## Convolution of SignalsIf \( y(t) = x(t) * h(t) \) (drawn below), then what is the value of the signal \( x(t + 3) * h(t - 2) \) when \( t = -1/2 \)?### Graph DescriptionThe 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 OptionsTo 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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Answered: If y(t) = x(t) * h(t) (drawn below),…

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)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

## 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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