Even and odd functions
Complex-valued functions

The definitions for even and odd symmetry for complex-valued functions of a real argument are similar to the real case. In signal processing, a similar symmetry is sometimes considered, which involves complex conjugation.

Conjugate symmetry:

A complex-valued function of a real argument f: R → C {\displaystyle f:\mathbb {R} \to \mathbb {C} } is called conjugate symmetric if

A complex valued function is conjugate symmetric if and only if its real part is an even function and its imaginary part is an odd function.

A typical example of a conjugate symmetric function is the cis function

Conjugate antisymmetry:

A complex-valued function of a real argument f: R → C {\displaystyle f:\mathbb {R} \to \mathbb {C} } is called conjugate antisymmetric if:

A complex valued function is conjugate antisymmetric if and only if its real part is an odd function and its imaginary part is an even function.
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