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Suppose that when x(t) u(t + 3) is the input to an LTI system with impulse response h(t), the output is y(t) (drawn below). What is h(t) ? = -3 -2 -1 (a) 8(t-1) + 8(t - 2) - 28(t - 5) (b) 8(t + 2) + 8(t+1) — 28(t − 2) (c) 8(t+5) + 8(t + 4) − 28(t + 1) 2 1 y(t) 0 1 2 t

Suppose that when x(t) u(t + 3) is the input to an LTI system with impulse response h(t), the output is y(t) (drawn below). What is h(t) ? = -3 -2 -1 (a) 8(t-1) + 8(t - 2) - 28(t - 5) (b) 8(t + 2) + 8(t+1) — 28(t − 2) (c) 8(t+5) + 8(t + 4) − 28(t + 1) 2 1 y(t) 0 1 2 t

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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### Problem Statement Suppose that when \( x(t) = u(t + 3) \) is the input to an LTI system with impulse response \( h(t) \), the output is \( y(t) \) (drawn below). What is \( h(t) \)? ### Graph Description The graph provided depicts the output function \( y(t) \) in red. Here's a detailed description of the graph: - The horizontal axis (t-axis) ranges from -3 to 3. - The vertical axis (y(t)-axis) is labeled with values from 0 to 2. - The graph is a piecewise constant function: - For \( t < -2 \), \( y(t) = 0 \). - For \( -2 \leq t < -1 \), \( y(t) = 1 \). - For \( -1 \leq t < 2 \), \( y(t) = 2 \). - For \( t \geq 2 \), \( y(t) = 0 \). ### Mathematical Options The choices for \( h(t) \) are given as: (a) \( \delta(t - 1) + \delta(t - 2) - 2\delta(t - 5) \) (b) \( \delta(t + 2) + \delta(t + 1) - 2\delta(t - 2) \) (c) \( \delta(t + 5) + \delta(t + 4) - 2\delta(t + 1) \) --- ### Analysis for Educational Purpose To solve this problem, we need to understand the relationship between the input and output in an LTI system. The convolution of the input \( x(t) = u(t + 3) \) with the impulse response \( h(t) \) should yield the output \( y(t) \). **Convolution** of \( x(t) \) and \( h(t) \) is: \[ y(t) = x(t) * h(t) \] Given the output function \( y(t) \), we need to deduce \( h(t) \) by analyzing the characteristics of the given response and the possible options. ### Selected Option Justification Review each option provided: - **(a)** This option does not align with the step changes observed in \( y(t) \
Transcribed Image Text:### Problem Statement Suppose that when \( x(t) = u(t + 3) \) is the input to an LTI system with impulse response \( h(t) \), the output is \( y(t) \) (drawn below). What is \( h(t) \)? ### Graph Description The graph provided depicts the output function \( y(t) \) in red. Here's a detailed description of the graph: - The horizontal axis (t-axis) ranges from -3 to 3. - The vertical axis (y(t)-axis) is labeled with values from 0 to 2. - The graph is a piecewise constant function: - For \( t < -2 \), \( y(t) = 0 \). - For \( -2 \leq t < -1 \), \( y(t) = 1 \). - For \( -1 \leq t < 2 \), \( y(t) = 2 \). - For \( t \geq 2 \), \( y(t) = 0 \). ### Mathematical Options The choices for \( h(t) \) are given as: (a) \( \delta(t - 1) + \delta(t - 2) - 2\delta(t - 5) \) (b) \( \delta(t + 2) + \delta(t + 1) - 2\delta(t - 2) \) (c) \( \delta(t + 5) + \delta(t + 4) - 2\delta(t + 1) \) --- ### Analysis for Educational Purpose To solve this problem, we need to understand the relationship between the input and output in an LTI system. The convolution of the input \( x(t) = u(t + 3) \) with the impulse response \( h(t) \) should yield the output \( y(t) \). **Convolution** of \( x(t) \) and \( h(t) \) is: \[ y(t) = x(t) * h(t) \] Given the output function \( y(t) \), we need to deduce \( h(t) \) by analyzing the characteristics of the given response and the possible options. ### Selected Option Justification Review each option provided: - **(a)** This option does not align with the step changes observed in \( y(t) \
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