Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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## Convolution of Signals If \( y(t) = x(t) * h(t) \) (drawn below), then what is the value of the signal \( x(t + 3) * h(t - 2) \) when \( t = -1/2 \)? ### Graph Description The figure displays a graph of the function \( y(t) \) as a red piecewise linear function of \( t \), which is represented on the x-axis. The y-axis represents the values of \( y(t) \). The function \( y(t) \) is defined as follows: - For \( -3 \le t < -2 \): \( y(t) = 0 \) - For \( -2 \le t < -1 \): \( y(t) = 1 \) - For \( -1 \le t < 0 \): \( y(t) = 2 \) - For \( 0 \le t < 1 \): \( y(t) = 1 \) - For \( 1 \le t \le 3 \): \( y(t) = 0 \) ### Question and Options To find the value of the signal \( x(t + 3) * h(t - 2) \) when \( t = -1/2 \), consider the following options: (a) \( \frac{3}{2} \) (b) \( \frac{1}{2} \) (c) \( -\frac{1}{2} \) Use this information and the properties of convolution to determine the correct option.
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Transcribed Image Text:## Convolution of Signals If \( y(t) = x(t) * h(t) \) (drawn below), then what is the value of the signal \( x(t + 3) * h(t - 2) \) when \( t = -1/2 \)? ### Graph Description The figure displays a graph of the function \( y(t) \) as a red piecewise linear function of \( t \), which is represented on the x-axis. The y-axis represents the values of \( y(t) \). The function \( y(t) \) is defined as follows: - For \( -3 \le t < -2 \): \( y(t) = 0 \) - For \( -2 \le t < -1 \): \( y(t) = 1 \) - For \( -1 \le t < 0 \): \( y(t) = 2 \) - For \( 0 \le t < 1 \): \( y(t) = 1 \) - For \( 1 \le t \le 3 \): \( y(t) = 0 \) ### Question and Options To find the value of the signal \( x(t + 3) * h(t - 2) \) when \( t = -1/2 \), consider the following options: (a) \( \frac{3}{2} \) (b) \( \frac{1}{2} \) (c) \( -\frac{1}{2} \) Use this information and the properties of convolution to determine the correct option.
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