From what I have read it seems that FPAA could provide a way to design a "programmable" analog computer, but are there any online resources on how to implement such a system?
Electronic – Use of Field Programmable Analog Arrays for analog computation
analog
Related Solutions
Jim Williams and friends, Analog Circuit Design.
Bob Pease, Troubleshooting Analog Circuits. Despite the name, this is as much about design as it is about troubleshooting.
OK now I'm confident to answer this: -
Analogue cable radio doesn't use FM or AM transmission - it uses data from a coax coming into your home.
If you do have analogue radios that work the traditional way you can buy small FM transmitters (intended for iPhone to car radio connections) just like these
You can get cheaper ones that just take an audi input jack too.
If you are still intent on making an FM transmitter (mono for simplicity) here's a link to a design site with several on.
Best Answer
Don't expect to build analog computers.
They are mainly useful for custom reconfigurable analog filters & some schemes with opamps, that's it.
Can't suggest any resources except datasheeds on your chips :-)