Phasor
It is common terminology to call![$ z_0 = Ae^{j\phi}$](http://www.dsprelated.com/josimages_new/mdft/img623.png)
![$ z_1^n = e^{j\omega n T}$](http://www.dsprelated.com/josimages_new/mdft/img624.png)
For a real sinusoid,
![$\displaystyle x_r(n) \isdef A \cos(\omega n T+\phi),
$](http://www.dsprelated.com/josimages_new/mdft/img625.png)
![$ z_0 = Ae^{j\phi}$](http://www.dsprelated.com/josimages_new/mdft/img623.png)
![$ z_1^n = e^{j\omega n T}$](http://www.dsprelated.com/josimages_new/mdft/img624.png)
![$\displaystyle x_r(n) =$](http://www.dsprelated.com/josimages_new/mdft/img626.png)
![$\displaystyle \left\{z_0z_1^n\right\}
$](http://www.dsprelated.com/josimages_new/mdft/img627.png)
![$ \left\vert z_0\right\vert=A$](http://www.dsprelated.com/josimages_new/mdft/img628.png)
![$ \angle{z_0}=\phi$](http://www.dsprelated.com/josimages_new/mdft/img629.png)
When working with complex sinusoids, as in Eq.(4.11), the phasor
representation
of a sinusoid can be thought of as simply the
complex amplitude of the sinusoid. I.e.,
it is the complex constant that multiplies the carrier term
.
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Why Phasors are Important
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FM Spectra