250+ TOP MCQs on Convolution : Impulse Response Representation for LTI Systems – 1 and Answers

Signals & Systems Multiple Choice Questions on “Convolution : Impulse Response Representation for LTI Systems – 1”.

1. Impulse response is the output of ______ system due to impulse input applied at time=0?
A. Linear
B. Time varying
C. Time invariant
D. Linear and time invariant

Answer: D
Clarification: Impulse response is the output of LTI system due to impulse input applied at time = 0 or n=0. Behaviour of an LTI system is characterised by the impulse response.

2. Which of the following is correct regarding to impulse signal?
A. x[n]δ[n] = x[0]δ[n]
B. x[n]δ[n] = δ[n]
C. x[n]δ[n] = x[n]
D. x[n]δ[n] = x[0]

Answer: A
Clarification: When the input x[n] is multiplied with an impulse signal, the result will be impulse signal with magnitude of x[n] at that time.

3. Weighted superposition of time-shifted impulse responses is termed as _______ for discrete-time signals.
A. Convolution integral
B. Convolution multiple
C. Convolution sum
D. Convolution

Answer: C
Clarification: Weighted superposition of time-shifted impulse responses is called convolution sum for discrete-time signals and convolution integral for continuous-time signals.

4. Which of the following is a correct expression for Impulse response?

Answer: A
Clarification: X [n] is represented as the weighted sum of time shifted impulses and concisely written as x[n] = ∑^∞_k=-∞ x[k]δ[n-k]..

7. Find the convolution sum of sequences x1[n] = (1, 2, 3) and x2[n] = (2, 1, 4).
A. {2, 5, 12, 11, 12}
B. {2, 12, 5, 11, 12}
C. {2, 11, 5, 12, 12}
D. {-2, 5,-12, 11, 12}

Answer: A
Clarification: x1[n] = δ(n)+2δ(n-1)+3δ(n-2) and x2[n] = 2δ(n)+δ(n-1)+4δ(n-2)
Y[n] = x1[n]*x2[n] by performing convolution operation on x1[n] and x2[n] we get the sequence as {2, 5, 12, 11, 12}.

8. Find the convolution sum of sequence x1[n] = {1, 2, 3} and
Answer: A
Clarification: x1[n] and x2[n] can be written as x1[n] = δ(n)+2δ(n-1)+3δ(n-2) and
x2[n] = δ(N+2) + 2 2δ(n+1) + 3δ(n) + 4δ(n-1) and convolving x1[n], x2[n] we get
Y [n] = {1, 4, 10, 16, 17, 12}.
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9. Determine the output of LTI with input x[n] =2δ(n)-δ(n-1) and h[n] given as below

Answer: B
Clarification: The h[n] can be written as
{1, 3, 2,-1, 1}.
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By convolving x[n] with the given h[n] we get the following sequence as result
Y [n] = {2, 5, 1, -4, 3, -1}.
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10. Consider h [n] as in figure 1 and x[n] = u[n] – u [n-3], determine the output y [n] of the LTI system?

Answer: A
Clarification: The h[n] can be written as
{1, 3, 2,-1, 1}.
↑
By convolving x [n] with the given h [n] we get the output
y [n] = {1,4,6,4,2,0,1}.
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