I haven't used anything like this is a while, but when I did, I used software and hardware called EyeTV.
I can't remember which version I have, but the hardware looked just like the one here:
Enjoy stunning quality HDTV on your Mac with EyeTV Hybrid. EyeTV Hybrid receives digital and analog TV by antenna or cable, so it not only turns your Mac into the world's most affordable flat-screen HDTV and DVR, it is also an excellent solution for the Digital Transition. EyeTV Hybrid also featu...
www.amazon.com
It came with a composite A/V dongle and has built in F-connector for RF, and plugged into the Mac using USB.
It was perfect for getting digital copies of old VHS tape.
It also had a DVR feature on it too.
I would bet that there is an updated version of this.