Even and odd

A function or continuous-time signal $f(x)$ is even if:

$$x(t)=x(-t)$$

i.e., it is symmetric about the $y$-axis. It’s odd if:

$$x(t)=-x(-t)$$

i.e., the reflection of the function about the $y$-axis is symmetric with respect to the $x$-axis.

We can additionally decompose any signal as:

$$x=x_{\text{even}}+x_{\text{odd}}$$ $$x_{\text{even}}=\frac{x(t)+x(-t)}{2}$$ $$x_{\text{odd}}=\frac{x(t)-x(-t)}{2}$$