Consider the continuous-domain signal : t<0 0 1 a(t): (1) : where t denotes time, and a > 0 is a constant. This signal is the input to a linear system described by the differential equation dx y(t) : (2) dt (a) Show (via several derivation steps) that the Laplace transform of x(t) is 1-e-(s+ 1) X(s) = (3) s2 s+a
Consider the continuous-domain signal : t<0 0 1 a(t): (1) : where t denotes time, and a > 0 is a constant. This signal is the input to a linear system described by the differential equation dx y(t) : (2) dt (a) Show (via several derivation steps) that the Laplace transform of x(t) is 1-e-(s+ 1) X(s) = (3) s2 s+a
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Digital signal Processing
![Consider the continuous-domain signal
: t< 0
r(t):
0 <t< 1
(1)
:
exp[-a(t – 1)]) : t>1
where t denotes time, and a > 0 is a constant. This signal is the input to a linear system
described by the differential equation
d.r
y(t) =
(2)
%3!
(a) Show (via several derivation steps) that the Laplace transform of x(t) is
1-e-(s + 1)
X(s) =
(3)
s2
s + a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d7f6948-48cd-485d-8fb5-86f828ecf26a%2F836b986f-980e-4432-94d6-fe909019727d%2Fm8uxtck_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the continuous-domain signal
: t< 0
r(t):
0 <t< 1
(1)
:
exp[-a(t – 1)]) : t>1
where t denotes time, and a > 0 is a constant. This signal is the input to a linear system
described by the differential equation
d.r
y(t) =
(2)
%3!
(a) Show (via several derivation steps) that the Laplace transform of x(t) is
1-e-(s + 1)
X(s) =
(3)
s2
s + a
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