Amplitude Response

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Definition: The amplitude response of a filter is defined as the magnitude of the frequency response

$\displaystyle G(k) \isdef \left\vert H(\omega_k)\right\vert.$

From the convolution theorem, we can see that the amplitude response

is the gain of the filter at frequency $\omega_k$ , since

$\displaystyle \left\vert Y(\omega_k)\right\vert = \left\vert H(\omega_k)X(\omega_k)\right\vert = G(k)\left\vert X(\omega_k)\right\vert,$

where $X(\omega_k)$ is the

th sample of the DFT of the input signal

, and

is the DFT of the output signal

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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