For a linear system, we are given two input-output pairs as follows: ● for input x₁(t) = [[0,1](t), the output y₁(t) = (1 − |t|) I[−1,1](t). ● for input x₂(t) = 21[0,2], the output y₂(t) = 2(1 + t)I{−1,1) (t) + 4(2 − t)I[1,2] (t). (a) Sketch the signals x₁, Y₁, x2, Y2. (b) True or False From the information given, we can infer the output y³(t) corresponding to the input x3(t) = −I(1,2] (t). Justify your answer. And if True, find and sketch the signal y3. (c) From the information given, can you infer whether or not the system is time-invariant? Justify your answer.

For a linear system, we are given two input-output pairs as follows: ● for input x₁(t) = [[0,1](t), the output y₁(t) = (1 − |t|) I[−1,1](t). ● for input x₂(t) = 21[0,2], the output y₂(t) = 2(1 + t)I{−1,1) (t) + 4(2 − t)I[1,2] (t). (a) Sketch the signals x₁, Y₁, x2, Y2. (b) True or False From the information given, we can infer the output y³(t) corresponding to the input x3(t) = −I(1,2] (t). Justify your answer. And if True, find and sketch the signal y3. (c) From the information given, can you infer whether or not the system is time-invariant? Justify your answer.

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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More details, step by step solution

For a linear system, we are given two input-output pairs as follows:

- For input \( x_1(t) = I_{[0,1]}(t) \), the output \( y_1(t) = (1 - |t|)I_{[-1,1]}(t) \).

- For input \( x_2(t) = 2I_{[0,2]} \), the output \( y_2(t) = 2(1 + t)I_{[-1,1]}(t) + 4(2 - t)I_{[1,2]}(t) \).

**(a)** Sketch the signals \( x_1, y_1, x_2, y_2 \).

**(b) True or False** From the information given, we can infer the output \( y_3(t) \) corresponding to the input \( x_3(t) = -I_{[1,2]}(t) \). Justify your answer. And if True, find and sketch the signal \( y_3 \).

**(c)** From the information given, can you infer whether or not the system is time-invariant? Justify your answer.

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