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# conv2() - Signal Processing

```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 is determined as follows:  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]).C = conv2(h1,h2,A) first
convolves each column of A with the vector h1 and
then convolves each row of the result with the vector h2.
The size of C is determined as follows: if n1
= length(h1) and n2 = length(h2), then mc
= max([ma+n1-1,ma,n1]) and nc = max([na+n2-1,na,n2]).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, size(C)
= max([ma-max(0,mb-1),na-max(0,nb-1)],0).
Note:

All numeric inputs to conv2 must be of
type double or single.```

### Syntax

`C = conv2(A,B)C = conv2(h1,h2,A)C = conv2(...,shape)`

### Example

```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  2.3576  3.1553  2.5373  1.0602
0.9986  2.3811  3.4302  3.5128  2.4489  0.8462
0.3089  1.1419  1.8229  2.1561  1.6364  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```