(a) Use the Fourier transform of x(t) = exp (-t) u (t) - exp (t) u (-t) where > 0 (b) Use the result

(a) Use the Fourier transform of x(t) = exp (-αt) u (t) - exp (αt) u (-t) where α > 0 

(b) Use the result above and the relation u(t) = 1/2[sgn (t) + 1] to find Fourier transform of the unit step.

(c) Use the integration theorem and the Fourier transform of the unit impulse function to find the Fourier transform of the unit step. Compare the result with part (b).

t > 0 1, sgn (t) = -1, t < 0