# Contributions to a DFT frequency bin

So, a frequency bin is centered around an interesting frequency $$f_0$$. Assume the spectrum is such that there is no spectral leakage from other frequencies to that specific frequency $$f_0$$. Now. I center a frequency bin around f0. The value (magnitude) of this bin is then the value of EXACTLY this frequency $$f_0$$ and is not affected by non-zero frequency values (magnitudes) of frequencies that also lie in that bin's range. A frequency bin 'only' covers the value of its center frequency (+ potential spectral leaks to that center frequency).

Is that correct?

No. All frequencies show up in all frequency bins EXCEPT frequencies that are an integer multiple of $$f_{\Delta}=f_s/N_{FFT}$$ sample rate divided by FFT length.