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Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) ∗ h(t) = y (t). Further, if x(t) ∗h(t)= z (t) , which of the following statements is true?
  • a)
    For some but not all t ∈(–∞, ∞), z(t) ≤ y (t)
  • b)
    For all t ∈(–∞, ∞), z(t ) ≥ y(t )
  • c)
    For all t ∈(–∞, ∞), z(t ) ≤ y(t )
  • d)
    For some but not all t ∈(–∞, ∞), z(t) ≥ y (t)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Suppose for input x(t) a linear time-invariant system with impulse res...
Since, y(t)= x(t) + h(t)
and z(t)= x(t) ×h(t)
Case - 1: 
 and 
then, 


Case-2:

then, y(t)= z(t)

Thus, z(t) ≥ y (t ), for all ‘t ’
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Most Upvoted Answer
Suppose for input x(t) a linear time-invariant system with impulse res...
Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) * h(t) = y(t), where * denotes convolution.

If we multiply both sides of the equation by a constant k, we get k * (x(t) * h(t)) = k * y(t). Since the system is linear, it follows that k * (x(t) * h(t)) = k * x(t) * h(t), where * now denotes scalar multiplication.

Therefore, k * x(t) * h(t) = k * y(t), which shows that scaling the input by a constant k results in scaling the output by the same constant k.

This property of linear time-invariant systems is known as the scaling property. It states that if the input is scaled by a constant, the output will also be scaled by the same constant.
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Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) ∗ h(t) = y (t). Further, if x(t) ∗h(t)= z (t) , which of the following statements is true?a)For some but not all t ∈(–∞, ∞), z(t) ≤ y (t)b)For all t ∈(–∞, ∞), z(t ) ≥ y(t )c)For all t ∈(–∞, ∞), z(t ) ≤ y(t )d)For some but not all t ∈(–∞, ∞), z(t) ≥ y (t)Correct answer is option 'B'. Can you explain this answer?
Question Description
Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) ∗ h(t) = y (t). Further, if x(t) ∗h(t)= z (t) , which of the following statements is true?a)For some but not all t ∈(–∞, ∞), z(t) ≤ y (t)b)For all t ∈(–∞, ∞), z(t ) ≥ y(t )c)For all t ∈(–∞, ∞), z(t ) ≤ y(t )d)For some but not all t ∈(–∞, ∞), z(t) ≥ y (t)Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) ∗ h(t) = y (t). Further, if x(t) ∗h(t)= z (t) , which of the following statements is true?a)For some but not all t ∈(–∞, ∞), z(t) ≤ y (t)b)For all t ∈(–∞, ∞), z(t ) ≥ y(t )c)For all t ∈(–∞, ∞), z(t ) ≤ y(t )d)For some but not all t ∈(–∞, ∞), z(t) ≥ y (t)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) ∗ h(t) = y (t). Further, if x(t) ∗h(t)= z (t) , which of the following statements is true?a)For some but not all t ∈(–∞, ∞), z(t) ≤ y (t)b)For all t ∈(–∞, ∞), z(t ) ≥ y(t )c)For all t ∈(–∞, ∞), z(t ) ≤ y(t )d)For some but not all t ∈(–∞, ∞), z(t) ≥ y (t)Correct answer is option 'B'. Can you explain this answer?.
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