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Digital Convolution数字卷积
Moving Average
Filtering
滑动平均滤波
Boundary Effects边界效应
Digital
Convolution数字卷积
Definition定义:
Table Representation表格表示:
x[n]=[2,1,-2]
h[n]=[1,2,-1]
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x[k]
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2
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1
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-2
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y[n]
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h[0-k]
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-1
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2
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1
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y[0]= 2
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h[1-k]
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-1
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2
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1
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y[1]= 5
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h[2-k]
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-1
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2
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1
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y[2]=-2
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h[3-k]
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-1
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2
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1
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y[3]=-5
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h[4-k]
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-1
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2
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1
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y[4]= 2
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h[5-k]
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-1
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2
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1
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y[5]= 0
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Convolution and Difference Equation
卷积与差分方程
MA Model:
y[n]
= b0 x[n] + b1
x[n-1] + L+ bM
x[n-M]
Difference Equation:
y[n]
= h[0]x[n] + h[1]x[n-1] + L+ h[M]x[n-M]
General Model:
y[n]
=L+ h[-2]x[n+2]
+ h[-1]x[n+1] +
+h[0]x[n]
+ h[1]x[n-1] + L
Convolution vs
Correlation
Boundary Effects边界效应
h=[4,
-1, 2, -3]
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x[k]:
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h[-k]:
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h[1-k]:
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h[2-k]:
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h[3-k]:
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...
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h[9-k]:
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h[10-k]:
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h[11-k]:
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h[12-k]:
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1
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-2
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3
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1
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5
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2
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0
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1
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2
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4
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-1
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4
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2
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-1
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4
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-3
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2
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-1
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4
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-3
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2
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-1
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4
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...
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-3
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2
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-1
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4
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-3
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2
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-1
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4
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-3
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2
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-1
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-3
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2
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y[n]
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y[0]=4 ?
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y[1]=-9 ?
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y[2]=16 ?
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y[3]=-6
?/span>
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...
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y[9]=16 ?/span>
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y[10]=-3 ?
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y[11]=2 ?
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y[12]=-12 ?
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Transients瞬态 & Steady State稳态
(FIR Filter)
Approximately近似 Steady State
(Stable IIR
Filter)
M-Term MA Filter滑动平均滤波器
1-D M-term MA Filter
2-D M-term
MA Filter
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Convolution Kernel卷积核：
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Mistake on page 163
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