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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

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)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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### 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.
Transcribed Image Text:### 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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