Editing Discrete Fourier transform (section)

===Time and frequency reversal===
Reversing the time (i.e. replacing <math>n</math> by <math>N-n</math>){{
efn-ua|Time reversal for the DFT means replacing <math>n</math> by <math>N-n</math> and not <math>n</math> by <math>-n</math> to avoid negative indices.
}} in <math>x_n</math> corresponds to reversing the frequency (i.e. <math>k</math> by <math>N-k</math>).<ref name=ProakisManolakis/>{{rp|p.421}} Mathematically, if <math>\{x_n\}</math> represents the vector '''x''' then

:if <math>\mathcal{F}(\{x_n\})_k=X_k</math>
:then <math>\mathcal{F}(\{ x_{N-n} \})_k=X_{N-k}</math>