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 the zeros often provide compensating attenuation. This is especially true of filters with sharp transitions in their frequency response, such as the elliptic-function-filter example on page ; in such filters, the sharp transitions are achieved using near pole-zero cancellations close to the unit circle in the plane.^10.4

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.