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Problem 1 (a) Suppose the Laplace transform of a causal signal x₁ (t) is given by S X₁(s) = 52 +2 Using the Laplace transform properties, find the Laplace transform of the following signal x2(t). x2(t) = e2t+1 x₁(t − 1) - tx₁(2t - 1) (b) Suppose an LTI system T whose impulse response is given by h(t) e 2t 1(t) t 1(t) +28(t) What is the transfer function of the system? (c) If the input x2 (t) is applied to the system T, what will be the output Y₂(s)? Note, you just need to provide Laplace transform of the output y₂(t). Simplification is not needed in any part of this question.

Problem 1 (a) Suppose the Laplace transform of a causal signal x₁ (t) is given by S X₁(s) = 52 +2 Using the Laplace transform properties, find the Laplace transform of the following signal x2(t). x2(t) = e2t+1 x₁(t − 1) - tx₁(2t - 1) (b) Suppose an LTI system T whose impulse response is given by h(t) e 2t 1(t) t 1(t) +28(t) What is the transfer function of the system? (c) If the input x2 (t) is applied to the system T, what will be the output Y₂(s)? Note, you just need to provide Laplace transform of the output y₂(t). Simplification is not needed in any part of this question.

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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Problem 1 (a) Suppose the Laplace transform of a causal signal x₁ (t) is given by S X₁(s) = 52 +2 Using the Laplace transform properties, find the Laplace transform of the following signal x2(t). x2(t) = e2t+1 x₁(t − 1) - tx₁(2t - 1) (b) Suppose an LTI system T whose impulse response is given by h(t) e 2t 1(t) t 1(t) +28(t) What is the transfer function of the system? (c) If the input x2 (t) is applied to the system T, what will be the output Y₂(s)? Note, you just need to provide Laplace transform of the output y₂(t). Simplification is not needed in any part of this question.
Transcribed Image Text:Problem 1 (a) Suppose the Laplace transform of a causal signal x₁ (t) is given by S X₁(s) = 52 +2 Using the Laplace transform properties, find the Laplace transform of the following signal x2(t). x2(t) = e2t+1 x₁(t − 1) - tx₁(2t - 1) (b) Suppose an LTI system T whose impulse response is given by h(t) e 2t 1(t) t 1(t) +28(t) What is the transfer function of the system? (c) If the input x2 (t) is applied to the system T, what will be the output Y₂(s)? Note, you just need to provide Laplace transform of the output y₂(t). Simplification is not needed in any part of this question.
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