Amplitude Response

Definition. The amplitude response $G(\omega)$ of an LTI filter is defined as the magnitude (or modulus) of the (complex) filter frequency response $H(e^{j\omega T})$, i.e.,

$$\zbox {G(\omega) \isdefs \left\vert H(e^{j\omega T})\right\vert.}$$

Another common name for the amplitude response is magnitude frequency response.

The real-valued amplitude response $G(\omega)$ specifies the amplitude gain that the filter provides at each frequency $\omega T \in[-\pi,\pi]$.