摺積定理.pptVIP

摺積定理(Convolution) 第一步 : 程式寫作參考圖 x[] = x[0] x[1] x[2] h[] = h[0] h[1] h[2] y[] = y[0] y[1] y[2] y[3] y[4] x[0] x[1] x[2] 0 0 0 0 h[2] h[1] h[0] 1st step h[0] 0 0 h[2] h[1] y[0] = x[0]h[0] 2nd step h[1] h[0] 0 0 h[2] y[1] = x[0]h[1] + x[1]h[0] 3rd step h[2 ] h[1] h[0] 0 0 y[2] = x[0]h[2] + x[1]h[1]+x[2]h[0] 4th step 0 h [2] h[1] h[0] 0 5th step 0 0 h[2] h[1] h[0] * 2 3 1 5 1 2 3 4 y[n] x[n] h[n] 0 0 0 0 0 0 0 i=n y[n] = Σx[i] * h[n-i] i=0 x[0] x[1] x[2] x[3] h[0] h[1] h[2] h[3] y[0] y[1] y[2] y[3] y[4] y[5] y[6] 公式 : 2 3 1 5 1 2 3 4 y[n] x[n] h[n-i] 2 0 0 0 0 0 0 i=0 i=0 y[0] = Σ x[i] * h[0-i] = Σ x[i] * h[-i] = x[0] * h[0] = 2 * 1 = 2 i=0 i=0 y[0] y[1] y[2] y[3] y[4] y[5] y[6] i=n y[n] = Σx[i] * h[n-i] i=0 x[0] x[1] x[2] x[3] h[3] h[2] h[1] h[0] 第二步 : 2 3 1 5 1 2 3 4 y[n] x[n] 2 7 0 0 0 0 0 y[0] y[1] y[2] y[3] y[4] y[5] y[6] + x[0] x[1] x[2] x[3] h[3] h[2] h[1] h[0] h[n-i] i=1 i=1 y[1] = Σ x[i] * h[n-i] = Σ x[i] * h[1-i] = x[0] * h[1] + x[1] * h[0] = (2*2) + (3*1) = 7 i=0 i=0 | --- i=0 ---- | | ---- i=1 ----| 第三步 : 2 3 1 5 1 2 3 4 y[n] x[n] 2 7 13 0 0 0 0 y[0] y[1] y[2] y[3] y[4] y[5] y[6] + x[0] x[1] x[2] x[3] h[3] h[2] h[1] h[0] h[n-i] i=2 y[2] = Σ x[i] * h[2-i] = x[0]*h[2]+x[1]*h[1]+x[2]*h[0] = (2*3) + (3*2) + (1*1) = 13 i=0 | -- i=0 --- | | --- i=1 --| |--- i=2 ---| + 第四步 : 2 3 1 5 1 2 3 4 y[n] x[n] 2 7 13 24 0 0 0 y[0] y[1] y[2] y[3] y[4] y[5] y[6] + x[0] x[1] x[2] x[3