The Linear Cochlear Model

The CARFAC model starts with a cascade of asymmetric resonators (CAR): linear two-pole– two-zero filters. We just need a recipe for how many sections to use, and how to set their coefficients to get a reasonable match to a linearized model of the human cochlea, at a range of levels.

The pole frequencies are chosen to correspond to equal spacing along the place dimension of the cochlea, by using the Greenwood map discussed in Chapter 14. The zeros are spaced a fraction of an octave above the pole frequencies.

Since we plan to extend this linear filter to incorporate nonlinearity through movement of the poles and zeros, we start with a filter form optimized to support that. A direct-form two-pole–two-zero filter stage with the input connected as shown in Figure 8.19 has a DC gain that does not vary as the coefficients are varied to move the poles. That implementation, referred to as PZFC in previous reports (Lyon et al., 2010b; Lyon, 2010), has been used in several applications of our cochlear modeling concept. But since the zeros don't move with the poles, it does not satisfy the physiologically observed condition that the impulse response zero crossings are very nearly unchanged with variation in level (Carney et al., 1999). For that, we need to move the zeros, too. The coupled form in Figure 16.1 makes it easy to move the zeros the same amount as the poles, which gives nearly the condition that we want.