient structure for FIR or IIR filters. Compared to classical direct forms, it uses more computations but less bits are necessary for the same precision. These properties made it well conditioned for fixed point arithmetic and its implementations are economical and numerically efficient comparing to other forms. In other hand, Residue Number Systems (RNS) offer an interesting parallelism where operations are made on small values. RNS are well known for improving the performances of DSP filters. We compare our RNS approach to fixed-point implementations of DFI and ρ-DFIIt.