Time Reversal

For any complex signal $x(n)$, $n\in(-\infty,\infty)$, we have

$$\zbox {\hbox{\sc Flip}(\overline{x}) \;\longleftrightarrow\;\overline{X}}$$

where $\hbox{\sc Flip}_n(x)\isdef x(-n)$, and $\overline{x(n)}$ denotes the complex conjugate of $x(n)$. In the typical special case of real signals ( $x(n)\in{\bf R}$), we have

$$\zbox {\hbox{\sc Flip}(x) \;\longleftrightarrow\;\overline{X}}$$

Thus, reversing a signal in time congugates its spectrum.