Question 3.PE.S2.3: The Nyquist sampling interval for the signal sinc (700t) + s......

Wiley Acing The Gate Electrical Engineering [1079382]

The Nyquist sampling interval for the signal sinc (700t) + sinc (500t) is

(a) $\frac{1}{350} s$ (b) $\frac{π}{350} s$

(c) $\frac{1}{700} s$ (d) $\frac{1}{700} s$

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(c)

$\begin{aligned}x & =\sin c(700 t)+\sin c(500 t) \\& =\frac{\sin c(700 \pi t)}{700 \pi t}+\frac{\sin c(500 \pi t)}{500 \pi t}\end{aligned}$

The maximum frequency component is $f_{\max }=350$ Hz

The Nyquist rate, $f_{ s }=2 \times f_{\max }=2 \times 350=700 Hz$

Nyquist sampling interval $=\frac{1}{f_{ s }}=\frac{1}{2 f_{\max }}=\frac{1}{700} s$

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