72
D. Rocchesso: Sound Processing
-m
m
a
0
m
m
m
m
1
2
3
N-2
N-1
a
a
a
1
2
N
a
N-1
1
(a)
(b)
-d
1
6
5
4
3
2
N
+
+
+
+
+
+
z
+
+
z
x(n)
A
y(n)
C
C
C
C
C
C
Figure 14: Moorer's reverberator
and granularity. The feedback attenuation coefficients g
i
and the lowpass filters
of the comb filters can be tuned to resemble a realistic and smooth decay. In
particular, the attenuation coefficients g
i
determine the overall decay time of the
series of echoes generated by each comb filter. If the desired decay time (usually
defined for an attenuation level of 60dB) is T
d
, the gain of each comb filter has
to be set to
g
i
= 10
-3
TdFs
mi
,
(39)
where F
s
is the sample rate and m
i
is the delay length in samples. Further at-
tenuation at high frequencies is provided by the feedback lowpass filters, whose
coefficient can also be related with decay time at a specific frequency or fine
tuned by direct experimentation. In [61], an example set of feedback attenua-
tion and allpass coefficients is provided, together with some suggested values
of the delay lengths of the comb filters. As a rule of thumb, they should be
distributed over a ratio 1 : 1.5 between 50 and 80ms. Schroeder suggested a
number-theoretic criterion for a more precise choice of the delay lengths [91]:
the lengths in samples should be mutually coprime (or incommensurate) to re-
duce the superimposition of echoes in the impulse response, thus reducing the
so called flutter echoes. This same criterion might be applied to the distances
between each echo and the direct sound in early reflections. However, as it was
noticed by Moorer [61], the results are usually better if the taps are positioned
according to the reflections computed by means of some geometric modeling
technique, such as the image method [3, 18]. Indeed, even the lengths of the
recirculating delays can be computed from the geometric analysis of the normal
modes of actual room shapes.
Feedback Delay Networks
In 1982, J. Stautner e M. Puckette [101] introduced a structure for artificial
reverberation based on delay lines interconnected in a feedback loop by means
of a matrix (see fig. 15). Later, structures such as this have been called Feedback