DAFX: Digital Audio Effects, Second Edition

2.5 Basic Delay Structures

2.5.1 FIR Comb Filter

The A network that simulates a single delay is called a FIR comb filter. The input signal is delayed by a given time duration. The effect will be audible only when the processed signal is combined (added) to the input signal, which acts here as a reference. This effect has two tuning parameters: the amount of time delay τ and the relative amplitude of the delayed signal to that of the reference signal. The difference equation and the transfer function are given by

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The time response of this filter is made up of the direct signal and the delayed version. This simple time-domain behavior comes along with interesting frequency-domain patterns. For positive values of g, the filter amplifies all frequencies that are multiples of 1/τ and attenuates all frequencies that lie in-between. The transfer function of such a filter shows a series of spikes and it looks like a comb (Figure 2.27), hence the name. For negative values of g, the filter attenuates frequencies that are multiples of 1/τ and amplifies those that lie in-between. The gain varies between 1 + g and 1 − g [Orf96]. The following M-file 2.5 demonstrates a sample-by-sample ...