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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.
Top left: X1 of omega, an even staircase spectrum, a higher flat level between -B1/2 and B1/2 and a lower flat step from B1/2 to B1 and from -B1 to -B1/2, zero beyond plus or minus B1. Top right: X2 of omega, a triangle peaking at omega equal 0 and reaching zero at -B2 and B2. Bottom: x1 of t and x2 of t enter a multiplier, whose output feeds a block h of t equal e to the power -2|t|, giving output y of t.
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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