Are the following systems linear? Is it memoryless? Is it causal? Explain your answer. Can impulse response and transfer function be found for systems? Find if it can be found, if not, explain why. (Note: The input of the system is "u(t)" and the output is "y(t)". “8(t)" is unit impulse, "1(t)" is unit step function. In some cases, impulse response or transfer function is already given In this case, find what is not given if it can be found.) 1. System with input-output relation y(t) + ý(t) = 2u(t) 2. System with input-output relationship y(t) = u(t)u(t – 1) 3. System with input-output relationship y(t) = u(t)u(1 – t)

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If I have to ask the question piece by piece, write down how I should ask it.
Subject : "Lineer Algebra"(ElectricalEngineering)
Books about the question:
“Chi Tsong Chen, Linear System Theory and Design"
“John S. Bay, Fundamentals of Linear State Space Systems"
NOTE:ACalculatorOrComputerCanBeUsedForNumericalCalculations(MatrixMultiplication,Polynom-
ialRoots, Etc.),ButTheQuestionsCannotBeSolvedByTheComputer.SomeQuestionsMayNotHaveSolut-
ions,ExplainThemWithTheirReasons.
Are the following systems linear? Is it memoryless? Is it causal? Explain your answer.
Can impulse response and transfer function be found for systems?
Find if it can be found, if not, explain why.
(Note: The input of the system is "uft)" and the output is “y(t)". "8(t)" is unit impulse, "1(t)" is
unit step function. In some cases, impulse response or transfer function is already given In this
case, find what is not given if it can be found.)
1. System with input-output relation
y(t) + ý(t) = 2u(t)
2. System with input-output relationship
y(t) = u(t)u(t – 1)
3. System with input-output relationship
y(t) = u(t)u(1 – t)
4. System with impulse response
g(t, t) = sin(t) cos(t)
5. System with impulse response
g(t, t) = [sin(t) cos(t) – sin(t) cos(t)]1(t – t)
6. System with impulse response
g(t, t) = 48(t – t)
Transcribed Image Text:If I have to ask the question piece by piece, write down how I should ask it. Subject : "Lineer Algebra"(ElectricalEngineering) Books about the question: “Chi Tsong Chen, Linear System Theory and Design" “John S. Bay, Fundamentals of Linear State Space Systems" NOTE:ACalculatorOrComputerCanBeUsedForNumericalCalculations(MatrixMultiplication,Polynom- ialRoots, Etc.),ButTheQuestionsCannotBeSolvedByTheComputer.SomeQuestionsMayNotHaveSolut- ions,ExplainThemWithTheirReasons. Are the following systems linear? Is it memoryless? Is it causal? Explain your answer. Can impulse response and transfer function be found for systems? Find if it can be found, if not, explain why. (Note: The input of the system is "uft)" and the output is “y(t)". "8(t)" is unit impulse, "1(t)" is unit step function. In some cases, impulse response or transfer function is already given In this case, find what is not given if it can be found.) 1. System with input-output relation y(t) + ý(t) = 2u(t) 2. System with input-output relationship y(t) = u(t)u(t – 1) 3. System with input-output relationship y(t) = u(t)u(1 – t) 4. System with impulse response g(t, t) = sin(t) cos(t) 5. System with impulse response g(t, t) = [sin(t) cos(t) – sin(t) cos(t)]1(t – t) 6. System with impulse response g(t, t) = 48(t – t)
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