I am using fft to plot the signal spectrum (convert real and imaginary components to amplitude values). If my signal is of odd length, I take $fft[0]$ as DC and use $fft[1;(N-1)/2)]$ values to get the amplitudes of the harmonics (from 1 Hz to (N-1)/2 Hz). But if my signal is of even length, the $fft$ element with index $fft[N/2]$ represents Nyquist frequency. Is it correct to use this frequency when plotting the amplitudes spectrum? Or in this case I should only consider elements in the range $fft[1; N/2-1]$ and DC at $fft[0]$?

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    $\begingroup$ It depends on what you are using the results for. As demonstrated in this link: dsp.stackexchange.com/questions/82273/… the Nyquist bin when shared (for even length sequences) can be split (in complex conjugate halves) between the positive and negative spectrum in situations where we need a components at each location, since that spectral location is the same. $\endgroup$ Commented Feb 7, 2023 at 17:32
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    $\begingroup$ What @DanBoschen said, except that in a lot of circumstances, if you have bins with significant energy in your FFT all the way up to the Nyquist frequency, then that's a strong indication that your real signal was aliased, and those frequency bins aren't valid anyway. $\endgroup$
    – TimWescott
    Commented Feb 8, 2023 at 15:43
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    $\begingroup$ Yes a most excellent point. What @TimWescott said, for all cases with real signals $\endgroup$ Commented Feb 8, 2023 at 17:22


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