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Compute Linear convolution of causal x(n) and h(n) using overlap add method in time domain X(n) = {1, 2, 3, 4, 5, 6, 7, 8 }, h(n) = {1, 1, 1 }

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Compute Linear convolution of causal x(n) and h(n) using overlap add method in time domain X(n) = {1, 2, 3, 4, 5, 6, 7, 8 }, h(n) = {1, 1, 1 }

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written 7.3 years ago by |

$x(n) = {1, 2, 3, 4, 5, 6, 7, 8 } \
h(n) = {1, 1, 1 } \
\therefore, h(n) = {1, 1, 1, 0} \
x_1(n)= {1, 2, 0, 0} \
x_2(n)= {3, 4, 0, 0} \
x_3(n)={5, 6, 0, 0} \
x_4(n)={7, 8, 0, 0} \

y_1(n) = x_1(n) \otimes h_1(n)$
![enter image description here][1]
$\therefore, y_1$(n) = {1, 2, 3, 2}
$y_2(n) = x_2(n) \otimes h_2(n)$
![enter image description here][2]
$\therefore, y_2(n)$ = {3, 7, 7, 4}
$y_3(n) = x_3(n) \otimes h_3(n)$
![enter image description here][3]
$\therefore, y_3(n)$ = {5, 11, 11, 6}
$y_4(n) = x_4(n) \otimes h_4(n)$
![enter image description here][4]
$\therefore, y_4(n)$ = {7, 15, 15, 8}

**Result: y(n) = {1, 3, 6, 9, 12, 15, 18, 21, 15, 8}**

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