Solve the third one sketch plot ### Impulse Response and System Analysis#### Problem 1:**Objective:** Find the impulse response for $ 0 \leq n \leq 4 $. Determine if the system is FIR or IIR.\[ y[n] = 3x[n] - 2x[n-1] + 5x[n-2] + 4x[n-3] \]#### Problem 2:**Objective:** Find the impulse response for $ 0 \leq n \leq 4 $. Determine if the system is FIR or IIR.\[ y[n] = -\frac{2}{3} y[n-1] + 3x[n] \]#### Problem 3:**Objective:** Given the system and input function $ x[n] $, find the output $ y[n] $.\[ y[n] = 2x[n] - x[n-1] \]\[ x[n] = 3\delta[n] + 5\delta[n-1] - 2\delta[n-2] \]### Explanation:- **FIR (Finite Impulse Response) systems** have impulse responses that become zero after a finite number of steps. - **IIR (Infinite Impulse Response) systems** have impulse responses that do not become zero, continuing indefinitely.For each system problem, determine the impulse response by using the given equations and assess whether the system is FIR or IIR based on the response behavior.

Answered: Given 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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Solve the third one sketch plot

### Impulse Response and System Analysis

#### Problem 1:
**Objective:** Find the impulse response for $ 0 \leq n \leq 4 $. Determine if the system is FIR or IIR.

\[ y[n] = 3x[n] - 2x[n-1] + 5x[n-2] + 4x[n-3] \]

#### Problem 2:
**Objective:** Find the impulse response for $ 0 \leq n \leq 4 $. Determine if the system is FIR or IIR.

\[ y[n] = -\frac{2}{3} y[n-1] + 3x[n] \]

#### Problem 3:
**Objective:** Given the system and input function $ x[n] $, find the output $ y[n] $.

\[ y[n] = 2x[n] - x[n-1] \]

\[ x[n] = 3\delta[n] + 5\delta[n-1] - 2\delta[n-2] \]

### Explanation:

- **FIR (Finite Impulse Response) systems** have impulse responses that become zero after a finite number of steps.
- **IIR (Infinite Impulse Response) systems** have impulse responses that do not become zero, continuing indefinitely.

For each system problem, determine the impulse response by using the given equations and assess whether the system is FIR or IIR based on the response behavior.

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Since user has asked for the solution of third one, we will provide the solution of third one only.

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$straight y open square brackets straight n close square brackets space equals space 2 straight x open square brackets straight n close square brackets space minus space straight x open square brackets straight n minus 1 close square brackets semicolon straight x open square brackets straight n close square brackets space equals space 3 straight delta open square brackets straight n close square brackets space plus space 5 straight delta open square brackets straight n minus 1 close square brackets space minus space 2 straight delta open square brackets straight n minus 2 close square brackets semicolon$

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