Inverse fourier transform of X(w) = (sin(w/2).exp(-j2w))/(jw + 2)
exp(-bt).u(t) → 1/(jw+b)
multiplication by sin: x(t)sin(w0t → j/2[X(w+w0)-X(w-w0]
w0 being 0.5 here.
shifted left or right in time: x(t-c) → X(W)exp(-jwc)
The Attempt at a Solution
I got x(t) = j/2[exp(-2(t-1.5)).u(t-1.5) - exp(-2(t-2.5).u(t-2.5)]
but I think it should be: x(t) = j/2[exp(-2(t-2.5).u(t-2.5) - exp(-2(t-1.5)).u(t-1.5)]