Starting with the Fourier transform pair

and using no integration, indicate the properties of the Fourier transform that will allow you to compute the Fourier transform of the following signals (do not find the Fourier transforms):

(a) x₁(t) = ˆ’u(t + 2) + 2u(t) ˆ’ u(t ˆ’ 2)        

(b) x₂(t) = 2 sin(t)/t

(c) x₃(t) = 2[u(t + 0.5) ˆ’ u(t ˆ’ 0.5)]             

(d) x₄(t) = cos(0.5Ï€t)[u(t + 1) ˆ’ u(t ˆ’ 1)]

(e) x₅(t) = X(t)

You may want to plot the different signals to help you get the answers.

2 sin() X(N) = x(t) = u(t + 1) – u(t – 1)