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Consider the following block diagram for a discrete time system. Recall that z-1 is a unit delay and that triangles represent constant gains of ci and c2. x[n] y[n] C2

Consider the following block diagram for a discrete time system. Recall that z-1 is a unit delay and that triangles represent constant gains of ci and c2. x[n] y[n] C2

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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(a) Determine the system transfer function H(z). Show work.
(b) Find the poles and zeros.

**Block Diagram Explanation** **Description:** This is a block diagram of a discrete-time system. It features several components which process an input signal \( x[n] \) to produce an output signal \( y[n] \). **Components:** 1. **Delay Elements (\( z^{-1} \))**: - These square blocks with the notation \( z^{-1} \) represent unit delays. A unit delay shifts the signal by one time unit. 2. **Gain Elements (\( c_1, c_2 \))**: - These are represented as triangles in the diagram. They apply constant gains \( c_1 \) and \( c_2 \) to their respective input signals. 3. **Summation Point**: - The circle with a plus sign indicates a summation operation. It combines multiple input signals into a single output signal by adding them together. **Signal Flow:** - The input signal \( x[n] \) enters the system and is first delayed by a unit delay block (\( z^{-1} \)). - The delayed signal then branches to two paths: 1. One path is multiplied by the gain \( c_1 \). 2. The other path leads directly to the summation point. - From the summation point, the combined signal is delayed again by another unit delay block (\( z^{-1} \)) before exiting as the output signal \( y[n] \). - Additionally, the signal from the output of the first \( z^{-1} \) block also branches out to another gain, \( c_2 \), whose output joins at the summation point. This block diagram represents a linear system where the delayed input signal is linearly combined with its scaled versions to produce the output signal. This kind of configuration is often used in digital signal processing to design filters and other signal processing systems.
Transcribed Image Text:**Block Diagram Explanation** **Description:** This is a block diagram of a discrete-time system. It features several components which process an input signal \( x[n] \) to produce an output signal \( y[n] \). **Components:** 1. **Delay Elements (\( z^{-1} \))**: - These square blocks with the notation \( z^{-1} \) represent unit delays. A unit delay shifts the signal by one time unit. 2. **Gain Elements (\( c_1, c_2 \))**: - These are represented as triangles in the diagram. They apply constant gains \( c_1 \) and \( c_2 \) to their respective input signals. 3. **Summation Point**: - The circle with a plus sign indicates a summation operation. It combines multiple input signals into a single output signal by adding them together. **Signal Flow:** - The input signal \( x[n] \) enters the system and is first delayed by a unit delay block (\( z^{-1} \)). - The delayed signal then branches to two paths: 1. One path is multiplied by the gain \( c_1 \). 2. The other path leads directly to the summation point. - From the summation point, the combined signal is delayed again by another unit delay block (\( z^{-1} \)) before exiting as the output signal \( y[n] \). - Additionally, the signal from the output of the first \( z^{-1} \) block also branches out to another gain, \( c_2 \), whose output joins at the summation point. This block diagram represents a linear system where the delayed input signal is linearly combined with its scaled versions to produce the output signal. This kind of configuration is often used in digital signal processing to design filters and other signal processing systems.
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