Plotting Complex Sinusoids versus Frequency
As discussed in the previous section, we regard the signal
as a
positive-frequency sinusoid when
![$ \omega_x>0$](http://www.dsprelated.com/josimages_new/mdft/img472.png)
. In a
manner analogous to spectral magnitude plots (discussed in
§
4.1.6), we can plot this
complex sinusoid over a frequency
axis as a vertical line of length
![$ A_x$](http://www.dsprelated.com/josimages_new/mdft/img473.png)
at the point
![$ \omega=\omega_x$](http://www.dsprelated.com/josimages_new/mdft/img474.png)
, as shown in Fig.
4.10. Such a plot of
amplitude versus frequency may be called a
spectral plot, or
spectral representation [
44] of the (
zero-phase)
complex sinusoid.
figure[htbp]
More generally, however, a complex sinusoid has both an amplitude and
a phase (or, equivalently, a complex amplitude):
To accommodate the phase angle
![$ \theta_x$](http://www.dsprelated.com/josimages_new/mdft/img476.png)
in spectral plots, the
plotted vector may be rotated by the angle
![$ \theta_x$](http://www.dsprelated.com/josimages_new/mdft/img476.png)
in the plane
orthogonal to the frequency axis passing through
![$ \omega_x$](http://www.dsprelated.com/josimages_new/mdft/img477.png)
, as done
in Fig.
4.16b below (p.
![[*]](../icons/crossref.png)
)
for phase angles
![$ \theta_x=\pm \pi/2$](http://www.dsprelated.com/josimages_new/mdft/img478.png)
.
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