Dealing with spectral leakage between two frequency bins I'm looking for two signals embedded in very noisy data. I know they are close to periodic and integral with the run, but are rather close (30s and 21s during a 210s measurement), and our sampling rate is low (1.25s). We have multiple observations to work with per sample.

I am wondering how I might deal with the problem of spectral leakage: it is evident in the FFT of our samples. Since our two signals of interest are so close together (10 and 7 cycles per measurement), it may well be that spectral power is leaking from the stronger of the two signals into the weaker one.

Will zero-padding with a window (rectangular or hamming) allow us to define a boundary between the two signal? Would another approach would be to concatenate these observations, driving the periodicities further apart (20 and 14)?

Thanks for your help, joseph
Yes, concatenating the data will greatly reduce the spectral leakage problem.  There will still be spectral leakage of course, but there will be more bins in between your signals-of-interest, so they won't leak as much into each other.

And yes, windowing should help too.  You are already using a "rectangular" window.  I would suggest trying other windows such as Hamming.