How to transform a streaming IP video into a CATV signal?
I wanted to create a circuit,

Um, no. What you describe encompasses at least one relatively beefy computer that has a network interface and runs an operating system with a network stack.

What kind of things should I start to learn and where.

Honestly, &quot;recognizing things you can and cannot build with your current resources&quot; is what you should learn first.
Essentially, you're saying &quot;I want to build a high-bandwidth SDR and a cable television encoder; then some amplifiers to supply a CATV network, potentially&quot;.
You, however, don't seem to be aware of much of the underlying technology. It would indicate that the first thing you'd need to learn is how to look up things!
For example, &quot;Cable TV&quot; is an article on Wikipedia, and you might want to look into the standards mentioned there.
Then, you'd look up the standards (and will hopefully decide that implementing them yourself is a job for a group of experienced engineers with lots of background in the field, not for a one-off project), and then look for existing products or implementations.
There's ready-to-buy Cable TV modulators, and that's very likely the route you want to take (PC to receive your video stream + GPU + Modulator). If you actually want to build an SDR system of your own, you'd start looking for DVB-C implementations on the internet (you'll find a lot about GNU Radio).