The GATE Grind

GATE 2023 IN – Question 36

Signals and Systems · Signals and linear time-invariant systems · 2 marks · Multiple choice

An LTI system has impulse response $h(t)=\delta(t)+0.5\delta(t-4)$, where $\delta$ is the continuous-time unit impulse. For $x(t)=\cos(7\pi t/4)$, its output is

  1. $0.5\cos(7\pi t/4)$
  2. $1.5\cos(7\pi t/4)$
  3. $0.5\sin(7\pi t/4)$
  4. $1.5\sin(7\pi t/4)$

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Correct answer: (A) $0.5\cos(7\pi t/4)$

Explanation

Convolution gives $y(t)=x(t)+0.5x(t-4)$. The delay phase is $(7\pi/4)(4)=7\pi$, so $x(t-4)=-x(t)$.

Therefore $y(t)=0.5\cos(7\pi t/4)$, **A**.