Convolution

convolution

http://en.wikipedia.org/wiki/Convolution



http://en.wikipedia.org/wiki/File:Convolution_of_box_signal_with_itself2.gif

		n=	0	1	2	3	4	5	6	7
		x[]=	10	20	30	40
		h[]=	1	2	3	4	5
		y[]= (x*h)[]=	?
x0=	10	h0[]=	1	2	3	4	5
x1=	20	h1[]=		1	2	3	4	5
x2=	30	h2[]=			1	2	3	4	5
x3=	40	h3[]=				1	2	3	4	5
h0=	1	x0[]=	10	20	30	40
h1=	2	x1[]=		10	20	30	40
h2=	3	x2[]=			10	20	30	40
h3=	4	x3[]=				10	20	30	40
h4=	5	x4[]=					10	20	30	40

my interpretation about convolution
我的解釋：

using x[k] as weight to  h[n-k], which is the shift version of h[n],
or
using h[k] as weight to  x[n-k], which is the shift version of x[n],

then sum them all.

用 x[k] 當權重，乘上 h[n-k]，那是把 h[n] 右移k的結果，
或者
用 h[k] 當權重，乘上 x[n-k]，那是把 x[n] 右移k的結果，

然後，通通加起來。