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! Required information A system has an impulse response h(t) = 3e-'u(t) and the excitation x(t) = rect (2 (t – 4)) Plot the response y() of the given system. Please upload your response/solution using the controls below.

! Required information A system has an impulse response h(t) = 3e-'u(t) and the excitation x(t) = rect (2 (t – 4)) Plot the response y() of the given system. Please upload your response/solution using the controls below.

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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### Required Information A system has an impulse response: \[ h(t) = 3e^{-4t}u(t) \] and the excitation: \[ x(t) = \text{rect}\left( 2 \left( t - \frac{1}{4} \right) \right) \] **Task**: Plot the response \( y(t) \) of the given system. Please upload your response/solution using the controls below. --- **Explanation:** - **Impulse Response \( h(t) \):** - \( h(t) = 3e^{-4t}u(t) \) signifies an exponentially decaying function multiplied by a unit step function \( u(t) \). This indicates that the system responds from \( t=0 \) onwards. - **Excitation \( x(t) \):** - \( x(t) = \text{rect}\left( 2 \left( t - \frac{1}{4} \right) \right) \) describes a rectangular function centered at \( t = \frac{1}{4} \) with a scaling factor of 2, altering its width and position. The task is to find and plot the response \( y(t) \) of the system when it is excited by \( x(t) \).
Transcribed Image Text:### Required Information A system has an impulse response: \[ h(t) = 3e^{-4t}u(t) \] and the excitation: \[ x(t) = \text{rect}\left( 2 \left( t - \frac{1}{4} \right) \right) \] **Task**: Plot the response \( y(t) \) of the given system. Please upload your response/solution using the controls below. --- **Explanation:** - **Impulse Response \( h(t) \):** - \( h(t) = 3e^{-4t}u(t) \) signifies an exponentially decaying function multiplied by a unit step function \( u(t) \). This indicates that the system responds from \( t=0 \) onwards. - **Excitation \( x(t) \):** - \( x(t) = \text{rect}\left( 2 \left( t - \frac{1}{4} \right) \right) \) describes a rectangular function centered at \( t = \frac{1}{4} \) with a scaling factor of 2, altering its width and position. The task is to find and plot the response \( y(t) \) of the system when it is excited by \( x(t) \).
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