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In digital signal processing, a digital down-converter (DDC) converts a digitized real signal centered at an intermediate frequency (IF) to a basebanded complex signal centered at zero frequency
What is the difference between a real signal and a complex signal?
A complex signal is an analytic signal that is represented by samples that are complex numbers instead of real numbers.
Analog downconverter exist; they work just like a digital down-converter, but mixing and filtering are done :with analog components. Downsampling isn't present because there is no sampling.