Numerical Robustness of TDF-II

An advantage of the transposed direct-form II structure (depicted in Fig.9.4) is that the zeros effectively precede the poles in series order. As mentioned above, in many digital filters design, the poles by themselves give a large gain at some frequencies, and zeros are often used to compensate. This is especially true of filters with sharp transitions in their frequency response; in such filters, the sharp transitions are achieved using near pole-zero cancellations close to the unit circle in the $z$ plane.