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 ? (a) 3/2 (b) 1/2 -1/2 y(t) A 0 1 -3 -2 7 2 3 t
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 ? (a) 3/2 (b) 1/2 -1/2 y(t) A 0 1 -3 -2 7 2 3 t
Introductory Circuit Analysis (13th Edition)
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66bc14d7-9bd5-4ef7-a060-9dc8d70059dc%2F516e73b7-dc5c-4df1-b3c9-3a5d78b04f1a%2Fvdt79sv_processed.jpeg&w=3840&q=75)
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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