21. Find the region of convergence in the z plane (if it exists) of the z transform of these signals. (b) x[n]= (5/4)" u[n]+(10/7)" u[-n]

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### Existence of the \( z \) Transform

#### 21. Find the region of convergence in the \( z \) plane (if it exists) of the \( z \) transform of these signals.

(b) \( x[n] = \left(\frac{5}{4}\right)^n u[n] + \left(\frac{10}{7}\right)^n u[-n] \)

#### Explanation:
- \( u[n] \) is the unit step function.
- \( u[-n] \) is the unit step function for negative \( n \).
Transcribed Image Text:### Existence of the \( z \) Transform #### 21. Find the region of convergence in the \( z \) plane (if it exists) of the \( z \) transform of these signals. (b) \( x[n] = \left(\frac{5}{4}\right)^n u[n] + \left(\frac{10}{7}\right)^n u[-n] \) #### Explanation: - \( u[n] \) is the unit step function. - \( u[-n] \) is the unit step function for negative \( n \).
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