comb filters

the recursive comb filters (section 3.4) and the delay-based allpass filters (sec-
tion 3.4.1) as computational structures suitable for the inexpensive simulation of
complex patterns of echoes. These structures rapidly became standard compo-
nents used in almost all the artificial reverberators designed until nowadays [61].
It is usually assumed that the allpass filters do not introduce coloration in the
input sound. However, this assumption is valid from a perceptual viewpoint only
if the delay line is much shorter than the integration time of the ear, i.e. about
50ms [111]. If this is not the case, the time-domain effects become much more
relevant and the timbre of the incoming signal is significantly affected.

allpass filter to a multi-input multi-output structure, where the delay line of m
samples has been replaced by a order-N unitary network [40]. Examples of trivial
unitary networks are orthogonal matrices, parallel connections of delay lines,
or allpass filters. The idea behind this generalization is that of increasing the
complexity of the impulse response without introducing appreciable coloration
in frequency. According to Gerzon's generalization, allpass filters can be nested
within allpass structures, in a telescopic fashion. Such embedding is shown to be
equivalent to lattice allpass structures [39], and it is realizable as long as there
is at least one delay element in the block A(z) of fig. 8.

conducted by Andy Moorer in the late seventies [61]. He extended the work done
by Schroeder [90] in relating some basic computational structures (e.g., tapped
delay lines, comb and allpass filters) with the physical behavior of actual rooms.
In particular, it was noticed that the early reflections have great importance
in the perception of the acoustic space, and that a direct-form FIR filter can
reproduce these early reflections explicitly and accurately. Usually this FIR filter
is implemented as a tapped delay line, i.e. a delay line with multiple reading
points that are weighted and summed together to provide a single output. This
output signal feeds, in Moorer's architecture, a series of allpass filters and a
parallel of comb filters(see fig. 14) . Another improvement introduced by Moorer
was the replacement of the simple gain of feedback delay lines in comb filters
with lowpass filters resembling the effects of air absorption and lossy reflections.

ence. Several structures and many parameterizations were proposed in the past,
especially in non-disclosed form within commercial reverb units [29]. In most
cases, the various structures are combinations of comb and allpass elementary
blocks, as suggested by Schroeder in the early works. As an example, we look
more carefully at the Moorer's preferred structure [61], depicted in fig.14. The
block (a) takes care of the early reflections by means of a tapped delay line.
The resulting signal is forwarded to the block (b), which is the parallel of a di-
rect path on one branch, and a delayed, attenuated diffuse reverberator on the
other branch. The output of the reverberator is delayed in such a way that the
last of the early echoes coming out of block (a) reaches the output before the
first of the non-null samples coming out of the diffuse reverberator. In Moorer's
preferred implementation, the reverberator of block (b) is best implemented as
a parallel of six comb filters, each with a first-order lowpass filter in the loop,
and a single allpass filter. In [61], it is suggested to set the allpass delay length
to 6ms and the allpass coefficient to 0.7. Despite the fact that any allpass filter
does not add coloration in the magnitude frequency response, its time response
can give a metallic character to the sound, or add some unwanted roughness