Question

A continuous time signal x(t) is obtained at the output of an ideal low pass filter with cut off frequency ${\omega }_c=1000\pi$. If instantaneous sampling is performed on x(t). Which of the following sampling periods will guarantee that x(t) can be recovered properly from its sampled version using an appropriate low-pass filters?

• A. $T=3\times {10}^{-3}sec$
• B. $T={10}^{-4}sec$
• C. $T=1.5\times {10}^{-3}sec$
• D. $T=2\times {10}^{-3}sec$

Answer 1

The correct option is B $T={10}^{-4}sec$

Since x(t) is obtained at output of an ideal low-pass filter with cut-off frequency ${\omega }_c=1000\pi$. Thus the maximum frequency present at output is $1000\pi$

${\omega }_m=1000\pi$

$f_m=500$

Sampling rate $\ge 2f_m$

$f_s\ge 2\times 500$

$f_s\ge 1000Hz$

$T_s\le \frac{1}{1000}$

$T_s\le {10}^{-3}sec$