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

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)