Filtered-Feedback Comb Filters

The *filtered-feedback comb filter* (FFBCF) uses filtered
feedback instead of just a feedback gain.

Denoting the feedback-filter transfer function by , the transfer function of the filtered-feedback comb filter can be written as

Note that when is a causal filter, the FFBCF can be considered mathematically a special case of the general allpole transfer function in which the first denominator coefficients are constrained to be zero:

It is this ``sparseness'' of the filter coefficients that makes the FFBCF more computationally efficient than other, more general-purpose, IIR filter structures.

In §2.6.2 above, we mentioned the physical interpretation
of a feedback-comb-filter as simulating a plane-wave bouncing back and
forth between two walls. Inserting a lowpass filter in the feedback
loop further simulates frequency dependent *losses* incurred
during a propagation round-trip, as naturally occurs in real rooms.

The main physical sources of plane-wave attenuation are *air
absorption* (§B.7.15) and the *coefficient of
absorption* at each wall [352]. Additional ``losses'' for
plane waves in real rooms occur due to *scattering*. (The plane
wave hits something other than a wall and reflects off in many
different directions.) A particular scatterer used in concert halls
is *textured wall surfaces*. In ray-tracing simulations,
reflections from such walls are typically modeled as having a
*specular* and *diffuse* component. Generally speaking,
wavelengths that are large compared with the ``grain size'' of the
wall texture reflect specularly (with some attenuation due to any wall
motion), while wavelengths on the order of or smaller than the texture
grain size are scattered in various directions, contributing to the
diffuse component of reflection.

The filtered-feedback comb filter has many applications in computer music. It was evidently first suggested for artificial reverberation by Schroeder [415, p. 223], and first implemented by Moorer [317]. (Reverberation applications are discussed further in §3.6.) In the physical interpretation [432,208] of the Karplus-Strong algorithm [238,234], the FFBCF can be regarded as a transfer-function physical-model of a vibrating string. In digital waveguide modeling of string and wind instruments, FFBCFs are typically derived routinely as a computationally optimized equivalent forms based on some initial waveguide model developed in terms of bidirectional delay-lines (``digital waveguides'') (see §6.10.1 for an example).

For *stability*, the amplitude-response of the feedback-filter
must be less than
in magnitude at all frequencies, *i.e.*,
.

[How to cite this work] [Order a printed hardcopy] [Comment on this page via email]

Copyright ©

Center for Computer Research in Music and Acoustics (CCRMA), Stanford University