Lowpass-Feedback Comb Filter

Inspection of comb.h in the Freeverb source shows that Freeverb's ``comb'' filter is more specifically a lowpass-feedback-comb filter (LBCF^4.11--§2.6.5). It is constructed using a delay line whose output is lowpass-filtered and summed with the delay-line's input. The particular lowpass used in Freeverb is a unity-gain one-pole lowpass having the transfer function

When , the LBCF reduces to the feedback comb filter (FBCF) of §2.6.2 in which the feedback was not filtered. The overall LBCF transfer function is then

This structure was introduced for artificial reverberation by Schroeder [412] and Moorer [314].

In Freeverb's comb section (comb.h and comb.cpp), the ``damping'' is set initially to

The lowpass scale-factor is called feedback in the source, and it is set initially to

Increasing the roomsize parameter (typically brought out to a GUI slider) increases and hence the reverberation time. Since is required for dc stability, the roomsize must be less than 1.0714, and so the GUI slider max is typically 1 ().

The feedback variable mainly determines reverberation time at low-frequencies at which the feedback lowpass has negligible effect. The feedback lowpass causes the reverberation time to decrease with frequency, which is natural. At very high frequencies--those for which the lowpass gain times is much less than 0.5--the reverberation time becomes dominated by the diffusion allpass filters (which have a fixed feedback coefficient of ). Thus, in Freeverb, the ``room size'' parameter can be interpreted as setting the low-frequency T60 (time to decay 60 dB), while the ``damping'' parameter controls how rapidly T60 shortens as a function of increasing frequency. A lower-limit on T60 is given by the four diffusion allpass filters.

In terms of the physical interpretation of the filtered-feedback comb-filter discussed in §2.6.5, Freeverb's roomsize parameter can be interpreted as the square-root of the low-frequency reflection-coefficient of each wall. That is, when a planewave bounces back and forth between two walls, the attenuation coefficient is roomsize after one round trip (two wall reflections). Therefore, a better name in this interpretation would be liveness or reflectivity. Since the round-trip delay is given in samples by the delay-line length, changing the roomsize requires changing the delay-line lengths in this interpretation.

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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.