Phasing with First-Order Allpass Filters

The block diagram of a typical inexpensive phase shifter for guitar players is shown in Fig.8.23.^9.20 It consists of a series chain of first-order allpass filters,^9.21 each having a single time-varying parameter controlling the pole and zero location over time, plus a feedforward path through gain which is a fixed depth control. Thus, the delay line of the flanger is replaced by a string of allpass filters. (A delay line is of course an allpass filter itself.)

In analog hardware, the first-order allpass transfer function [449, Appendix E, Section 8]^9.22is

(In classic phaser circuits such as the Univibe, is used, but since there is an even number (four) of allpass stages, there is no difference.) In discrete time, the general first-order allpass has the transfer function

We now consider the analog and digital cases, respectively.

---

Subsections

• Classic Analog Phase Shifters
• Classic Virtual Analog Phase Shifters

---

Previous: Virtual Analog Example: Phasing
Next: Classic Analog Phase Shifters

Order a Hardcopy of Physical Audio Signal Processing

---

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.