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

  1. $\left(\dfrac{\sin (\pi t/5)}{\pi t/5}\right)e^{j\dfrac{\pi}{4}}$
  2. $\left(\dfrac{\sin (\pi t/5)}{\pi t/5}\right)e^{-j\dfrac{\pi}{4}}$
  3. $\sqrt{2} \left(\dfrac{\sin (\pi t/5)}{\pi t/5}\right)e^{j\dfrac{\pi}{4}}$
  4. $\sqrt{2} \left(\dfrac{\sin (\pi t/5)}{\pi t/5}\right)e^{-j\dfrac{\pi}{4}}$
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