The complex envelope of the bandpass signal x( t ) = sqrt 2 ( sin ( t over 5 ) over t over 5 )sin ( t - over 4 ), centered about f = 1 over 2Hz, is

sqrt 2 ( sin ( t over 5 ) over t over 5e^j over 4 )

This question belongs to Electronics And Communications Engineering Signal Processing

Signal Processing

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 & Solution

Correct Answer: Option C

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The complex envelope of the bandpass signal x left( t right)...

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

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