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Which one of the following gives the linear convolution of two finite length sequences x(n) = {1, 3, 1, 2} and y(n) = {1, 2, 3}?
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- {3, 10, 8, 14, 7, 5, 2}
- {2, 10, 7, 14, 6, 6, 3}
- {3, 9, 8, 14, 7, 5, 2}
- {1, 5, 8, 10, 14, 5, 6}
Correct Option: D
The linear convolution of x(n) and y(n) can be given as
r(n) = | ![]() | x(k) y(n – k) |

r(n) = 1 (3 + 2) (1 + 6 + 1) (2 + 2 + 3 + 3) (4 + 1 + 9) (2 + 3) 6
or r(n) = {1 5 8 10 14 5 6}