Multiple choice

The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h[0] = 1, we can conclude that

  1. h[n] is real for all n

  2. h[n] is purely imaginary for all n

  3. h[n] is real for only even n

  4. h[n] is purely imaginary for only odd n
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