# How to combine bins of my DFT

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?

• what is the statistical model of noise ? – AlexTP May 22 '17 at 8:49
• I don't have one. the background to question is that i plot the spectrum. i would like it to be more visually pleasing, while still being essentially correct and taking advantage of the fact that I have the data at a higher resolution in principle. – fft_newbie May 22 '17 at 9:04
• "essentially correct", however, depends on whether you correctly represent your signal or noise, and that can only be said about something that you have a model for. There's no "universally right" approach here, you need to model things. – Marcus Müller May 22 '17 at 9:05
• to be quite frank, I dont know how to get a precise model. The only thing I can say is that it is vibration data, and I'm interested in frequencies below 200 Hz. I assume the signal to be the superposition of sines and some white noise (I guess). Could you give me some keywords regarding to what exactly you mean with a model, and especially on how then to decide how to combine the frequency bins based on that model? – fft_newbie May 22 '17 at 12:28