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Even and Odd Signals

Module by: Harika Basana. E-mail the author

An even signal is any signal ff such that ft=ft 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=ft f t f t .

Figure 1
(a) An even signal
Figure 1(a) (sigclass8.png)
(b) An odd signal
Figure 1(b) (sigclass9.png)

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+ft)+12(ftft) f t 1 2 f t f t 1 2 f t f t
By multiplying and adding this expression out, it can be shown to be true. Also, it can be shown that ft+ft f t f t fulfills the requirement of an even function, while ftft f t f t fulfills the requirement of an odd function.

Example 1

Figure 2
(a) The signal we will decompose using odd-even decomposition
Figure 2(a) (sigclass10.png)
(b) Even part: et=12(ft+ft) e t 1 2 f t f t
Figure 2(b) (sigclass11.png)
(c) Odd part: ot=12(ftft) o t 1 2 f t f t
Figure 2(c) (sigclass12.png)
(d) Check: et+ot=ft e t o t f t
Figure 2(d) (sigclass13.png)

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