Documentation

# convn

N-D convolution

## Description

example

C = convn(A,B) returns the N-dimensional convolution of arrays A and B.

example

C = convn(A,B,shape) returns a subsection of the convolution according to shape. For example, C = convn(A,B,'same') returns the central part of the convolution, which is the same size as A.

## Examples

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You can control the size of the output of the convn function. For example, the 'same' option trims the outer part of the convolution and returns only the central part, which is the same size as the input.

Convolve a random 2-by-3-by-2 array A with a 2-by-2-by-2 kernel B. The result is a 3-by-4-by-3 array, which is size(A) + size(B) - 1.

A = rand(2,3,2);
B = 0.25*ones(2,2,2);
C = convn(A,B)
C =
C(:,:,1) =

0.2037    0.2354    0.1898    0.1581
0.4301    0.6902    0.4426    0.1825
0.2264    0.4548    0.2527    0.0244

C(:,:,2) =

0.2733    0.5444    0.4686    0.1975
0.6365    1.3772    1.2052    0.4645
0.3632    0.8327    0.7366    0.2670

C(:,:,3) =

0.0696    0.3090    0.2788    0.0394
0.2063    0.6869    0.7627    0.2821
0.1367    0.3779    0.4839    0.2426

sizeC = size(A) + size(B) - 1
sizeC = 1×3

3     4     3

Return the central part of the convolution, which is the same size as A.

C = convn(A,B,'same')
C =
C(:,:,1) =

1.3772    1.2052    0.4645
0.8327    0.7366    0.2670

C(:,:,2) =

0.6869    0.7627    0.2821
0.3779    0.4839    0.2426

## Input Arguments

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Input array, specified as vector, a matrix, or a multidimensional array.

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical
Complex Number Support: Yes

Second input array, specified as a vector, a matrix, or a multidimensional array to convolve with A. The array B does not have to be the same size as A.

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical
Complex Number Support: Yes

Subsection of the convolution, specified as one of these values:

• 'full' — Return the full N-D convolution.

• 'same' — Return the central part of the convolution, which is the same size as A.

• 'valid' — Return only parts of the convolution that are computed without zero-padded edges.

## Output Arguments

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N-D convolution, returned as a vector, a matrix, or a multidimensional array. If A and B have the same number of dimensions, the full convolution C = convn(A,B) has size size(A)+size(B)-1.

When one or both of A and B are of type single, then the output is of type single. Otherwise, convn converts inputs to type double and returns type double.

Data Types: double | single

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### N-D Convolution

For discrete, N-dimensional variables A and B, this equation defines the convolution of A and B:

$C\left({j}_{1},{j}_{2},...,{j}_{N}\right)=\sum _{{k}_{1}}\sum _{{k}_{2}}...\sum _{{k}_{N}}A\left({k}_{1},{k}_{2},...,{k}_{N}\right)B\left({j}_{1}-{k}_{1},{j}_{2}-{k}_{2},...,{j}_{N}-{k}_{N}\right)$

Each ki runs over all values that lead to legal subscripts of A and B.