Low-sensitivity digital-filter structures which are amenable to error-spectrum shaping

A systematic and exhaustive procedure is used to generate a class of new low-sensitivity second-order digital-filter structures which are amenable to error-spectrum shaping (ESS). Collectively, these structures can realize any stable second-order transfer function. For every transfer function, a choice of at least two structures is available but, through a sensitivity analysis, the optimum one can always be identified. The paper concludes with sensitivity and roundoff-noise comparisons which show that the new structures are usually superior relative to corresponding direct canonic structures and also relative to the state-space section-optimal structure.