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I have an FFT of a radio signal, to look at "what's happening" in the frequency domain. I'm interested in signals that are "wide enough", eg 1MHz, and thus would like to smooth the result to filter out narrow changes/noise, eg over less than 0.25MHz.

Should I simply use bigger bins for my FFT, or should I use smaller bins but then use a filter, eg a filter Savitzky-Golay? Does it depend on the type of signal/data?

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You should use a windowed FFT. Maybe a Gaussian that is nonzero over 75% of the FFT size. A single perfect sinewave would then show up as a signal with a significant width - but with a Gaussian shape. You would need to compute many more transforms if you want sensitivity. The window of transform N should have its 6 dB point at the 6 dB point of the window of transform N+1. (Maybe even 3 dB points.) I call this "sliding FFT" and it is a way to produce extremely sensitive power spectra and waterfall graphs.

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