Convolution

컨볼루션 속성

- Commutative .. x[n]*h[n] = h[n]*x[n]

- Distributive .. x[n] * {h1[n] + h2[n]} = x[n]*h1[n] + x[n]*h2[n]

- Associative .. {x[n]*h1[n]}*h2[n] = x[n]*{h1[n]*h2[n]}

 

컨볼루션 계산

- Direct evaluation

- Graphical apprach

 

Direct Evaluation

x[n] = {3, 4, 5}, h[n] = {2, 1}

시작 포인트: 0 + 0

끝 포인트: 2 + 1 = 3

 

y[0] = x[0]h[0] = 6

y[1] = x[0]h[1] + x[1]h[0] = 3 + 8 = 11

y[2] = x[0]h[2] + x[1]h[1] + x[2]h[0] = 0 + 4 + 10 = 14

y[3] = x[0]h[3] + x[1]h[2] + x[2]h[1] + x[3]h[0] = 5

 

y[n] = {6, 11, 14, 5}

 

Graphical Approach

y[n] = {2, 5, 4, 6, 1, 2}