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Modulation by a Complex Sinusoid
Figure:
System diagram for complex demodulation (frequencyshifting) by
.

Figure 9.12 shows the system diagram for complex
demodulation.^{10.2}The input signal
is multiplied by a
complex sinusoid to produce the frequencyshifted result

(10.8) 
Given a signal expressed as a sum of sinusoids,

(10.9) 
then the demodulation produces

(10.10) 
We see that frequency
is downshifted to
. In particular, frequency
(the
``center frequency'') is downshifted to dc.
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