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

• A. \(\left( {\frac{{\sin \left( {\frac{{\pi t}}{5}} \right)}}{{\frac{{\pi t}}{5}}}} \right){e^{j\frac{\pi }{4}}}\)
• B. \(\left( {\frac{{\sin \left( {\frac{{\pi t}}{5}} \right)}}{{\frac{{\pi t}}{5}}}} \right){e^{ - j\frac{\pi }{4}}}\)
• C. \(\sqrt 2 \left( {\frac{{\sin \left( {\frac{{\pi t}}{5}} \right)}}{{\frac{{\pi t}}{5}}}} \right){e^{j\frac{\pi }{4}}}\)
• D. \(\sqrt 2 \left( {\frac{{\sin \left( {\frac{{\pi t}}{5}} \right)}}{{\frac{{\pi t}}{5}}}} \right){e^{ - j\frac{\pi }{4}}}\)