### Modulation by a Complex Sinusoid

Figure 9.12 shows the system diagram for complex demodulation.10.2The input signal is multiplied by a complex sinusoid to produce the frequency-shifted 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 down-shifted to . In particular, frequency (the center frequency'') is down-shifted to dc.

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