structural:summarization
Frequency shifting

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