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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.,

$\displaystyle \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]$ .


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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA