Electronics and Communication Engineering - Exam Questions Papers - Discussion

The given signal can be expressed as multiplication of x₁(t) and x₂(t) as shown below, where A = 2, T/2 = 0.25 ⇒ T = 0.5

∴ x(t) = x₁(t) x x₂(t)

⇒ X(f) = X₁(f) * X₂(f)

Now X₁(f) = [δ(f - f₀) + δ(f + f₀)]

where

and X₂(f) = T . sin c[fT]

⇒ X(f) = [δ(f - f₀) + δ(f + f₀)]

*T. sinc(fT)

= [sinc[T(f - f₀)] + sinc [T(f + f₀)]]

Now, A = 2, T = 0.5

and

⇒ X(f) = 0.5[sin c(0.5(f - 1)) + sinc(0.5(f + 1))].