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A) Find the Transfer Function B) find the step response x[n] = u[n]

A) Find the Transfer Function B) find the step response x[n] = u[n]

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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A) Find the Transfer Function B) find the step response x[n] = u[n]
### System Diagram Analysis for Discrete-Time Signal Processing This diagram represents a discrete-time system involving delay elements, multipliers, and a summing junction, commonly encountered in digital signal processing (DSP) applications. #### Components: 1. **Delay Elements (D):** - There are three delay elements, depicted as boxes labeled 'D'. These elements delay the input signal by one unit of time (n), which is essential for implementing systems that use past values of the signal. 2. **Multipliers:** - Two multiplier blocks are present: - **Multiplier 1:** Multiplies the signal by -0.7. - **Multiplier 2:** Multiplies the signal by 0.1. 3. **Summing Junction:** - This element combines multiple inputs to produce a single output. It has several input arrows, each joined via summation with others based on their sign, either adding or subtracting the incoming signals. #### Signal Flow: - The input signal \( x[n] \) is fed into the system. The path for this signal is processed through different components, ultimately producing the output signal \( y[n] \). - The output of the initial delay element is fed into the \(-0.7\) multiplier. The resulting signal is then passed back into one of the inputs of the summing junction. - Similarly, the \0.1\ multiplier takes its input from the delayed signal and feeds into another input of the summing junction. - The remaining signal paths shown in the diagram involve additional processing through the delay elements, feeding back into both the multipliers and the summing junction to achieve the desired output response. #### Input-Output Relationship: - The equation \( x[n] = u[n] \) refers to an impulse or step input, typically noted as the unit step function \( u[n] \) in DSP terms. This indicates that the system response shown is based on this standard input signal. The overall architecture of the diagram suggests it represents a feedback or recursive filter, given the interconnected nature of delays and multipliers feeding back into each other and the summing junction.
Transcribed Image Text:### System Diagram Analysis for Discrete-Time Signal Processing This diagram represents a discrete-time system involving delay elements, multipliers, and a summing junction, commonly encountered in digital signal processing (DSP) applications. #### Components: 1. **Delay Elements (D):** - There are three delay elements, depicted as boxes labeled 'D'. These elements delay the input signal by one unit of time (n), which is essential for implementing systems that use past values of the signal. 2. **Multipliers:** - Two multiplier blocks are present: - **Multiplier 1:** Multiplies the signal by -0.7. - **Multiplier 2:** Multiplies the signal by 0.1. 3. **Summing Junction:** - This element combines multiple inputs to produce a single output. It has several input arrows, each joined via summation with others based on their sign, either adding or subtracting the incoming signals. #### Signal Flow: - The input signal \( x[n] \) is fed into the system. The path for this signal is processed through different components, ultimately producing the output signal \( y[n] \). - The output of the initial delay element is fed into the \(-0.7\) multiplier. The resulting signal is then passed back into one of the inputs of the summing junction. - Similarly, the \0.1\ multiplier takes its input from the delayed signal and feeds into another input of the summing junction. - The remaining signal paths shown in the diagram involve additional processing through the delay elements, feeding back into both the multipliers and the summing junction to achieve the desired output response. #### Input-Output Relationship: - The equation \( x[n] = u[n] \) refers to an impulse or step input, typically noted as the unit step function \( u[n] \) in DSP terms. This indicates that the system response shown is based on this standard input signal. The overall architecture of the diagram suggests it represents a feedback or recursive filter, given the interconnected nature of delays and multipliers feeding back into each other and the summing junction.
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