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Phase and Group Delay

In the previous sections we looked at the two most important frequency-domain representations for LTI digital filters, the transfer function $ H(z)$ and the frequency response:

$\displaystyle H(e^{j\omega T}) \isdefs \left.H(z)\right\vert _{z=e^{j\omega T}}

We looked further at the polar form of the frequency response $ H(e^{j\omega T})=
G(\omega)e^{j\Theta(\omega)}$ , thereby breaking it down into the amplitude response $ G(\omega)$ times the phase-response term $ e^{j\Theta(\omega)}$ .

In the next two sections we look at two alternative forms of the phase response: phase delay and group delay. After considering some examples and special cases, poles and zeros of the transfer function are discussed in the next chapter.

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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition)
Copyright © 2024-05-20 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University