GATE 2017 EC (EC2) – Question 17
An LTI system with unit sample response $h[n]=5\delta[n]-7\delta[n-1]+7\delta[n-3]-5\delta[n-4]$ is a
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Correct answer: (C) band-pass filter
Explanation
The frequency response is $H(e^{j\omega})=5-7e^{-j\omega}+7e^{-j3\omega}-5e^{-j4\omega}$.
At DC, $H(1)=5-7+7-5=0$. At the highest discrete-time frequency $\omega=\pi$, it is $5+7-7-5=0$ as well.
The response is not identically zero; for example, at $\omega=\pi/2$ its value is $14j$. It rejects both frequency extremes while passing intermediate frequencies, so the intended classification is **band-pass, C**.