Freeverb Allpass Approximation

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Index: Physical Audio Signal Processing

Physical Audio Signal Processing

Freeverb

Lowpass-Feedback Comb Filter

Conclusions

A Schroeder allpass filter can be obtained by replacing the unit-delay with a delay-line of arbitrary length in a first-order allpass filter. — Click for https://ccrma.stanford.edu/~jos/pasp/Allpass_Filters.html

A comb filter is made from a delay line using a linear combination of its input and output signals. — Click for https://ccrma.stanford.edu/~jos/pasp/Comb_Filters.html

The feedforward comb filter is made by forming a linear combination of the input and output of a delay line. — Click for https://ccrma.stanford.edu/~jos/pasp/Feedforward_Comb_Filters.html

A feedback comb filter is made from a delay line by scaling its output signal by some coefficient and summing that with the delay-line input signal. — Click for https://ccrma.stanford.edu/~jos/pasp/Feedback_Comb_Filters.html

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Index: Physical Audio Signal Processing

Physical Audio Signal Processing

Freeverb

Lowpass-Feedback Comb Filter

Conclusions

Freeverb Allpass Approximation

In Eq.(3.2) we defined the allpass notation $\hbox{AP}_{N}^{\,g}$ by

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

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. §2.6)

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

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 . A detailed discussion of feedforward and feedback comb filters appears in §2.6, and corresponding Schroeder allpass filters are described in §2.8.

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Freeverb Allpass Approximation

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4 Copyright © 2024-06-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University