Fourier Transform Symmetries

#Math

$\displaystyle f(t)\text{ even} \leftrightarrow F(j\omega)\text{ even}$

$\displaystyle f(t)\text{ odd} \leftrightarrow F(j\omega)\text{ odd}$

$\displaystyle f(t) \text{ real} \leftrightarrow F(-j\omega)=F^{*}(j\omega)$

$\displaystyle f(t)\text{ imaginary} \leftrightarrow F(-j\omega)=-F^{*}(j\omega)$

$\displaystyle f(t) \text{ real and even} \leftrightarrow F(j\omega) \text{ real and even}$

$\displaystyle f(t)\text{ real and odd} \leftrightarrow F(j\omega)\text{ imaginary and odd}$

$\displaystyle f(t)\text{ imaginary and odd} \leftrightarrow F(j\omega) \text{ real and odd}$

$\displaystyle f(t)\text{ imaginary and even} \leftrightarrow F(j\omega)\text{ imaginary and even}$