This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Continuous Time Convolution – I”.

For all the following questions, ‘*’ indicates convolution.$ indicates integral

1. Find the value of h[n]*d[n-1], d[n] being the delta function.

a) h[n-2]
b) h[n]
c) h[n-1]
d) h[n+1]
View Answer

Explanation: Convolution of a function with a delta function shifts accordingly.

2. Evaluate (exp(-at)u(t))*u(t), u(t) being the heaviside function.

a) (1-exp(at))u(t)/a

b) (1-exp(at))u(-t)/a

c) (1-exp(-at))u(t)/a

d) (1+exp(-at))u(t)/a

View Answer

Explanation: Use the convolution formula.

3. Find the value of h[n]*d[n-5], d[n] being the delta function.

a) h[n-2]
b) h[n-5]
c) h[n-4]
d) h[n+5]
View Answer

Explanation: Convolution of a function with a delta function shifts accordingly.

a) (1-exp(4t))u(t)/a

b) (1-exp(-4t))u(t)/a

c) (1-exp(=4t))u(t)/a

d) (1+exp(-4t))u(t)/a

View Answer

Explanation: Use the convolution formula.

5. Find the value of h[n-1]*d[n-1], d[n] being the delta function.

a) h[n-2]
b) h[n]
c) h[n-1]
d) h[n+1]
View Answer

Explanation: Convolution of a function with a delta function shifts accordingly.

6. Find the convolution of x(t) = exp(2t)u(-t), and h(t) = u(t-3)

a) 0.5exp(2t-6)u(-t+3) + 0.5u(t-3)

b) 0.5exp(2t-3)u(-t+3) + 0.8u(t-3)

c) 0.5exp(2t-6)u(-t+3) + 0.5u(t-6)

d) 0.5exp(2t-6)u(-t+3) + 0.8u(t-3)

View Answer

Explanation: Divide it into 2 sectors and apply the convolution formula.

7. Find the value of h[n]*d[n+1], d[n] being the delta function.

a) h[n-2]
b) h[n]
c) h[n-1]
d) h[n+1]
View Answer

Explanation: Convolution of a function with a delta function shifts accordingly.

8. Find the convolution of x(t) = exp(3t)u(-t), and h(t) = u(t-3)

a) 0.33exp(2t-6)u(-t+3) + 0.5u(t-3)

b) 0.5exp(4t-3)u(-t+3) + 0.8u(t-3)

c) 0.33exp(2t-6)u(-t+3) + 0.5u(t-6)

d) 0.33exp(3t-6)u(-t+3) + 0.33u(t-3)

View Answer

Explanation: Divide it into 2 sectors and apply the convolution formula.

a) x(t+56)

b) x(t+32)

c) x(t+22)

d) x(t-22)

View Answer

Explanation: Convolution of a function with a delta function shifts accordingly.

10. Find x(t)*u(t)

a) tx(t)

b) t^2x(t)

c) $x(t^2)

d) $x(t)

View Answer

Explanation: Apply the convolution formula. The above corollary exists for any x(t) [not impulsive].

**Sanfoundry Global Education & Learning Series – Signals and Systems.**

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