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:

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

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.