# Engineering Tables/DFT Transform Properties

Notation ${\displaystyle {\tilde {x}}[n]}$ ${\displaystyle {\tilde {x}}[k]}$ periodic with period N
Linearity ${\displaystyle a_{1}{\tilde {x}}_{1}[n]+a_{2}{\tilde {x}}_{2}[n]\ }$ ${\displaystyle a_{1}{\tilde {X}}_{1}[k]+a_{2}{\tilde {X}}_{2}[k]\ }$
${\displaystyle {\tilde {X}}[n]}$ ${\displaystyle N{\tilde {x}}[-k]}$
Time shifting ${\displaystyle {\tilde {x}}[n-m]\ }$ ${\displaystyle W_{N}^{km}{\tilde {X}}[k]\ }$