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The impulse response. h[n] of a linear time invariant system is given by h[n] = u[n + 3] + u[n - 3] - 2u[n - 7], the above system is
  • a)
    stable but not causal.
  • b)
    stable and causal.
  • c)
    causai but unstable.
  • d)
    unstable and not causal.
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The impulse response. h[n] of a linear time invariant system is given ...
The given impulse response of a system

h[n] = u[n + 3] + u[n – 2] – 2u[n – 7]

The given system equation is non-causal for any value of n, since output depends upon the future input.

The given system is stable.
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Most Upvoted Answer
The impulse response. h[n] of a linear time invariant system is given ...
Answer:

To determine the stability and causality of the given system, we need to analyze the impulse response h[n] = u[n-3] - u[n-7].

Stability:
A system is considered stable if its impulse response is absolutely summable, i.e., the sum of the magnitudes of all the samples is finite. In other words, if ∑|h[n]| < ∞,="" then="" the="" system="" is="" />

Let's calculate the sum of the magnitudes of all the samples in h[n]:

∑|h[n]| = ∑|u[n-3] - u[n-7]|

Considering the given impulse response, we can observe that only three samples have non-zero values: n = 3, n = 4, and n = 5. For all other values of n, h[n] = 0.

∑|h[n]| = |1| + |1| + |1| = 3 < />

Since the sum of the magnitudes of all the samples is finite, the system is stable.

Causality:
A system is considered causal if the output depends only on present and past inputs, i.e., for n < 0,="" the="" output="" is="" zero.="" in="" other="" words,="" if="" h[n]="0" for="" n="" />< 0,="" then="" the="" system="" is="" />

Let's analyze the given impulse response h[n]:

h[n] = u[n-3] - u[n-7]

For n < 3,="" both="" u[n-3]="" and="" u[n-7]="" are="" zero,="" so="" h[n]="0." therefore,="" the="" system="" is="" />

Conclusion:
Based on the analysis, we can conclude that the given system is stable (option 'A') and causal.
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The impulse response. h[n] of a linear time invariant system is given by h[n] = u[n + 3] + u[n - 3] - 2u[n - 7], the above system isa)stable but not causal.b)stable and causal.c)causai but unstable.d)unstable and not causal.Correct answer is option 'A'. Can you explain this answer?
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The impulse response. h[n] of a linear time invariant system is given by h[n] = u[n + 3] + u[n - 3] - 2u[n - 7], the above system isa)stable but not causal.b)stable and causal.c)causai but unstable.d)unstable and not causal.Correct answer is option 'A'. 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 The impulse response. h[n] of a linear time invariant system is given by h[n] = u[n + 3] + u[n - 3] - 2u[n - 7], the above system isa)stable but not causal.b)stable and causal.c)causai but unstable.d)unstable and not causal.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The impulse response. h[n] of a linear time invariant system is given by h[n] = u[n + 3] + u[n - 3] - 2u[n - 7], the above system isa)stable but not causal.b)stable and causal.c)causai but unstable.d)unstable and not causal.Correct answer is option 'A'. Can you explain this answer?.
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