Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Transcribed Image Text:**Problem 3**
**Task:** Determine the input-output relationship, the system transfer function, and plot the pole-zero pattern for the discrete-time system shown below.
**Diagram Explanation:**
The system is represented using a flow diagram with the following components:
1. **Input:** The input to the system is denoted as \(x(n)\).
2. **Adders:**
- There are two adders (+) that combine incoming signals.
3. **Branches and Coefficients:**
- Four branches originating from or leading to the adders have coefficients \(r \cos \theta\) and \(-r \cos \theta\), affecting the horizontal paths, and \(r \sin \theta\) and \(-r \sin \theta\), affecting the vertical paths.
4. **Delay Elements:**
- Two sections with delay elements (\(z^{-1}\)) store and delay the signals by one time step.
5. **Output:** The overall system output is shown in the rightmost part of the diagram after signal processing.
**Function of the System:**
- The system processes the input \(x(n)\) through a specific configuration of adders, coefficients, and delay elements to produce the output. The coefficients \(r \cos \theta\) and \(r \sin \theta\) suggest a potential transformation involving trigonometric components.
This setup is often used in signal processing to model or manipulate signals with specific frequency characteristics or to implement filters. The task involves calculating the exact transfer function to understand the system’s behavior fully.
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