Digital Allpass Filter

The allpass filter has the unique property that it passes all frequencies equally. This property makes it useful in reverberator design because it increases echo density while reducing signal coloration (an allpass filter is NOT transparent to transient signals, as it does have a phase response). The basic transfer function of an allpass filter is

In a pole-zero plot, the poles and zeros occupy conjugate reciprocal locations. The proof of the flat frequency response is as follows:

The structure of an allpass filter is similar to the comb filter, but it contains an additional feedforward path. The structure is shown in Figure 1, and the impulse response is shown in Figure 2. The delay can be any positive number of samples and still feature a flat frequency response.

Figure 1: Flow diagram of an allpass filter.

Figure 2: Impulse response of an allpass filter.

In reverb applications, the delay used in an allpass filter is generally measured in milliseconds. This keeps the 'reflections' spaced apart in a similar fashion to a room's impulse response.