A Digital Down Converter (DDC) is usually used to convert Real Digital Signals at a high frequency to baseband (centered around 0Hz). DDC does this so by producing negative and positive frequencies.

However, **at the same time**, perhaps using an approach as follows, is it possible to **downconvert** a real digital signal present at the DDC as well as **generate the corresponding I,Q** from it? How can we prove that it can be done? (mathematically or by other means)

[![enter image description here](https://i.stack.imgur.com/LjD6C.png)](https://i.stack.imgur.com/LjD6C.png)