Sign in

username:

password:



Not a member?

Search Online Books



Search tips

Free Online Books

Chapters

Physical Audio Signal Processing
    Artificial Reverberation
       Freeverb
          Freeverb Allpass Approximation

Chapter Contents:

Search Physical Audio Signal Processing

  

Book Index | Global Index

Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?

  

Freeverb Allpass Approximation

In Eq.$ \,$(2.2) we defined the allpass notation $ \hbox{AP}_{N}^{\,g}$ by

$\displaystyle \hbox{AP}_{N}^{\,g} \isdef \frac{-g + z^{-N}}{1 - g z^{-N}} \protect$

A look at allpass.h reveals that Freeverb implements

$\displaystyle \hbox{AP}_{N}^{\,g} \approx \frac{-1 + (1+g)z^{-N}}{1 - g z^{-N}}. $

As a result, each of the four Freeverb ``allpass'' sections is really a feedback comb-filter $ \hbox{FBCF}_{N}^{\,g}$ in series with a feedforward comb-filter $ \hbox{FFCF}_{N}^{\,-1,1+g}$, where (cf. §1.6)

\begin{eqnarray*} \hbox{FBCF}_{N}^{\,g} &\isdef & \frac{1}{1 - g\,z^{-N}}\\ [5pt] \hbox{FFCF}_{N}^{\,-1,1+g} &\isdef & -1 + (1+g)z^{-N}. \end{eqnarray*}

A true allpass is obtained only for $ g=(\sqrt{5}-1)/2\approx 0.618$ (reciprocal of the ``golden ratio''). The default value used in Freeverb (see revmodel.cpp) is $ 0.5$. A detailed discussion of feedforward and feedback comb filters appears in §1.6, and corresponding Schroeder allpass filters are described in §1.8.

Order a Hardcopy of Physical Audio Signal Processing

Previous: Moorer Lowpass Feedback Comb Filter
Next: Conclusions
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.


Comments

No comments yet for this page


Add a Comment
You need to login before you can post a comment (best way to prevent spam). ( Not a member? )