### Plotting Complex Sinusoids versus Frequency

As discussed in the previous section, we regard the signal

as a positive-frequency sinusoid when . 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 at the point , 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 in spectral plots, the plotted vector may be rotated by the angle in the plane orthogonal to the frequency axis passing through , as done in Fig.4.16b below (p. ) for phase angles .

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