GATE 2017 EC – Question 62
A continuous time signal $x(t) = 4\cos(200\pi t) + 8\cos(400\pi t)$, where $t$ is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response
$$h(t) = \begin{cases} \dfrac{2\sin(300\pi t)}{\pi t}, & t \neq 0 \\ 600, & t = 0. \end{cases}$$
Let $y(t)$ be the output of this filter. The maximum value of $|y(t)|$ is ________.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 8
Explanation
The impulse response $\frac{2\sin(300\pi t)}{\pi t}$ belongs to an ideal low-pass filter with gain 2 and a cutoff of 150 Hz, which also matches $h(0) = 600$. The input has components at 100 Hz and 200 Hz. The 100 Hz component passes with gain 2, which gives $2 \times 4\cos(200\pi t) = 8\cos(200\pi t)$. The 200 Hz component is above the cutoff and is removed. So $y(t) = 8\cos(200\pi t)$ and the maximum of $|y(t)|$ is 8.