En algunas ocasiones se define la transformada con un factor multiplicativo diferente de ${\displaystyle \textstyle {\frac {1}{\sqrt {2\pi }}}}$, siendo frecuente en ingeniería el uso de un factor unidad en la transformada directa y un factor de ${\displaystyle \textstyle {\frac {1}{2\pi }}}$ en la transformada inversa. A continuación se lista una tabla de funciones y sus transformadas de Fourier con un factor unidad. Si se desea utilizar otro factor, sólo debe multiplicar la segunda columna por ese factor.

${\displaystyle \delta (t)\!}$ ${\displaystyle 1\!}$
${\displaystyle u(t)\!}$ (Función unitaria de Heaviside) ${\displaystyle 1/2(\delta (f)+1/(i\pi f))\!}$
${\displaystyle \sin(w_{0}t)\!}$ ${\displaystyle {\frac {\pi }{i}}[\delta (w-w_{0})-\delta (w+w_{0})]\!}$
${\displaystyle \cos(w_{0}t)\!}$ ${\displaystyle \pi [\delta (w-w_{0})+\delta (w+w_{0})]\!}$
${\displaystyle 1\!}$ ${\displaystyle \delta (f)=2\pi \delta (w)\!}$
${\displaystyle e^{-at}u(t),\quad \mathrm {Re} (a)>0\!}$ ${\displaystyle {\frac {1}{a+iw}}\!}$
${\displaystyle e^{-a|t|},\!}$ ${\displaystyle {\frac {2a}{a^{2}+w^{2}}}\!}$
${\displaystyle te^{-at}u(t),\quad \mathrm {Re} (a)>0\!}$ ${\displaystyle {\frac {1}{(a+iw)^{2}}}\!}$
${\displaystyle {\begin{cases}\cos w_{0}x&|x|\leq A\\0&|x|>A\end{cases}}}$ ${\displaystyle {\frac {\sin A(w-w_{0})}{2\pi (w-w_{0})}}+{\frac {\sin A(w+w_{0})}{2\pi (w+w_{0})}}}$
${\displaystyle x(t)={\begin{cases}1,&{\mbox{si }}|t|T_{1}\end{cases}}\!}$ ${\displaystyle 2T_{1}\mathrm {sinc} \left({\frac {wT_{1}}{\pi }}\right)=2{\frac {\sin(wT_{1})}{w}}}$
${\displaystyle x(t)=\mathrm {tri} \left({\frac {t}{2T_{1}}}\right)={\begin{cases}1-{\frac {|t|}{T_{1}}},&{\mbox{si }}|t|T_{1}\end{cases}}\!}$ ${\displaystyle \mathrm {sinc} ^{2}\left({\frac {wT_{1}}{\pi }}\right)}$
${\displaystyle x(t)=e^{-t^{2}/a^{2}},\quad \mathrm {Im} (a)=0\!}$ ${\displaystyle {\frac {a}{\sqrt {2}}}e^{-a^{2}w^{2}/4}}$