FFT - How is the signal distributed between different frequency bins?

Let's say I have a sampling rate of 1000 GHz and an 8192 FFT size. My frequency resolution is then 122MHz. So the first FFT bin would represent 0 Hz, the second 122MHz, the third 244 MHz and so on. Let's say my signal has a frequency of 183 MHz. Into which bin would it fall? What if it was slightly greater or slightly smaller but still between the frequencies of the second and third bins? Does it all get sent into one bin or is there some sort of distributive algorithm in place when using matlab's FFT function?

Answer 1

[dpb]

The frequency bins are fixed by the sampling rate; the magnitude of each bin is determined by the computation of the fourier coefficient from the signal for each bin. A noise-free signal that happened to be halfway between two bins will have half its energy in each; to get the total energy of the peak one has to integrate over the width of the peak. When noise is present and with a mixture of frequencies and with the effects of finite signal length, etc., energy is "smeared" across bins.

It's easy enough to see the effects if you just take, for example, the PSD example at doc fft and move the frequency of the signal around with and with out noise and/or change the FFT binning. Some months ago I did quite an illustration of this for another poster and posted a link to that Answer again within the last couple of weeks...