Topic: Signals and Systems
The z-transform of the signal x(n) = {1 for n=-1; 2 for n=0; -1 for n=1; 1 for n=2; 0 otherwise}
- A. z + 2 - z^-1 + z^-2
- B. z^-1 + 2 - z + z²
- C. z + 2z^2 - z^-1 + z^-2
- D. z + 2 - z^+1 + z^-2
Answer: A. z + 2 - z^-1 + z^-2
Explanation: By definition, X(z) = sum_{n=-infinity}^{infinity} x(n)z^{-n}. Plugging in the values: X(z) = 1*z^{-(-1)} + 2*z^{0} + (-1)*z^{-1} + 1*z^{-2} = z + 2 - z^-1 + z^-2.