Linearity

$$\zbox{\alpha x_1 + \beta x_2 \leftrightarrow \alpha X_1 + \beta X_2}$$

or

$$\begin{eqnarray*} \hbox{\sc DFT}(\alpha x_1 + \beta x_2) & = & \alpha\cdot \hbox{\sc DFT}(x_1) + \beta \cdot\hbox{\sc DFT}(x_2) \\ \alpha, \beta & \in & \mathbb{C}\\ x_1, x_2, X_1, X_2 & \in & \mathbb{C}^N \end{eqnarray*}$$

The Fourier Transform ``commutes with mixing.''