### Modulation by a Complex Sinusoid

Figure 9.12 shows the system diagram for *complex
demodulation*.^{10.2}The 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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The Running-Sum Lowpass Filter