Question

What are the basic crieterion to check whether a signal is odd or even in signal or system

Answer 1

signal x(t) is said to be,

Even if,

(1)

x(t)=x(−t)

Odd if,

(2)

x(t)=−x(−t)

(3)

x(t)=−x(−t)

The following figures illustrate clearly,



Any signal x(t) can be written as the sum of an even signal and odd signal.

(4)

x(t)=xe(t)+xo(t)

where, xe(t) is the even part and xo(t) is the odd part.

(5)

x(t)=12[x(t)+x(−t)]+12[x(t)−x(−t)]

So,

(6)

xe(t)=12[x(t)+x(−t)]⇒xe(−t)=12[x(−t)+x(t)]

Therefore,

(7)

xe(t)=xe(−t)⇒xe(t) is even

And,

(8)

xo(t)=12[x(t)−x(−t)]⇒xo(−t)=12[