Register modeling for the unification of quantization analysis in IIR digital filters

Unified statistical coefficient quantization noise (SCQN) and roundoff noise (RON) analysis for a fixed-point arithmetic are proposed. Assumptions, including the hardware model, are derived so that the output error variance due to the SCQN source is interpreted by RON under single length accumulation. The unified approach is applied to the second-order direct form (DF) and minimum roundoff noise (MRON) filters. From the uncorrelatedness of each noise source, a general formula for total quantization noise (TQN) of the DF filter is obtained. It is shown that the DF structure has better numerical performance around the imaginary axis in the z-plan, so outside of this region the MRON structure should be considered for the design of high-Q filters if the complexity is not very important