Let x1(t) ↔ X1(ω) and x2(t) ↔ X2(ω) be two signals whose Fourier transforms are as shown in the figure below. In the figure, h(t) = e^□2|t | denotes the impulse response. For the given system, the minimum sampling rate required to sample y(t), so that y(t) can be uniquely reconstructed from its

Question

Let [latex]x_1(t) \leftrightarrow X_1(\omega) ext { and } x_2(t) \leftrightarrow X_2(\omega)[/latex] be two signals whose Fourier transforms are as shown in the figure below. In the figure, [latex] h(t)=e^{□ 2|t|}[/latex] denotes the impulse response. For the given system, the minimum sampling rate required to sample y(t), so that y(t) can be uniquel reconstructed from its samples, is

(a) [latex]2 B_1[/latex] (b) [latex]2\left(B_1+B_2 ight)[/latex]

(c) [latex]4\left(B_1+B_2 ight)[/latex] (d) [latex]∞[/latex]

Accepted Answer

For the given system:

[latex]Y(j \omega)=\left[X_1(j \omega)^* X_2(j \omega)\right] H(j \omega)[/latex]

Bandwidth of [latex]X_1=B_1[/latex] and bandwidth of [latex]X_2=B_2[/latex] therefore, bandwidth of

[latex]X_1 * X_2=B_1+B_2[/latex]

Therefore, bandwidth of

[latex]Y(j \omega)=B_1+B_2[/latex]

Hence sampling frequency [latex]\geq 2\left(B_1+B_2\right)[/latex]

Question 2016.S2.28: Let x1(t) ↔ X1(ω) and x2(t) ↔ X2(ω) be two signals whose Fo......

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