Section G.1. FREQUENCY RESPONSE OF A COMB FILTER

G 1 FREQUENCY RESPONSE OF A COMB FILTER

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

Equation G-2

Using Euler's identity 2jsin(a) = eja – e–ja, we arrive at

Equation G-3

Replacing j with ejp/2, we have

Equation G-4

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

Equation G-5

with the maximum magnitude being 2.

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Understanding Digital Signal Processing
Understanding Digital Signal Processing (2nd Edition)
ISBN: 0131089897
EAN: 2147483647
Year: 2004
Pages: 183
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