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Let X(z) = 1/(1 - z⁻³) be the Z-transform of a causal signal x[n]. Then, the values of x[2] and x[3] are

1. 0 and 0
2. 0 and 1
3. 1 and 0
4. 1 and 1

Correct answer: 0 and 1

Solution

Expanding X(z)=1/(1-z^-3)=1+z^-3+z^-6+... gives x[n]=1 at n=0,3,6,... and 0 elsewhere. Thus x[2]=0 and x[3]=1, which is option 1; the stored '0 and 0' is wrong.

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