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Embedded SystemsFPGAElectronics

Introduction to Digital Filters
    Frequency Response Analysis
       Amplitude Response

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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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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


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