### Modulation by a Complex Sinusoid

Figure 8.12 shows the system diagram for *complex
demodulation*.^{9.2}The input signal is multiplied by a
complex sinusoid to produce the frequency-shifted result

Given a signal expressed as a sum of sinusoids,

*down-shifted*to . In particular, frequency (the ``center frequency'') is down-shifted to

*dc*.

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