GATE ECE 2024 | Question: 38

Question

​​​​A continuous time signal $x(t)=2 \cos (8 \pi t+\pi / 3)$ is sampled at a rate of $15 \mathrm{~Hz}$. The sampled signal $x_{s}(t)$ when passed through an LTI system with impulse response
\[
h(t)=\left(\frac{\sin 2 \pi t}{\pi t}\right) \cos (38 \pi t-\pi / 2)
\]
produces an output $x_{o}(t)$. The expression for $x_{o}(t)$ is $\_\_\_\_\_$.

• A. $15 \sin (38 \pi t+\pi / 3)$
• B. $15 \sin (38 \pi t-\pi / 3)$
• C. $15 \cos (38 \pi t-\pi / 6)$
• D. $15 \cos (38 \pi t+\pi / 6)$

 

Answer 1

C