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a) H(z) = 3(Z+0.9) z(Z-0.9)(z-1.2) 3(z-1)² b) H(z) = 73-1.82² +0.81z

a) H(z) = 3(Z+0.9) z(Z-0.9)(z-1.2) 3(z-1)² b) H(z) = 73-1.82² +0.81z

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
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Find the Impulse Response of the systems and determine whether they are stable.
**Title: Understanding Transfer Functions in Z-Domain** In digital signal processing, transfer functions represent the relationship between input and output in the z-domain. Below are two examples of transfer functions, denoted as \( H(z) \). **Example A** \[ H(z) = \frac{3(z+0.9)}{z(z-0.9)(z-1.2)} \] - **Explanation**: The numerator consists of a polynomial with a single term, while the denominator is a product of three terms, including a complex pole. **Example B** \[ H(z) = \frac{3(z-1)^2}{z^3 - 1.8z^2 + 0.81z} \] - **Explanation**: The numerator has a quadratic term \((z-1)^2\), and the denominator is a cubic polynomial. These examples demonstrate different complexities and poles/zeros arrangements in transfer functions. Understanding these is crucial for designing and analyzing digital filters and control systems.
Transcribed Image Text:**Title: Understanding Transfer Functions in Z-Domain** In digital signal processing, transfer functions represent the relationship between input and output in the z-domain. Below are two examples of transfer functions, denoted as \( H(z) \). **Example A** \[ H(z) = \frac{3(z+0.9)}{z(z-0.9)(z-1.2)} \] - **Explanation**: The numerator consists of a polynomial with a single term, while the denominator is a product of three terms, including a complex pole. **Example B** \[ H(z) = \frac{3(z-1)^2}{z^3 - 1.8z^2 + 0.81z} \] - **Explanation**: The numerator has a quadratic term \((z-1)^2\), and the denominator is a cubic polynomial. These examples demonstrate different complexities and poles/zeros arrangements in transfer functions. Understanding these is crucial for designing and analyzing digital filters and control systems.
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