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GATE 2022 BM – Question 38

Signals and Systems · Laplace and Fourier Transforms · 2 marks · Multiple choice

A system has the magnitude and phase responses shown. For step input x(t)=u(t), its output crosses zero at t=t_d>0. Find t_d in μs.

Diagram for GATE 2022 BM question 38
  1. 100 ln(2)
  2. 10 ln(2)
  3. 1000 ln(2)
  4. ln(2)

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Show answer and explanation

Correct answer: (A) 100 ln(2)

Explanation

The response has unit magnitude and phase passing through −90° at 10⁴ rad/s, identifying the first-order all-pass H(s)=(a−s)/(a+s), a=10⁴ s⁻¹. For a unit step, y(t)=1−2e⁻ᵃᵗ. Setting y=0 gives t=ln2/a=100ln2 μs, A.

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