功能：是二維卷積運算函數（與convmtx2相似）。如果a和b是兩個離散變量n1和n2的函數，則關于a和b的二維卷積運算數學公式如下：



用法：C = conv2(A,B)
C = conv2(hcol,hrow,A)
C = conv2(...,'shape')
C = conv2(A,B)計算數組A和B的卷積。如果一個數組描述了一個二維FIR濾波器，則另一個數組被二維濾波。當A的大小為[ma,na],B的大小為[mb,nb]時，C的大小為[ma+mb-1,mb+nb-1]。‘shape’見下表
參數值
含義
‘full’
默認值，返回全部二維卷積值。
‘same’
返回與A大小相同卷積值的中間部分
‘valid’
當all(size(A)>=size(B)),C的大小為[ma+mb-1,mb+nb-1]；否則，C返回[]。在n維卷積運算中，C的大小為max(size(A)- size(B)+1,0)

例子：

s = [1 2 1; 0 0 0; -1 -2 -1];

A = zeros(10);

A(3:7,3:7) = ones(5);

H = conv2(A,s);

mesh(H)

Matlab的幫助：

conv2

2-D convolution

Syntax

C = conv2(A,B)
C = conv2(hcol,hrow,A)
C = conv2(...,'shape')

Description

C = conv2(A,B) computes the two-dimensional convolution of matrices A and B. If one of these matrices describes a two-dimensional finite impulse response (FIR) filter, the other matrix is filtered in two dimensions.

The size of C in each dimension is equal to the sum of the corresponding dimensions of the input matrices, minus one. That is, if the size of A is [ma,na] and the size of B is [mb,nb], then the size of C is [ma+mb-1,na+nb-1].

The indices of the center element of B are defined as floor(([mb nb]+1)/2).

C = conv2(hcol,hrow,A) convolves A first with the vector hcol along the rows and then with the vector hrow along the columns. If hcol is a column vector and hrow is a row vector, this case is the same as C = conv2(hcol*hrow,A).

C = conv2(...,'shape') returns a subsection of the two-dimensional convolution, as specified by the shape parameter:

full

Returns the full two-dimensional convolution (default).

same

Returns the central part of the convolution of the same size as A.

valid

Returns only those parts of the convolution that are computed without the zero-padded edges. Using this option, C has size [ma-mb+1,na-nb+1] when all(size(A) >= size(B)). Otherwise conv2 returns [].

Note?? If any of A, B, hcol, and hrow are empty, then C is an empty matrix [].

Algorithm

conv2 uses a straightforward formal implementation of the two-dimensional convolution equation in spatial form. If and are functions of two discrete variables, and , then the formula for the two-dimensional convolution of and is

In practice however, conv2 computes the convolution for finite intervals.

Note that matrix indices in MATLAB always start at 1 rather than 0. Therefore, matrix elements A(1,1), B(1,1), and C(1,1) correspond to mathematical quantities a (0,0), b (0,0), and c (0,0).

Examples

Example 1

For the 'same' case, conv2 returns the central part of the convolution. If there are an odd number of rows or columns, the "center" leaves one more at the beginning than the end.

This example first computes the convolution of A using the default ('full') shape, then computes the convolution using the 'same' shape. Note that the array returned using 'same' corresponds to the underlined elements of the array returned using the default shape.

A = rand(3);B = rand(4);C = conv2(A,B); % C is 6-by-6
C = 0.1838 0.2374 0.9727 1.2644 0.7890 0.3750 0.6929 1.2019 1.5499 2.1733 1.3325 0.3096 0.5627 1.5150 1.0602 0.9986 2.3811 0.8462 0.3089 1.1419 0.6841 0.3287 0.9347 1.6464 1.7928 1.2422 0.5423 Cs = conv2(A,B,'same') % Cs is the same size as A: 3-by-3 Cs = 2.3576 3.1553 2.5373 3.4302 3.5128 2.4489 1.8229 2.1561 1.6364

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