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GATE EE 2016 Set 2 — Question 38

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MCQ+2 / -0.67MediumFourier Transform PropertiesFourier Analysis & SamplingSignals & SystemsSampling Theorem

Signals & Systems → Fourier Analysis & Sampling → Fourier Transform Properties

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Question

Let x1(t)↔X1(ω)x_1(t) \leftrightarrow X_1(\omega) and x2(t)↔X2(ω)x_2(t) \leftrightarrow X_2(\omega) be two signals whose Fourier Transforms are as shown in the figure below. In the figure, h(t)=e−2∣t∣h(t) = e^{-2|t|} denotes the impulse response.
Fourier transforms $X_1(\omega)$ and $X_2(\omega)$ and a system block diagram
For the system shown above, the minimum sampling rate required to sample y(t)y(t), so that y(t)y(t) can be uniquely reconstructed from its samples, is
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