The direct wave form digital filter structure: an easy alternative for the direct form

Although the Direct Form is still widely used in IIR digital filter design, this structure is known to have a high coefficient sensitivity and to produce high levels of quantization noise. Even if only second-order sections are used to design higher order filters, the sections with poles close to the unit circle and/or with angles close to 0 or p have unacceptably high noise levels, specifically in fixed-point applications. As an easy alternative for the second-order Direct Form we present the second-order DirectWave Form. Comparable to the Direct Form, this structure uses only five multipliers which are directly linked to the five coefficients of a general second-order transfer function. It is shown how the Direct Wave From can be properly scaled with an L2 scaling measure as well as with the more conservative L1 scaling measure. It is then shown, by looking at the secondorder modes of a general second-order transfer function that the DirectWave Form has a superior noise behaviour that is close to being optimal (within 3dB). The Direct Wave Form is also shown to be overflow stable and free from limit cycles.