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A continuous-time LTI system with system function H(ω) has the following pole-zero plot. For this system, which of the alternatives is TRUE?

EE Signals and Systems mobile Images-Q63

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  1. |H(0 | > | ω |;| ω |>0
  2. H(ω)| has multiple maxima, at ω1 and ω2
  3. | H(0) | < |H(ω)| ; | ω | > 0
  4. | H(ω) | = constant; -∞ < ω < ∞

Answer (Detailed Solution Below)

Option 4 : | H(ω) | = constant; -∞ < ω < ∞
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Detailed Solution

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Pole zero plot is redrawn as

EE Signals and Systems mobile Images-Q63.1

As observed from the given pole-zero plot, poles & zeros are located symmetrically.

Therefore, it is all pass filter.

As we know that, from the property of all pass filter is,

  • |H(jω)| = constant for all values of ω
  • ∠H(jω) = Linearly vary with ω

Hence, the correct option is (4)

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