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Suppose the Laplace transform of a causal signal x₁ (t) is given by X₁(s) s+2 s²+1 (a) What is the Fourier transform X₁ (w) of the signal? (b) Using the Laplace transform properties, find the Laplace transform of the following signal x2(t). x2(t) = e³ x₁(t−1)-4x₁(4) Note, you do not need to simplify the expression of X2(s). However, state whether it is possible to write X2(s) as a rational fraction (i.e. ratio of polynomials) in s.

Suppose the Laplace transform of a causal signal x₁ (t) is given by X₁(s) s+2 s²+1 (a) What is the Fourier transform X₁ (w) of the signal? (b) Using the Laplace transform properties, find the Laplace transform of the following signal x2(t). x2(t) = e³ x₁(t−1)-4x₁(4) Note, you do not need to simplify the expression of X2(s). However, state whether it is possible to write X2(s) as a rational fraction (i.e. ratio of polynomials) in s.

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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Suppose the Laplace transform of a causal signal x₁ (t) is given by X₁(s) s+2 s²+1 (a) What is the Fourier transform X₁ (w) of the signal? (b) Using the Laplace transform properties, find the Laplace transform of the following signal x2(t). x2(t) = e³ x₁(t−1)-4x₁(4) Note, you do not need to simplify the expression of X2(s). However, state whether it is possible to write X2(s) as a rational fraction (i.e. ratio of polynomials) in s.
Transcribed Image Text:Suppose the Laplace transform of a causal signal x₁ (t) is given by X₁(s) s+2 s²+1 (a) What is the Fourier transform X₁ (w) of the signal? (b) Using the Laplace transform properties, find the Laplace transform of the following signal x2(t). x2(t) = e³ x₁(t−1)-4x₁(4) Note, you do not need to simplify the expression of X2(s). However, state whether it is possible to write X2(s) as a rational fraction (i.e. ratio of polynomials) in s.
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