# Tapped delay line

A tapped delay line is a collection of simple delays with various gains and amounts of delay. A discrete output signal y(k) of a tapped delay line with N taps is computed from the input x(k) with the formula

$$y(k)=x(k)+g_1\, x(k-M_1 )+g_2 \, x(k-M_2 )+⋯+g_N \, x(k-M_N)$$

where gn are the gains and Mn are the delays in number of samples.

This formula computes the output as the sum of many repetitions of the input signal with various delays and gains (decays). This effect may be similar to the echo or a feedback comb filter, but it may be very different, as here there is no relationship between the gains gn or the delays Mn and there is only a finite number of repetitions N.

The tapped delay line is usually used to model the early reflections of reverb – the initial distinct repetitions in the first 100 ms or so of the reverb. The remaining portion of the reverb is modeled separately with, for example, the Shroeder reverb. By itself, the tapped delay line is simply a multitap delay, but without any feedback.

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