The complex envelope of the bandpass signal $$x\left( t \right) = \sqrt 2 \left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}} \right)\sin \left( {\pi t - {\pi \over 4}} \right),$$     centered about $$f = {1 \over 2}Hz,$$   is

A. $$\left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}{e^{j{\pi \over 4}}}} \right)$$

B. $$\left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}{e^{ - j{\pi \over 4}}}} \right)$$

C. $$\sqrt 2 \left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}{e^{j{\pi \over 4}}}} \right)$$

D. $$\sqrt 2 \left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}{e^{ - j{\pi \over 4}}}} \right)$$

Answer: Option C