### Problem Statement1. **Objective:** Determine the z-transform, including the region of convergence (ROC), of the following signals:2. **Signal Definition:** \[ x_3[n] = \begin{cases} \left(\frac{1}{3}\right)^n - 2^n, & n \geq 0 \\ 0, & n < 0 \end{cases} \]### Explanation- The given signal \( x_3[n] \) is a piecewise function that consists of two separate components depending on the value of \( n \).- For \( n \geq 0 \), the signal is defined as \( \left( \frac{1}{3} \right)^n - 2^n \).- For \( n < 0 \), the signal is zero.The task is to compute the z-transform of this signal and determine the region in the z-plane where the transform converges (the ROC). The z-transform is a powerful mathematical tool used in signal processing to analyze discrete-time signals.

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Answered: 1. Determine the z-transform, including…

1. Determine the z-transform, including the region of convergence (ROC), of the following signals: 2. xıln] = {) - 2", n 2 9 2. x3[n] = 0, п <0

Introductory Circuit Analysis (13th Edition)

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Publisher:Robert L. Boylestad

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Question

### Problem Statement

1. **Objective:**
Determine the z-transform, including the region of convergence (ROC), of the following signals:

2. **Signal Definition:**
\[
x_3[n] =
\begin{cases}
\left(\frac{1}{3}\right)^n - 2^n, & n \geq 0 \\
0, & n < 0
\end{cases}
\]

### Explanation

- The given signal \( x_3[n] \) is a piecewise function that consists of two separate components depending on the value of \( n \).
- For \( n \geq 0 \), the signal is defined as \( \left( \frac{1}{3} \right)^n - 2^n \).
- For \( n < 0 \), the signal is zero.

The task is to compute the z-transform of this signal and determine the region in the z-plane where the transform converges (the ROC). The z-transform is a powerful mathematical tool used in signal processing to analyze discrete-time signals.

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