# Signals & Systems Questions and Answers – Continuous Time Convolution – 1

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This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Continuous Time Convolution – 1”.

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].

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

Explanation: Use the convolution formula.
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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].

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

4. Evaluate (exp(-4t)u(t))*u(t), u(t) being the heaviside function.
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

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].

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)

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].

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)

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

9. Find the value of d(t-34)*x(t+56), d(t) being the delta function.
a) x(t + 56)
b) x(t + 32)
c) x(t + 22)
d) x(t – 22)

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

10. Find x(t)*u(t)
a) tx(t)
b) t2x(t)
c) \$x(t2)
d) \$x(t)

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

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