Feedforward Comb Filters

The *feedforward comb filter* is shown in Fig.2.23. The
direct signal ``feeds forward'' around the delay line. The output
is a linear combination of the direct and delayed signal.

The ``difference equation'' [452] for the feedforward comb filter is

We see that the feedforward comb filter is a particular type of FIR filter. It is also a special case of a TDL.

Note that the feedforward comb filter can implement the echo simulator
of Fig.2.9 by setting
and
. Thus, it is is a
*computational physical model* of a single discrete echo. This
is one of the simplest examples of acoustic modeling using signal
processing elements. The feedforward comb filter models the
superposition of a ``direct signal''
plus an attenuated,
delayed signal
, where the attenuation (by
) is
due to ``air absorption'' and/or spherical spreading losses, and the
delay is due to acoustic propagation over the distance
meters,
where
is the sampling period in seconds, and
is sound speed.
In cases where the simulated propagation delay needs to be more
accurate than the nearest integer number of samples
, some kind of
*delay-line interpolation* needs to be used (the subject of
§4.1). Similarly, when air absorption needs to be
simulated more accurately, the constant attenuation factor
can
be replaced by a linear, time-invariant filter
giving a
different attenuation at every frequency. Due to the physics of air
absorption,
is generally lowpass in character [352, p. 560], [47,321].

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