Linear convolution multiple choice questions

Linear convolution 

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

A) x[n] = ∑∞k=-∞ x[k]δ[n-k]

B) x[n] = ∑∞k=-∞ x[k]δ[nk]

C) x[n] = ∑∞k=-∞ x[k]δ[k]

D) x[n] = ∑∞k=-∞ x[k]δ[n]

Answer: x[n] = ∑∞k=-∞ x[k]δ[n-k]

2. The convolution sum is given by _____ equation.

A) x[n]*h[n] = ∑∞k=-∞ x[k]h[n-k]

B) x[n]*h[n] = ∑∞k=-∞ x[n]h[n-k]

C) x[n]*h[n] = ∑∞k=-∞ x[k]h[nk]

D) x[n]*h[n] = ∑∞k=-∞ x[k]h[k]

Answer: x[n]*h[n] = ∑∞k=-∞ x[k]h[n-k].

3. 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: Linear and time invariant

4. 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: x[n]δ[n] = x[0]δ[n]

5. 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: Convolution sum

6. 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: {2, 5, 12, 11, 12}

7. When the sequences x1 [n] = u [n] and x2 [n] = u [n-3], the output of LTI system is given as _____
A) y[n] = n-2, n>3
B) y[n] = n-2, n≥3
C) y[n] = n+2, n>3
D) y[n] = n-2, n≤3
Answer: y[n] = n-2, n≥3

8. The impulse response h (t) of an LTI system is given by e^-2t.u(t) . What is the step response?
A) y(t) = ¹⁄₂ (1 – e^-2t) u (t)
B) y(t) = ¹⁄₂ (1 – e^-2t)
C) y(t) = (1- e^-2t) u (t)
D) y(t) = ¹⁄₂ (e^-2t) u (t)
Answer: y(t) = ¹⁄₂ (1 – e^-2t) u (t)

9. Is (t)*h(t) = h(t)*x(t)?
A) True
B) False
Answer: True

10. Compute u (t) convolved with itself?
A) y(t)=t.u(t)
B) y(t)=u(t)
C) y(t)=t².u(t)
D) y(t)=t.u(t-1)
Answer: y(t)=t.u(t)

11. Convolve the signals e^-2t u(t), e^-3t u(t). Determine the output?
A) y(t) = (e^-2t – e^-3t)u(t)
B) y(t) = (e^-2t – e^-3t)
C) y(t) = (e^-3t – e^-2t)u(t)
D) y(t) = (e^-t – e^-3t)u(t)
Answer: y(t) = (e^-2t – e^-3t)u(t)

12. Find the convolution of x1[n] = {1, 2, 3, 4} and x2[n] = {2, 1, 2, 1}.
A) Y[n] = {14, 10, 14, 10}
B) Y [n] = {14, 16, 14, 16}
C) Y [n] = {14, 16,-14,-16}
D) Y [n] = {14,-16,-14, 16}
Answer: Y [n] = {14, 16, 14, 16}