Roundoff noise minimization in a direct form delta operator structure

Delta operator realizations of IIR filters have received a lot of interest due to their good finite-wordlength properties. We present a detailed analysis of the computationally efficient transposed direct form II delta structure, which is also known to have excellent roundoff noise performance under fast sampling. The focus is on the roundoff noise minimization in fixed-point implementations. The free Δ parameter in the delta operator is optimized with respect to the output roundoff noise within the scaling constraints. Moreover, the required internal wordlength to obtain a prespecified noise performance is derived