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GATE 2014 EC (EC2) – Question 28

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

$x[n]=x[-n]$, and X(z) is its z-transform. If $0.5+j0.25$ is a zero, which must also be a zero?

  1. $0.5-j0.25$
  2. $1/(0.5+j0.25)$
  3. $1/(0.5-j0.25)$
  4. $2+j4$

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Show answer and explanation

Correct answer: (B) $1/(0.5+j0.25)$

Explanation

For x[n]=x[−n], substitution in the bilateral z-transform gives X(z)=X(1/z). Thus if z0=0.5+j0.25is a zero, its reciprocal1/z0must also be a zero, **B**. A conjugate zero additionally requires a real sequence, which the question does not state.