The relationship between the input x(t) and output y(t) of a causal continuous-time LTI system is described by the differential equation given below. (a) (b) (c) dy(t) dt + 3y(t) = 2x(t) Find the transfer function H(s) for this system Find the impulse response h(t) for this system. Is this system stable? Give a reason for your answer.
The relationship between the input x(t) and output y(t) of a causal continuous-time LTI system is described by the differential equation given below. (a) (b) (c) dy(t) dt + 3y(t) = 2x(t) Find the transfer function H(s) for this system Find the impulse response h(t) for this system. Is this system stable? Give a reason for your answer.
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![The relationship between the input \( x(t) \) and output \( y(t) \) of a causal continuous-time LTI system is described by the differential equation given below.
\[
\frac{dy(t)}{dt} + 3y(t) = 2x(t)
\]
(a) Find the transfer function \( H(s) \) for this system.
(b) Find the impulse response \( h(t) \) for this system.
(c) Is this system stable? Give a reason for your answer.
(d) Find an expression for the frequency response \( H(\Omega) \) for this system.
(e) Find the system output \( y(t) \) due to the input \( x(t) = 5e^{-2t}u(t) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b207c38-3ae5-4958-b6f8-8e524b4be30c%2F7939d1da-7e43-4e21-a9e2-139460f75f7d%2Fhpk02j_processed.png&w=3840&q=75)
Transcribed Image Text:The relationship between the input \( x(t) \) and output \( y(t) \) of a causal continuous-time LTI system is described by the differential equation given below.
\[
\frac{dy(t)}{dt} + 3y(t) = 2x(t)
\]
(a) Find the transfer function \( H(s) \) for this system.
(b) Find the impulse response \( h(t) \) for this system.
(c) Is this system stable? Give a reason for your answer.
(d) Find an expression for the frequency response \( H(\Omega) \) for this system.
(e) Find the system output \( y(t) \) due to the input \( x(t) = 5e^{-2t}u(t) \).
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d) Find an expression for the frequency response H(Ω) for this system.
(e) Find the system output y(t) due to the input x(t) = 5e^(-2t) u(t).
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