Low roundoff noise augmented IIR filters based on normal realization

As second-order normal subfilters can be expressed as first-order complex subfilters, the authors decompose IIR digital filters into a parallel combination of first-order complex subfilters, in which each subfilter is augmented with one complex pole-zero cancellation pair and realized in complex direct form II. Under the l₂ dynamic range constraint, explicit expressions for the optimal complex pole-zero cancellation pair and the minimum roundoff noise of complex augmented subfilters are derived. Compared to normal realization, the noise reduction of this optimal complex augmented realization approaches its upper bound of about 6 dB as the desired filter bandwidth decreases. In addition, several suboptimal realizations are investigated and shown to achieve a greater performance-to-cost ratio