Sketch each signal given below and find its Fourier transform. Plot the amplitude and phase spectra of each signal (A  and τ are positive constants).

(a) x₁(t) = A exp (-t/τ) u(t) 

(b) x₂(t) = A exp (t/τ) u(-t)

(c) x₃(t) = x₁ (t) - x₂ (t) 

(d) x₄(t) = x₁ (t) + x₂ (t). Does the result check with the answer found using Fourier-transform tables?

(e) x₅(t) = x₁ (t - 5) 

(f) x₆(t) = x₁ (t) - x₁ (t - 5)