[anthomtb]

I realize FM radio is strictly an example, but would you not rely on bandpass sampling? Where you sample at some multiple of your bandwidth and rely on the spectral replication effect to get your waveform.

Ref: https://en.wikipedia.org/wiki/Undersampling (funny enough, this article explicitly calls out the FM radio use case).

[immibis]

You need a very stable clock for that, which was also called out as a thing. With some PLLs you could lower the needed frequency. I think you're really looking for a small FPGA though.