Error feedback for floating-point cascade-form digital filters

The authors propose the use of error feedback for roundoff noise reduction in cascade-form recursive digital filters employing floating-point arithmetic. The floating-point error feedback has a similar mechanism to the fixed-point error feedback. However, the optimal error feedback solution (in the sense of minimum mean-square error) for the floating-point case is different from the corresponding fixed-point case. The formulated optimal feedback coefficients are shown to be independent of the section of ordering and zero-pole pairing, which does not hold in the fixed-point case. Finally, a suboptimal error feedback is proposed and shown to provide a constant output SNR (signal-to-noise ratio) independent of the specific characteristics of the filter except the filter´s order. Several examples are given to verify these results