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Draw the Parallel Form implementation of the system of transfer function 1+3z¹ 1-22-¹ 1+22-¹ 1-3z-1 H (2) = Hint: If you put H(z) in a different form, go backward to see if you retrieve the original H(2). Warning: Beware of sign mistakes.

Draw the Parallel Form implementation of the system of transfer function 1+3z¹ 1-22-¹ 1+22-¹ 1-3z-1 H (2) = Hint: If you put H(z) in a different form, go backward to see if you retrieve the original H(2). Warning: Beware of sign mistakes.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Title: Understanding Parallel Form Implementation of Transfer Functions** **Objective:** Draw the Parallel Form implementation of the system of transfer function. **Transfer Function:** \[ H(z) = \frac{1 + 3z^{-1}}{1 + 2z^{-1}} - \frac{1 - 2z^{-1}}{1 - 3z^{-1}} \] **Hint:** If you put \( H(z) \) in a different form, go backward to see if you retrieve the original \( H(z) \). **Warning:** Beware of sign mistakes. --- **Explanation:** The task involves expressing the given transfer function, \( H(z) \), in its parallel form. This involves separating the given function into simpler fractional components, which can often be executed through partial fraction decomposition. The hint suggests re-expressing \( H(z) \) and checking your work by reverting back to the form provided to ensure accuracy. Pay special attention to sign conventions, as errors in signs can lead to incorrect representations and faulty solutions. This exercise is crucial in systems and control theory, where transfer functions are widely used to represent linear, time-invariant systems. Understanding their parallel form implementation helps in simplifying the design and analysis of complex systems.
Transcribed Image Text:**Title: Understanding Parallel Form Implementation of Transfer Functions** **Objective:** Draw the Parallel Form implementation of the system of transfer function. **Transfer Function:** \[ H(z) = \frac{1 + 3z^{-1}}{1 + 2z^{-1}} - \frac{1 - 2z^{-1}}{1 - 3z^{-1}} \] **Hint:** If you put \( H(z) \) in a different form, go backward to see if you retrieve the original \( H(z) \). **Warning:** Beware of sign mistakes. --- **Explanation:** The task involves expressing the given transfer function, \( H(z) \), in its parallel form. This involves separating the given function into simpler fractional components, which can often be executed through partial fraction decomposition. The hint suggests re-expressing \( H(z) \) and checking your work by reverting back to the form provided to ensure accuracy. Pay special attention to sign conventions, as errors in signs can lead to incorrect representations and faulty solutions. This exercise is crucial in systems and control theory, where transfer functions are widely used to represent linear, time-invariant systems. Understanding their parallel form implementation helps in simplifying the design and analysis of complex systems.
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