GATE Electrical Engineering (EE) 2016 Shift 2 Solved Paper

Let ${\mathit{x}}_1\left(\mathit{t}\right)\leftrightarrow {\mathit{X}}_1\left(\mathit{\omega }\right)$ and ${\mathit{x}}_2\left(\mathit{t}\right)\leftrightarrow {\mathit{X}}_2\left(\mathit{\omega }\right)$ be two signals whose Fourier Transforms are as shown in the figure below. In the figure, $\mathit{h}\left(\mathit{t}\right)={\mathit{e}}^{-2|\mathit{t}\frac{}{}|}$ denotes the impulse response.

For the system shown above, the minimum sampling rate required to sample y(t), so that y(t) can be uniquely reconstructed from its samples, is