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Suppose the output from an LTI system is 2je³jt +e-2jt when the input is -e³jt+2e-2jt. What is the output from the same system when the input is 2e³jt-je-2jt ? (a) -4je³jt (j/2)e-2jt (b) 4je³jt+ (j/2)e-2jt (c) je³jt - 2je-2jt

Suppose the output from an LTI system is 2je³jt +e-2jt when the input is -e³jt+2e-2jt. What is the output from the same system when the input is 2e³jt-je-2jt ? (a) -4je³jt (j/2)e-2jt (b) 4je³jt+ (j/2)e-2jt (c) je³jt - 2je-2jt

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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### LTI System Input-Output Problem **Problem Statement:** Suppose the output from a Linear Time-Invariant (LTI) system is \(2je^{3jt} + e^{-2jt}\) when the input is \(-e^{3jt} + 2e^{-2jt}\). What is the output from the same system when the input is \(2e^{3jt} - je^{-2jt}\)? **Choices:** - (a) \(-4je^{3jt} - \frac{j}{2}e^{-2jt}\) - (b) \(4je^{3jt} + \frac{j}{2}e^{-2jt}\) - (c) \(je^{3jt} - 2je^{-2jt}\) **Discussion:** An LTI (Linear Time-Invariant) system creates specific outputs for given inputs and generally follows the principles of linearity and time invariance. In this problem, the goal is to find the resulting output of the system when presented with a specific new input. Understanding the problem's constraints (input-output relationships) and utilizing the property definitions of linear systems will help derive the correct output. **Detailed Explanation:** None required in this transcription. Use the dropdown or radio buttons to select the correct answer based on your calculations and understanding of the LTI system properties.
Transcribed Image Text:### LTI System Input-Output Problem **Problem Statement:** Suppose the output from a Linear Time-Invariant (LTI) system is \(2je^{3jt} + e^{-2jt}\) when the input is \(-e^{3jt} + 2e^{-2jt}\). What is the output from the same system when the input is \(2e^{3jt} - je^{-2jt}\)? **Choices:** - (a) \(-4je^{3jt} - \frac{j}{2}e^{-2jt}\) - (b) \(4je^{3jt} + \frac{j}{2}e^{-2jt}\) - (c) \(je^{3jt} - 2je^{-2jt}\) **Discussion:** An LTI (Linear Time-Invariant) system creates specific outputs for given inputs and generally follows the principles of linearity and time invariance. In this problem, the goal is to find the resulting output of the system when presented with a specific new input. Understanding the problem's constraints (input-output relationships) and utilizing the property definitions of linear systems will help derive the correct output. **Detailed Explanation:** None required in this transcription. Use the dropdown or radio buttons to select the correct answer based on your calculations and understanding of the LTI system properties.
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