You can create DC-centered spectra for even-sized input sequences by negating the odd elements of the input sequence.
You cannot create DC-centered spectra by directly negating the odd elements of an input time-domain sequence containing an odd number of elements because the Nyquist frequency appears between two frequency bins. To create DC-centered spectra for odd-sized input sequences, you must rotate the FFT arrays by the amount given in the following relationship:
For a DC-centered spectrum created from an odd-sized input sequence, the following equation computes x0.
