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Use graphical method to find the out of an LTI system with the given input and impulse response.

Use graphical method to find the out of an LTI system with the given input and impulse response.

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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Use graphical method to find the out of an LTI system with the given input and impulse response.

 

 

 

 

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The image depicts two graphs showing functions \( x_1(t) \) and \( x_2(t) \) on separate axes, with respect to time \( t \). ### Graph of \( x_1(t) \): - **Axes**: The vertical axis represents \( x_1(t) \), while the horizontal axis represents time \( t \). - **Plot Details**: - The graph is a triangular waveform. - It starts at the origin (0, 0). - It linearly increases to a maximum of 2 at \( t = 2 \). - It then linearly decreases back to 0 at \( t = 4 \). - The line segments form a symmetric triangle. ### Graph of \( x_2(t) \): - **Axes**: The vertical axis represents \( x_2(t) \), while the horizontal axis represents time \( t \). - **Plot Details**: - The graph is a step function. - The function is 0 at \( t < 0 \). - It jumps to 1 at \( t = 0 \) and remains constant until \( t = 2 \). - At \( t = 2 \), it returns to 0. - The step transition is vertical, indicating an instantaneous change at \( t = 0 \) and \( t = 2 \). These graphs illustrate different types of waveforms commonly used in signal processing and control systems analysis.
Transcribed Image Text:The image depicts two graphs showing functions \( x_1(t) \) and \( x_2(t) \) on separate axes, with respect to time \( t \). ### Graph of \( x_1(t) \): - **Axes**: The vertical axis represents \( x_1(t) \), while the horizontal axis represents time \( t \). - **Plot Details**: - The graph is a triangular waveform. - It starts at the origin (0, 0). - It linearly increases to a maximum of 2 at \( t = 2 \). - It then linearly decreases back to 0 at \( t = 4 \). - The line segments form a symmetric triangle. ### Graph of \( x_2(t) \): - **Axes**: The vertical axis represents \( x_2(t) \), while the horizontal axis represents time \( t \). - **Plot Details**: - The graph is a step function. - The function is 0 at \( t < 0 \). - It jumps to 1 at \( t = 0 \) and remains constant until \( t = 2 \). - At \( t = 2 \), it returns to 0. - The step transition is vertical, indicating an instantaneous change at \( t = 0 \) and \( t = 2 \). These graphs illustrate different types of waveforms commonly used in signal processing and control systems analysis.
Expert Solution
Step 1: State the given data.

An LTI system is having input 

Electrical Engineering homework question answer, step 1, image 1

The impulse response of the LTI system is

Electrical Engineering homework question answer, step 1, image 2

We need to find the output of the LTI system.

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