Fourier Transform Symmetries

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

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

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

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

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

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

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

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