Editing Even and odd functions (section)

===Complex-valued functions===
The definitions for even and odd symmetry for [[Complex number|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]].<ref name=Oppenheim>
{{Cite book |last1=Oppenheim |first1=Alan V. |author-link=Alan V. Oppenheim |last2=Schafer |first2=Ronald W. |author2-link=Ronald W. Schafer |last3=Buck |first3=John R. |title=Discrete-time signal processing |year=1999 |publisher=Prentice Hall |location=Upper Saddle River, N.J. |isbn=0-13-754920-2 |edition=2nd |page=55
}}</ref><ref name=ProakisManolakis/>

'''Conjugate symmetry:'''

A complex-valued function of a real argument <math>f: \mathbb{R} \to \mathbb{C}</math> is called ''conjugate symmetric'' if
:<math>f(x)=\overline{f(-x)} \quad \text{for all } x \in \mathbb{R}</math>

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]]
:<math>x \to e^{ix}=\cos x + i\sin x</math>

'''Conjugate antisymmetry:'''

A complex-valued function of a real argument <math>f: \mathbb{R} \to \mathbb{C}</math> is called ''conjugate antisymmetric'' if:
:<math>f(x)=-\overline{f(-x)} \quad \text{for all } x \in \mathbb{R}</math>

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.