Amplitude Response
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.
$](http://www.dsprelated.com/josimages_new/mdft/img1545.png)
![$ G(k)$](http://www.dsprelated.com/josimages_new/mdft/img1546.png)
![$ \omega_k$](http://www.dsprelated.com/josimages_new/mdft/img677.png)
![$\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,
$](http://www.dsprelated.com/josimages_new/mdft/img1547.png)
![$ X(\omega_k)$](http://www.dsprelated.com/josimages_new/mdft/img680.png)
![$ k$](http://www.dsprelated.com/josimages_new/mdft/img20.png)
![$ x(n)$](http://www.dsprelated.com/josimages_new/mdft/img45.png)
![$ Y$](http://www.dsprelated.com/josimages_new/mdft/img1442.png)
![$ y$](http://www.dsprelated.com/josimages_new/mdft/img26.png)
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Phase Response
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Frequency Response
Definition: The amplitude response of a filter is defined as
the magnitude of the frequency response