The correct option is (d) X (F) = \(\frac{1}{2} [X_l (F-F_c)+X_l^* (-F-F_c)]\)
Best explanation: X(F) = \(\frac{1}{2} [X_l (F-F_c)+X_l^* (-F-F_c)]\), where Xl(F) is the Fourier transform of xl(t). This is the basic relationship between the spectrum o f the real band pass signal x(t) and the spectrum of the equivalent low pass signal xl(t).