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Q1- Determine the Laplace transform and ROC of the following signals: I. x(t) = e5tu(-t + 3) († - 1)n = (1)x П. III. x(t) = e-2tu(t) +e-3tu(t)

Q1- Determine the Laplace transform and ROC of the following signals: I. x(t) = e5tu(-t + 3) († - 1)n = (1)x П. III. x(t) = e-2tu(t) +e-3tu(t)

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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Q1- Determine the Laplace transform and ROC of the following signals: I. x(t) = u(t - 4) II. x(t) = e5tu(-t + 3) III. x(t) = e-2tu(t) + e-3tu(t) IV. x(t) = e-t(t – 3)u(t – 3) Q2- Find the inverse Laplace transform of 3s+4 a) X(s) = (s+1)(s+2)² 2 %3D s-2 Q3- The relationship between the input x(t) and output y(t) of a causal system is described by the differential equation given below. Use Laplace transforms to determine the transfer function and impulse response of the system. d d? d drz y(t) + 3y(t) + 2y(t) = 3x(t) +x(t) dt° dt Q4- If we have 3s +1 -31 H(s) = x(t) = e*u(t) s² +6s + 5' Find y(t)
Transcribed Image Text:Q1- Determine the Laplace transform and ROC of the following signals: I. x(t) = u(t - 4) II. x(t) = e5tu(-t + 3) III. x(t) = e-2tu(t) + e-3tu(t) IV. x(t) = e-t(t – 3)u(t – 3) Q2- Find the inverse Laplace transform of 3s+4 a) X(s) = (s+1)(s+2)² 2 %3D s-2 Q3- The relationship between the input x(t) and output y(t) of a causal system is described by the differential equation given below. Use Laplace transforms to determine the transfer function and impulse response of the system. d d? d drz y(t) + 3y(t) + 2y(t) = 3x(t) +x(t) dt° dt Q4- If we have 3s +1 -31 H(s) = x(t) = e*u(t) s² +6s + 5' Find y(t)
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