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GATE 2018 EC – Question 23

Networks, Signals and Systems · Discrete-time Signals · 1 mark · Multiple choice

A discrete-time all-pass system has two of its poles at $0.25\angle0^\circ$ and $2\angle30^\circ$. Which one of the following statements about the system is TRUE?

  1. It has two more poles at $0.5\angle30^\circ$ and $4\angle0^\circ$.
  2. It is stable only when the impulse response is two-sided.
  3. It has constant phase response over all frequencies.
  4. It has constant phase response over the entire $z$-plane.

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Show answer and explanation

Correct answer: (B) It is stable only when the impulse response is two-sided.

Explanation

For an all-pass system the poles and zeros are at conjugate-reciprocal positions, so the extra poles are not fixed as in A, and the phase is not constant (C, D are false). One pole is inside the unit circle and another outside, so a stable (unit-circle-convergent) system needs a two-sided impulse response.