Correct Option: B

First approach:
y(t) = x(t) * x(t)
Y(jω) = X(jω) X(jω)

=	2 sin ω	.	2 sin ω
	ω		ω

=	4 sin2 ω
	ω2

Second approach
Given, waveform

slope =	2	= 1
	2

If
y(t) ←F.T.→ Y(jω)
then

d2	y(t) ←F.T.→ (jω)2 Y(jω)
dt2

y′′(t) = δ(t + 2) – 2δ(t) + δ(t – 2)
F{y′′(t)} = e^jω2 – 2 + e^–jω2

= 2		e2jω + e–2jω		- 2
		2

= 2.cos 2ω – 2
= 2(cos 2ω – 1)
= 2(1 – 2 sin² ω – 1)
= 2(– 2 sin² ω)
= – 4 sin² ω
Now, (– jω)² Y(jω) = – 4 sin² ω
or

Y(jω) =	4	sin2 ω
	ω2

Hence, alternative (A) is the correct choice.