#### Summing two signals

Comb filtering occurs when two audio signals are summed together with the difference in very small delay between them. This effect tends to happen a lot when two or more microphones are picking up the same audio signal. They then summit together to the same output. In other words, it can be stated that the comb filter is the result of the phase offset in the summed audio signal. The difference in the path lengths to the microphones causes this. This also results in multiple arrival times for the same signal at the summation point of the audio circuit.

#### Linear Time/Invariant

A comb filter is a Linear Time-Invariant (LTI) digital filter. Here, linear means that its output to a scaled sum of input digital signals is equal to the scaled sum of the outputs to every one of these input signals (i.e., the filter satisfies the superposition principle). In addition, Time-invariant means that, for any input signal that has a given delay, the output undergoes the same delay as the input.

The name comb is derived by the fact that its magnitude response resembles the teeth of a comb. Since there are several filters having magnitude responses with such characteristic, the term comb filter is rather general. The duration of the impulse response of comb filters can be either finite or infinite, i.e., there are Finite Impulse Response (FIR) comb filters and Infinite Impulse Response (IIR) comb filters.

#### Notches in a repeating pattern

In the audio signal processing term, the comb filter is a type of audio filter whose response curve contains a series of notches in a repeating pattern. Such filters produce a characteristic modification of an input audio signal. This results in a sound similar to listening with a long cardboard tube placed to one’s ear. Comb filters are seldom produced using discrete notch filters for each notch.

The easy way to do such filtering is to either delay the input signal or alter its phase. Then, one should mix this in some proportion with the original signal. If such a filter is varied over time so that the notches move up and down the frequency spectrum as a group, an effect known as flanging or phasing results. Comb filters also sometimes create formant effects. A visual appearance of comb filter has multiple regularly spaced narrow passbands giving the and form the appearance of a comb.

#### Feedback Comb Filter

There are variations of the comb filters and one of them to mention would be a feedback comb filter. The feedback comb filter is a special case of an Infinite Impulse Response (IIR) (“recursive”) digital filter, since there is feedback from the delayed output to the input. One can regard the feedback comb filter as a computational physical model of a series of echoes. It exponentially decays and uniformly spaces in time.

#### Additional Resources & Source Texts

https://www.dsprelated.com/freebooks/pasp/Comb_Filters.html