5.1 A causal signal x(t) having a Laplace transform with poles in the open-left s-plane (i.e., not including the jN axis) has a Fourier transform that can be found from its Laplace transform. Consider the following signals: x1(t) = e-2"u (t), x2(t) =r(t), x3(t) = x1(t)x2(t). 354 CHAPTER 5 FREQUENCY ANALYSIS: THE FOURIER TRANSFORM (a) Determine the Laplace transform of the above signals indicating their corresponding region of convergence. (b) Determine for which of these signals you can find its Fourier transform from its Laplace transform. Explain. (c) Give the Fourier transform of the signals that can be obtained from their Laplace transform. Answers: (a) X2(s) =1/s², o > 0; (b) x1(t) and x3(t).

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...
icon
Related questions
icon
Concept explainers
Question
Please write in clear handwriting or via Word
5.10 PROBLEMS
5.10.1 BASIC PROBLEMS
5.1 A causal signal x(t) having a Laplace transform with poles in the open-left s-plane (i.e., not
including the j2 axis) has a Fourier transform that can be found from its Laplace transform.
Consider the following signals:
x1(t) = e-2'u (t), x2(t)=r(t), x3(t) = x1(t)x2(t).
354
CHAPTER 5 FREQUENCY ANALYSIS: THE FOURIER TRANSFORM
(a) Determine the Laplace transform of the above signals indicating their corresponding region
of convergence.
(b) Determine for which of these signals you can find its Fourier transform from its Laplace
transform. Explain.
(c) Give the Fourier transform of the signals that can be obtained from their Laplace transform.
Answers: (a) X2(s) = 1/s², o > 0; (b) x1(t) and x3(t).
Transcribed Image Text:5.10 PROBLEMS 5.10.1 BASIC PROBLEMS 5.1 A causal signal x(t) having a Laplace transform with poles in the open-left s-plane (i.e., not including the j2 axis) has a Fourier transform that can be found from its Laplace transform. Consider the following signals: x1(t) = e-2'u (t), x2(t)=r(t), x3(t) = x1(t)x2(t). 354 CHAPTER 5 FREQUENCY ANALYSIS: THE FOURIER TRANSFORM (a) Determine the Laplace transform of the above signals indicating their corresponding region of convergence. (b) Determine for which of these signals you can find its Fourier transform from its Laplace transform. Explain. (c) Give the Fourier transform of the signals that can be obtained from their Laplace transform. Answers: (a) X2(s) = 1/s², o > 0; (b) x1(t) and x3(t).
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
8085 Microprocessor
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,