information:filtering, stylistic:style_transfer, information:highlighting
Time shifting

f (x − x 0) ⟺ F e − i 2 π x 0 ξ f ^ (ξ); x 0 ∈ R {\displaystyle f(x-x_{0})\ \ {\stackrel {\mathcal {F}}{\Longleftrightarrow }}\ \ e^{-i2\pi x_{0}\xi }\ {\widehat {f}}(\xi);\quad \ x_{0}\in \mathbb {R} }