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The question is about determining the Region of Convergence (ROC) for a given signal in the Z-transform. To select the correct option, let's first understand some basic principles about the ROC:

1. **ROC for a causal signal:** If the signal is causal (non-zero for \( n \geq 0 \)), the ROC is outside the outermost pole, i.e., \( |z| > r \), where \( r \) is the pole's radius.

2. **ROC for an anti-causal signal:** If the signal is anti-causal (non-zero for \( n < 0 \)), the ROC is inside the innermost pole, i.e., \( |z| < r \).

3. **ROC for a two-sided signal:** For a signal with both causal and anti-causal parts, the ROC will be a ring between two poles, i.e., \( r_1 < |z| < r_2 \).

4. **The ROC cannot include any poles.**

The given options are:
- (a) \( |z| > 2 \)
- (b) \( |z| < 2 \)
- (c) \( |z| = 1 \)
- (d) \( |z| \neq 0 \)

Without additional context, the most common ROC scenario is:
- For a causal system, the ROC is typically \( |z| > r \).
- For an anti-causal system, it is \( |z| < r \).

If \( r = 2 \), then option (a) \( |z| > 2 \) would likely be the correct choice for a causal signal.

Would you like more details, or do you have any questions? Here are some related questions for further study:

1. How does the location of poles affect the ROC in the Z-transform?
2. What is the significance of the ROC in determining system stability?
3. How does the Z-transform differ from the Laplace transform in terms of ROC?
4. What happens to the ROC if a signal is neither purely causal nor anti-causal?
5. Can a system have multiple ROCs? If so, what does that imply?

**Tip:** The ROC for a stable system must include the unit circle (\( |z| = 1 \)).

ROC is given by (a) |z| > 2 (b) |z| < 2 (c) |z| = 1 (d) |z| ≠ 0

Understand how to determine the Region of Convergence (ROC) for signals in the Z-transform. This problem discusses ROC for causal, anti-causal, and two-sided signals, with formulas for determining ROC based on the type of signal. Suitable for undergraduate students studying signal processing.

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