What can be said about the nature of the noise by looking at this spectrum?
Looks like you're in 50Hz-land, observing that there are about 10 cycles in 0.2 seconds in the second graph.

If whatever 50Hz signal you have is rich in harmonic content, the tenth harmonic will be pretty close to your sampling frequency. In fact I'll speculate it's 3.1Hz away (and will move around as the mains frequency drifts under load).

There's a reason sample data systems always need an anti-aliasing filter.

If you're not interested above 10Hz, you can use it to attenuate 50Hz too.