I have a time series and apply the FFT to get a spectrum.
Let's assume that my sampling frequency and the length of the time sample are chosen such that I end up with a $\Delta f = 0.1$ Hz.
As this is still rather noisy, I'd like to change $\Delta f$ to 0.5 Hz a posteriori.
How do I combine the fourier components of the adjacent bins? Am I right to just sum them? Or do I take the square root of the sum of squares? Is there a term for what I am trying to achieve, so that I can find some references on my own?