Phasing with 2nd-Order Allpass Filters

The allpass structure proposed in [429] provides a convenient means for generating nonuniformly spaced notches that are independently controllable to a high degree. An advantage of the allpass approach even in the case of uniformly spaced notches (which we call flanging, as introduced in §5.3) is that no interpolating delay line is needed.

The architecture of the phaser based on second-order allpasses is shown in Fig.8.27. It is identical to that in Fig.8.23 with each first-order allpass being replaced by a second-order allpass. I.e., replace in Fig.8.23 by , for , to get Fig.8.27. The phaser will have a notch wherever the phase of the allpass chain is at (180 degrees). It can be shown that these frequencies occur very close to the resonant frequencies of the allpass chain [429]. It is therefore convenient to use a single conjugate pole pair in each allpass section, i.e., use second-order allpass sections of the form

where

and is the radius of each pole in the complex-conjugate pole pair, and pole angles are . The pole angle can be interpreted as where is the resonant frequency and is the sampling interval.

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Subsections

• Phaser Notch Parameters
• Phaser Notch Distribution

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About the Author: 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.