The frequency response of a comb filter is Hcomb(z) evaluated on the unit circle. We start by substituting ejw for z in Hcomb(z) from Eq. (7-2), because z = ejw defines the unit circle, giving
Factoring out the half-angled exponential e–jwN/2, we have
Using Euler's identity 2jsin(a) = eja – e–ja, we arrive at
Replacing j with ejp/2, we have
Determining the maximum magnitude response of a filter is useful in DSP. Ignoring the phase shift term (complex exponential) in Eq. (G-4), the frequency-domain magnitude response of a comb filter is
with the maximum magnitude being 2.