Comb filter

In signal processing, a comb filter adds a delayed version of a signal to itself, causing constructive and destructive interference. The frequency response of a comb filter consists of a series of regularly spaced notches, giving the appearance of a comb.

Comb filters are used in a variety of signal processing applications. These include:

In acoustics, comb filtering can arise in some unwanted ways. For instance, when two loudspeakers are playing the same signal at different distances from the listener, there is a comb filtering effect on the signal. In any enclosed space, listeners hear a mixture of direct sound and reflected sound. Because the reflected sound takes a longer path, it constitutes a delayed version of the direct sound and a comb filter is created where the two combine at the listener.

Comb filters exist in two different forms, feedforward and feedback; the names refer to the direction in which signals are delayed before they are added to the input.

Comb filters may be implemented in discrete time or continuous time; this article will focus on discrete-time implementations; the properties of the continuous-time comb filter are very similar.

The general structure of a feedforward comb filter is shown on the right. It may be described by the following difference equation:

where ${\displaystyle K}$ is the delay length (measured in samples), and ${\displaystyle \alpha }$ is a scaling factor applied to the delayed signal. If we take the Z transform of both sides of the equation, we obtain:

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