Low Roundoff Noise Augmented IIR Filters Based on Normal Realization

Although addition of pole-zero cancellation pairs to direct form IIR digital (sub)filters reduces the output roundoff noise, the resulting designs still exhibit large roundoff noise in narrow-band applications. As an alternative to direct form, normal realization has low roundoff noise that is independent of filter bandwidth. As second-order normal subfilters can be expressed as first-order complex subfilters, we 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 l₂dynamic 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.