The complex envelope of the bandpass signal $x(t) = -\sqrt{2}\bigg( \frac{sin \Big(\frac{\pi t}{5}\Big)}{\frac{\pi t}{5}} \bigg) sin(\pi t - \frac{\pi}{4})$ centred about $f = \frac{1}{2}$ Hz, is
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$\bigg( \frac{sin \Big(\frac{\pi t}{5}\Big)}{\frac{\pi t}{5}} \bigg) e^{j \frac{\pi}{4}}$
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$\bigg( \frac{sin \Big(\frac{\pi t}{5}\Big)}{\frac{\pi t}{5}} \bigg) e^{-j \frac{\pi}{4}}$
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$\sqrt{2} \bigg( \frac{sin \Big(\frac{\pi t}{5}\Big)}{\frac{\pi t}{5}} \bigg) e^{j \frac{\pi}{4}}$
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$\sqrt{2} \bigg( \frac{sin \Big(\frac{\pi t}{5}\Big)}{\frac{\pi t}{5}} \bigg)$
