Question

Signal And System

(5 ) Consider a system as shown in Figure 5. x(t) . + 1 2 3 4 5 6 Figure 5

Answer 1

I will first write some theory for your understanding purpose:

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

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

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

x(t)= 1/2[x(t)+x(−t)]+1/2[x(t)−x(−t)]

So,

xe(t)=1/2[x(t)+x(−t)]

xe(−t)=1/2[x(−t)+x(t)]

Therefore,

xe(t)=xe(−t)⇒xe(t) is even

And,

xo(t)=1/2[x(t)−x(−t)]

⇒xo(−t)=1/2[x(−t)−x(t)]

Therefore,

xo(t)=−xo(−t)⇒xo(t) is odd

So let's start to solve given problem:

Xit) M. 2 3 4 5 6 for signal xit! Even component of Xect) = ctt Xect) 2 314 s -2 - signal. of for Rad component odd Xoct) 2 t 3 4 5 t Xo(t) = [a(t)- & cut)]