Quantization error and limit cycles analysis in residue number system coded recursive filters

The paper discusses the Residue Number System (RNS) implementation of second order recursive digital filter sections. The RNS offers the advantage of using integer based arithmetic operations and a simple hardware realization involving arrays of look up tables stored in high density ROMs, In residue number system scaling is necessary to keep the data within the limited dynamic range. The effects of residue scaling on the performance of second order sections are described here. An analysis of the quantization error accumulation associated with scaling in the proposed realizations shows that the residue architecture combines good quantization error performance with high speed implementation. The conditions for existance of zero input limit cycles in residue coded recursive sections is derived for certain cases. Regions on the coefficient space which allow limit cycles of period 1 (dc) and period 2 are determined and the bounds on their magnitude are derived.