Editing Discrete Fourier transform (section)

===Real and imaginary part===
This table shows some mathematical operations on <math>x_n</math> in the time domain and the corresponding effects on its DFT <math>X_k</math> in the frequency domain.

{| class="wikitable"
|-
! Property
! Time domain<br /><math>x_n</math>
! Frequency domain<br /><math>X_k</math>
|-
| Real part in time
| <math>\operatorname{Re}{\left(x_n\right)}</math>
| <math>\frac{1}{2}\left(X_k + X^*_{N-k}\right)</math>
|-
| Imaginary part in time
| <math>\operatorname{Im}{\left(x_n\right)}</math>
| <math>\frac{1}{2i}\left(X_k - X^*_{N-k}\right)</math>
|-
| Real part in frequency
| <math>\frac{1}{2}\left(x_n + x^*_{N-n}\right)</math>
| <math>\operatorname{Re}{\left(X_k\right)}</math>
|-
| Imaginary part in frequency
| <math>\frac{1}{2i}\left(x_n - x^*_{N-n}\right)</math>
| <math>\operatorname{Im}{\left(X_k\right)}</math>
|}