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
Given a signal expressed as a sum of sinusoids,
then the demodulation produces
We see that frequency is down-shifted to . In particular, frequency (the ``center frequency'') is down-shifted to dc.
Making a Bandpass Filter from a Lowpass Filter
The Running-Sum Lowpass Filter