GATE 2016 EE – SET 2 Question 28

Given that,

Bandwidth of $$X_{1}(\omega )=B_{1}$$ and bandwidth of $$X_{2}(\omega )=B_{2}$$

The input is, $$x_{1}(t)\cdot x_{2}(t)$$

Therefore, the bandwidths are added to get the highest frequency component = $$B_{1}+B_{2}$$

By Nyquist principle, the sampling rate is twice the output bandwidth $$\Rightarrow f_{s}=2[B_{1}+B_{2}]$$