The pole – zero diagram of a causal and stable discrete – time system is shown 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.

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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