varies periodically. Hence the magnitude response of the comb filter is periodic. The graphs show the magnitude response for various values of , demonstrating this periodicity. Some important properties: The response periodically drops to a local minimum (sometimes known as a notch), and periodically rises to a local maximum (sometimes known as a peak or a tooth). For positive values of , the first minimum occurs at half the delay period and repeat at even multiples of the delay frequency thereafter: . The levels of the maxima and minima are always equidistant from 1. When , the minima have zero amplitude. In this case, the minima are sometimes known as nulls. The maxima for positive values of coincide with the minima for negative values of , and vice versa. Impulse response The feedforward comb filter is one of the simplest finite impulse response filters. Its response is simply the initial impulse with a second impulse after the delay. Pole–zero interpretation Looking again at the -domain transfer function of the feedforward comb filter: the numerator is equal to zero whenever . This has solutions, equally spaced around a circle in the complex plane; these are the zeros of the transfer function. The denominator is zero at , giving poles at . This leads to a pole–zero plot like the ones shown. Feedback form Similarly, the general structure of a feedback comb filter is described by the difference equation: This equation can be rearranged so that all terms in are on the left-hand side, and then taking the transform: The transfer function is therefore: Frequency response Substituting into the -domain expression for the feedback comb filter: The magnitude response is as follows: Again, the response is periodic, as the graphs demonstrate. The feedback comb filter has some properties in common with the feedforward form: The response periodically drops to a local minimum and rises to a local maximum. The maxima for positive values of coincide with the minima for negative values of , and vice versa. For positive values of , the first maximum occurs at 0 and repeats at even multiples of the delay frequency thereafter: . However, there are also some important differences because the magnitude response has a term in the denominator: The levels of the maxima and minima are no longer equidistant from 1. The maxima have an amplitude of . The filter is only stable if is