An even signal is any signal
ff such that
ft=f−t
f
t
f
t
. Even signals can be easily spotted as they are
*symmetric* around the vertical axis. An
odd signal, on the other hand, is a signal
ff such that
ft=−f−t
f
t
f
t
(Figure 5).

Using the definitions of even and odd signals, we can show
that any signal can be written as a combination of an even and
odd signal. That is, every signal has an odd-even
decomposition. To demonstrate this, we have to look no
further than a single equation.

ft=12(ft+f−t)+12(ft−f−t)
f
t
1
2
f
t
f
t
1
2
f
t
f
t

(2)
By multiplying and adding this expression out, it can be shown
to be true. Also, it can be shown that

ft+f−t
f
t
f
t
fulfills the requirement of an even function, while

ft−f−t
f
t
f
t
fulfills the requirement of an odd function (

Figure 6).

Comments:"My introduction to signal processing course at Rice University."