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GATE 2017 EE (EE2) – Question 14

Signals and Systems · Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform · 1 mark · Multiple choice

Pole-zero plots for discrete-time systems P,Q,R are shown. Which statement about their frequency selectivity is true?

Diagram for GATE 2017 EE (EE2) question 14
  1. All three are high-pass filters.
  2. All three are band-pass filters.
  3. All three are low-pass filters.
  4. P is low-pass, Q is band-pass and R is high-pass.

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Show answer and explanation

Correct answer: (B) All three are band-pass filters.

Explanation

Each plot has zeros at z=+1 and z=−1. These locations correspond to ω=0 and ω=π, so each response rejects both DC and the highest discrete-time frequency.

Their nonzero intermediate-frequency response gives the intended **band-pass classification, B**. The different poles shape the passband, rather than changing those endpoint zeros.

**Source qualification:** R has poles on the unit circle at ±j. It is an ideal resonant limiting case and is not BIBO stable; the classification does not imply a realizable stable filter at those exact pole locations.

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