All-pass based robust low complexity structures for implementing recursive digital filters

A simplified version of a recently developed structure is derived for all-pass filters. The proposed structure possesses 4N non-trivial multipliers and 2N adders used for computing one output sample of an Nth order all-pass filter. It is shown that such a structure yields a roundoff noise gain of 4N, compared with that of (N +1)² for the classical minimum roundoff noise realizations that have in general (N+1)² multipliers and N(N + 1) adders. The proposed structure is applied to a class of all-pass based filters. The performance of such a filter is analyzed in terms of sensitivity measure and roundoff noise gain. Numerical examples are presented to demonstrate the excellent properties of the proposed structure in terms of robustness against quantization errors and reducing implementation complexity.