### Feedforward Comb FilterAmplitude Response

Comb filters get their name from the comb-like'' appearance of their amplitude response (gain versus frequency), as shown in Figures 2.25, 2.26, and 2.27. For a review of frequency-domain analysis of digital filters, see, e.g., [449].

The transfer function of the feedforward comb filter Eq.(2.2) is

 (3.3)

so that the amplitude response (gain versus frequency) is

 (3.4)

This is plotted in Fig.2.25 for , , and , , and . When , we get the simplified result

In this case, we obtain nulls, which are points (frequencies) of zero gain in the amplitude response. Note that in flangers, these nulls are moved slowly over time by modulating the delay length . Doing this smoothly requires interpolated delay lines (see Chapter 4 and Chapter 5).
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