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.

Figure 2.23: The feedforward comb filter.

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

$$y(n) = b_0 x(n) + b_M x(n-M). \protect$$ (3.2)

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 $b_0=1$ and $b_M=g$ . 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'' $b_0 x(n)$ plus an attenuated, delayed signal $b_M x(n-M)$ , where the attenuation (by $\vert b_M\vert<1$ ) is due to ``air absorption'' and/or spherical spreading losses, and the delay is due to acoustic propagation over the distance $cMT$ meters, where $T$ is the sampling period in seconds, and $c$ is sound speed. In cases where the simulated propagation delay needs to be more accurate than the nearest integer number of samples $M$ , 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 $b_M$ can be replaced by a linear, time-invariant filter $G(z)$ giving a different attenuation at every frequency. Due to the physics of air absorption, $G(z)$ is generally lowpass in character [352, p. 560], [47,321].