GATE Exam > GATE Questions > Let x[n] = e-2nu[n] be the input to a system.... Start Learning for Free
Let x[n] = e-2n u[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?
- a)h[n] = n
- b)h[n] = 1/n
- c)h[n] = 1/n2
- d)Both 2 & 3
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let x[n] = e-2nu[n] be the input to a system. Which of the following i...
A system is said to be BIBO stable if it’s impulse response is absolutely summable,
Out of all the responses only
is absolutely summable.
Is not absolutely summable it is divergent.
Out of all the responses only
is absolutely summable.Is not absolutely summable it is divergent.
Most Upvoted Answer
Let x[n] = e-2nu[n] be the input to a system. Which of the following i...
D) Both 2 and 3.
To determine if the output of a system is bounded, we need to check if the convolution sum is bounded. The convolution sum is given by:
y[n] = ∑(x[k]h[n-k])
For the given input x[n] = e^(-2n)u[n], we can substitute it into the convolution sum:
y[n] = ∑(e^(-2k)u[k]h[n-k])
Let's consider each option:
a) h[n] = n
Substituting this into the convolution sum:
y[n] = ∑(e^(-2k)u[k](n - k))
The sum is not bounded because the term (n - k) is unbounded.
b) h[n] = 1/n
Substituting this into the convolution sum:
y[n] = ∑(e^(-2k)u[k](1/n)(1/(n-k)))
The sum is not bounded because the term 1/(n-k) is unbounded.
c) h[n] = 1/n^2
Substituting this into the convolution sum:
y[n] = ∑(e^(-2k)u[k](1/n^2)(1/(n-k)))
The sum is bounded because both (1/n^2) and (1/(n-k)) are bounded.
Therefore, the impulse response h[n] = 1/n^2 gives the bounded output for the given input x[n] = e^(-2n)u[n].
To determine if the output of a system is bounded, we need to check if the convolution sum is bounded. The convolution sum is given by:
y[n] = ∑(x[k]h[n-k])
For the given input x[n] = e^(-2n)u[n], we can substitute it into the convolution sum:
y[n] = ∑(e^(-2k)u[k]h[n-k])
Let's consider each option:
a) h[n] = n
Substituting this into the convolution sum:
y[n] = ∑(e^(-2k)u[k](n - k))
The sum is not bounded because the term (n - k) is unbounded.
b) h[n] = 1/n
Substituting this into the convolution sum:
y[n] = ∑(e^(-2k)u[k](1/n)(1/(n-k)))
The sum is not bounded because the term 1/(n-k) is unbounded.
c) h[n] = 1/n^2
Substituting this into the convolution sum:
y[n] = ∑(e^(-2k)u[k](1/n^2)(1/(n-k)))
The sum is bounded because both (1/n^2) and (1/(n-k)) are bounded.
Therefore, the impulse response h[n] = 1/n^2 gives the bounded output for the given input x[n] = e^(-2n)u[n].
 | Explore Courses for GATE exam |  |
Top Courses for GATEView all
Top Courses for GATE
Question Description
Let x[n] = e-2nu[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?a)h[n] = nb)h[n] = 1/nc)h[n] = 1/n2d)Both 2 & 3Correct answer is option 'C'. Can you explain this answer? for GATE 2026 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let x[n] = e-2nu[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?a)h[n] = nb)h[n] = 1/nc)h[n] = 1/n2d)Both 2 & 3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let x[n] = e-2nu[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?a)h[n] = nb)h[n] = 1/nc)h[n] = 1/n2d)Both 2 & 3Correct answer is option 'C'. Can you explain this answer?.
Let x[n] = e-2nu[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?a)h[n] = nb)h[n] = 1/nc)h[n] = 1/n2d)Both 2 & 3Correct answer is option 'C'. Can you explain this answer? for GATE 2026 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let x[n] = e-2nu[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?a)h[n] = nb)h[n] = 1/nc)h[n] = 1/n2d)Both 2 & 3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let x[n] = e-2nu[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?a)h[n] = nb)h[n] = 1/nc)h[n] = 1/n2d)Both 2 & 3Correct answer is option 'C'. Can you explain this answer?.
Solutions for Let x[n] = e-2nu[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?a)h[n] = nb)h[n] = 1/nc)h[n] = 1/n2d)Both 2 & 3Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE. Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of Let x[n] = e-2nu[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?a)h[n] = nb)h[n] = 1/nc)h[n] = 1/n2d)Both 2 & 3Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let x[n] = e-2nu[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?a)h[n] = nb)h[n] = 1/nc)h[n] = 1/n2d)Both 2 & 3Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Let x[n] = e-2nu[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?a)h[n] = nb)h[n] = 1/nc)h[n] = 1/n2d)Both 2 & 3Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Let x[n] = e-2nu[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?a)h[n] = nb)h[n] = 1/nc)h[n] = 1/n2d)Both 2 & 3Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let x[n] = e-2nu[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?a)h[n] = nb)h[n] = 1/nc)h[n] = 1/n2d)Both 2 & 3Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GATE tests.
| Explore Courses for GATE exam | |
Top Courses for GATE
Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
