matlab中的conv2卷积运算的三种形式

thinkfunny

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. T) G5 a, o  L3 W4 Z7 }matlab中的conv2是用于对二维数据进行卷积运算，有三个参数可供选择，下面是help content of conv2

4 B; M- ~& z- H" x; g  ~conv2 Two dimensional convolution.
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2 r% x- I* a  k" X5 j    C = conv2(A, B) peRForms the 2-D convolution of matrices A and B.
, Z. O4 p/ K! t5 b" V# q    If [ma,na] = size(A), [mb,nb] = size(B), and [mc,nc] = size(C), then
    mc = max([ma+mb-1,ma,mb]) and nc = max([na+nb-1,na,nb]).
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    C = conv2(H1, H2, A) first convolves each column of A with the vector
" |- v# Z0 x! d/ F, k" O% L    H1 and then convolves each row of the result with the vector H2.  If
1 k, p5 P( Z" Q( |/ Z- p6 f    n1 = length(H1), n2 = length(H2), and [mc,nc] = size(C) then
    mc = max([ma+n1-1,ma,n1]) and nc = max([na+n2-1,na,n2]).
    conv2(H1, H2, A) is equivalent to conv2(H1(：)*H2(：).', A) up to
. q9 W$ E2 x" m& p    round-off.

    C = conv2(..., SHAPE) returns a subsection of the 2-D
0 \8 ~. F2 f: @( Z    convolution with size specified by SHAPE:
4 G- c8 j: Y  d: _. D4 C      'full'  - (default) returns the full 2-D convolution,
3 ]! q& L0 ~, Z- h$ z. M) D& ?2 c      'same'  - returns the central part of the convolution
4 X2 j$ j% E/ \: M3 V) R                that is the same size as A.
      'valid' - returns only those parts of the convolution
5 U; n: E; ?* N& B( d6 u& i/ l                that are computed without the zero-padded edges.
: b& `  R& j, L4 X& u, ~+ F                size(C) = max([ma-max(0,mb-1),na-max(0,nb-1)],0).


关于full, same以及valid三种参数的区别，如下面的实例所示：

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( [. a3 G; Q7 C7 U: H0 w3 D" hvalid

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yin123

三种形式的matlab中的conv2卷积运算