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Let $H(z)$ be the $z-$ transform of a real-valued discrete-time signal $h[n].$ If $P(z) = H(z) H(\frac{1}{z})$ has a zero at $z= \frac{1}{2}+\frac{1}{2}j,$ and $P(z)$ has a total of four zeros, which one of the following plots represents all the zeros correctly?

 

  1.   GATE2019-15
  2. GATE2019-15
  3. GATE2019-15
  4. GATE2019-15
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