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Determine and sketch the output.

Determine and sketch the output.

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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Consider a causal LTI system. When the input is \( x_0(t) = u(t-4) \), the Laplace transform of the output is \[ Y_0(s) = \frac{e^{-5s} - e^{-8s}}{s^2}. \] **Determine and sketch** the output of the system \( y(t) \) when the input is changed to \[ x(t) = u(t) - u(t-6). \] Try both of the following two methods: - **Method 1:** Find the system transfer function \( H(s) = Y_0(s)/X_0(s) \) from the input-output pair \((x_0(t), y_0(t))\), and then determine the Laplace transform \( Y(s) = H(s)X(s) \) of the output \( y(t) \). - **Method 2:** Express \( x(t) \) as a linear combination of some time-shifted copies of \( x_0(t) \), and then use the LTI properties to find \( Y(s) \) or \( y(t) \). Which one of the above two methods do you prefer in solving this problem?
Transcribed Image Text:Consider a causal LTI system. When the input is \( x_0(t) = u(t-4) \), the Laplace transform of the output is \[ Y_0(s) = \frac{e^{-5s} - e^{-8s}}{s^2}. \] **Determine and sketch** the output of the system \( y(t) \) when the input is changed to \[ x(t) = u(t) - u(t-6). \] Try both of the following two methods: - **Method 1:** Find the system transfer function \( H(s) = Y_0(s)/X_0(s) \) from the input-output pair \((x_0(t), y_0(t))\), and then determine the Laplace transform \( Y(s) = H(s)X(s) \) of the output \( y(t) \). - **Method 2:** Express \( x(t) \) as a linear combination of some time-shifted copies of \( x_0(t) \), and then use the LTI properties to find \( Y(s) \) or \( y(t) \). Which one of the above two methods do you prefer in solving this problem?
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