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?


A frequency bin 'only' covers the value of its center frequency (+ potential spectral leaks to that center frequency). Is that correct?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.

In other words a frequency bin is affected by ALL frequencies except the center frequencies of the other bins.

You need to take into account that the FFT assumes that the signal is periodic with N. For a periodic signal contains only integer multiples of the fundamental frequency.

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  • $\begingroup$ ok. I am wondering about OFDM transmission. Before computing the IFFT on the transmitter side I modulate my data stream and interpret the corresponding complex values as frequency bins of a DFT-spectrum. I assumed that those values correspond to the amplitude and phase of the corresponding subcarrier. Taking into account what you said, those values are, however, the sum of contributions of many different frequencies... How can a subcarrier then be exactly modulated? $\endgroup$ – fl0ta'' Aug 9 '19 at 14:52
  • $\begingroup$ you're not reading Hilmar's answer closely enough, @fl0ta''! except the center frequencies of the other bins, which is exactly where the IFFT in the transmitter puts all the symbols. $\endgroup$ – Marcus Müller Aug 9 '19 at 14:59
  • $\begingroup$ The center frequencies of the bins do not affect each other, ok.. So the dft-bin is then the value of ONLY the center frequency of that bin? Or do the other frequencies in the bin-range contribute to that bin's value? I am not understanding something here... $\endgroup$ – fl0ta'' Aug 9 '19 at 15:07
  • $\begingroup$ If the signal is truly periodic, there cannot be any other frequencies other than the bin centers. If you shove any other frequency in there, it will show up in all bins. It's going to be largest in the bin that's closest in center frequency but it shows up everywhere. That's because the periodic repetition causes discontinuity at the edges and it's not a sine wave any more $\endgroup$ – Hilmar Aug 9 '19 at 19:12

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