Homework Help Given the following system and input function $ x[n] $. Find the output $ y[n] $ for $ 0 \leq n \leq 5 $ and $ y[-1] = 2 $.\[ y[n] = \frac{2}{5} y[n-1] - x[n] \]### Graph ExplanationThe graph is a discrete-time signal plot with the horizontal axis labeled $ n $ and the vertical axis labeled $ y[n] $. The graph shows the response of the system at various points:- The horizontal axis $ n $ ranges from -1 to 3.- The vertical axis $ y[n] $ ranges from -1 to 2.- The plot has discrete points connected by green vertical and horizontal lines. Each point on the graph corresponds to a specific value of $ y[n] $ at a given time step $ n $. These points represent critical values of the output sequence $ y[n] $ as calculated from the given difference equation.

Given Data:The discrete-time system with,The difference equation The initial value The input To…

Answered: iven the following system and input…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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Given the following system and input function $ x[n] $. Find the output $ y[n] $ for $ 0 \leq n \leq 5 $ and $ y[-1] = 2 $.

\[ y[n] = \frac{2}{5} y[n-1] - x[n] \]

### Graph Explanation

The graph is a discrete-time signal plot with the horizontal axis labeled $ n $ and the vertical axis labeled $ y[n] $. The graph shows the response of the system at various points:

- The horizontal axis $ n $ ranges from -1 to 3.
- The vertical axis $ y[n] $ ranges from -1 to 2.
- The plot has discrete points connected by green vertical and horizontal lines.

Each point on the graph corresponds to a specific value of $ y[n] $ at a given time step $ n $. These points represent critical values of the output sequence $ y[n] $ as calculated from the given difference equation.

Expert Solution

Step 1: Summarize the details given:

Given Data:

The discrete-time system with,

The difference equation $y left square bracket n right square bracket equals 2 over 5 y open square brackets n minus 1 close square brackets minus x open square brackets n close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space$
The initial value $y open square brackets negative 1 close square brackets equals 2$
The input $x open square brackets n close square brackets equals open curly brackets 1 with upwards arrow below comma space 2 comma space minus 3 close curly brackets$

To Find:

The output $y open square brackets n close square brackets$ for $0 less or equal than n less or equal than 5$ .

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