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
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![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 y(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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F584ffa08-94ad-4eb4-a87d-fd258db9f802%2F8d5fc151-3698-418d-952a-fed3e15094f6%2Fdcx51ze_processed.png&w=3840&q=75)
Transcribed Image Text: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 y(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.
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