So to start off with what data I have - for one day, every few hours there's a small interval (~1 minute) in which there's less than 50 measurements (unevenly spread) of the amplitude of the signal. The signal is not periodic.
What I'm trying to figure out is what's the best way to get what frequencies appear in the signal over one day using some form of FT on the data. I'm familiar with what FT is and what it does, but I have never applied it to any real scenario, especially not one like this. Should I do FT on each interval seperately and then get some kind of average of the frequencies for the given day, or what is the best approach?
Feel free to ask more about the data, I didn't want to go into too much detail.
There are methods for taking the fft of unevenly sampled data. They do some approximations, but it will probably be good enough for what you need. (https://scicomp.stackexchange.com/questions/593/how-do-i-take-the-fft-of-unevenly-spaced-data)
So yes, I think you'll want to take the fft for each 1 min interval and average them over the course of a day..or how ever long you need to. That's pretty much all you CAN do.