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GATE 2023 EE – Question 36

Signals and Systems · Linear time invariant and causal systems · 2 marks · Multiple choice

The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is

Diagram for GATE 2023 EE question 36
  1. $2.51e^{-0.032s}$
  2. $\dfrac{e^{-2.514s}}{s+1}$
  3. $1.04e^{-2.514s}$
  4. $2.51e^{-1.047s}$

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Correct answer: (D) $2.51e^{-1.047s}$

Explanation

The magnitude is constant at 8 dB, i.e. a gain of $10^{8/20}=2.51$. The phase is a straight line through the origin reaching $-60^\circ=-1.047$ rad at $\omega=1$ rad/s, which is a pure delay $e^{-sT}$ with $T=1.047$ s. So $H(s)=2.51e^{-1.047s}$.