The Direct Wave Form Digital Filter Structure: an Easy Alternative for the Direct Form

Abstract — 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 pi have unacceptably high noise levels, specifically in fixed-point ap-plications. As an easy alternative for the second-order Direct Form we present the second-order Direct Wave Form. Com-parable to the Direct Form, this structure uses only five mul-tipliers 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 L∞ scaling measure. It is then shown, by looking at the second-order modes of a general second-order transfer function that the Direct Wave 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. Keywords—Digital filter design; wave digital filters; quan-tization noise; scaling, second-order modes. I