62
D. Rocchesso: Sound Processing
allpass comb filter
-1
0
1
-1
-0.5
0
0.5
1
Re
Im
Figure 7: Zeros and poles of an IIR comb filter
z
-g
g
x
y
-m
Figure 8: Allpass comb filter
to see that the transfer function of the filter of fig. 8, called the allpass comb
filter can be written as
H(z) =
-g + z
-m
1 - gz
-m
,
(26)
which has the structure of an allpass filter. It is interesting to note that the
direct path introduces a nonzero sample at the time instant zero in the impulse
response. All the following samples are just a scaled version of those of the
impulse response of the comb filter, with a scaling factor equal to 1 - g
2
. The
time properties, such as the time decay, are substantially unvaried. The allpass
comb filter does not introduce any coloration in stationary signals. On the other
hand, its effect is evident on signals exhibiting rapid transients, and for these
signals we can not state that the filter is transparent.
3.5
Sound Effects Based on Delay Lines
Many of the effects commonly used in electroacoustic music are obtained by
composition of time-varying delay lines, i.e., by lines whose length is modulated
by slowly-varying signals. In order to avoid discontinuities in the signals, it is
necessary to interpolate the delay lines in some way. The interpolation by means
of allpass filters is applicable only for very slow modulations or for narrow-width
modulations, since sudden changes in the state of allpass filters give rise to tran-
sients that can be perceived as signal distortions [30]. On the other hand, linear
(or, more generally, polynomial) interpolation introduces frequency-dependent