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GATE 2018 EC – Question 49

Communications · Analog Communications · 2 marks · Numerical answer

The input $4\,\text{sinc}(2t)$ is fed to a Hilbert transformer to obtain $y(t)$, as shown in the figure below.

Here, $\text{sinc}(x)=\dfrac{\sin(\pi x)}{\pi x}$. The value (accurate to two decimal places) of $\displaystyle\int_{-\infty}^{\infty}|y(t)|^2dt$ is ________.

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Correct answer: 8

Explanation

A Hilbert transformer has unit gain at all frequencies (only the phase changes), so it preserves energy. The energy of $4\,\text{sinc}(2t)$ is $16\int\text{sinc}^2(2t)dt=16\times\frac12=8$.