Question

The initial value of \( x[n] \) is _______, if \[ X(z) = \frac{3z^2}{(z+3)(z-3)} \]

• A. 3
• B. 6
• C. \( \infty \)
• D. 0

Hint:

Use \( x[0] = \lim_{z \to \infty} X(z) \) for initial value from Z-transform.

Answer 1

The Correct Option is A

Step 1: Use Initial Value Theorem for Z-transform
\[ x[0] = \lim_{z \to \infty} X(z) \] Step 2: Apply Limit to Given \( X(z) \)
\[ X(z) = \frac{3z^2}{(z+3)(z-3)} \Rightarrow \lim_{z \to \infty} \frac{3z^2}{z^2 - 9} = \frac{3}{1} = 3 \] Conclusion:
Option (1) is correct.