convmtx (Signal Processing Toolbox)

Convolution matrix.

Syntax

A = convmtx(c,n)
A = convmtx(r,n)

Description

A convolution matrix is a matrix, formed from a vector, whose inner product with another vector is the convolution of the two vectors.

A = convmtx(c,n)

where c is a length m column vector returns a matrix A of size (m + n-1)-by-n. The product of A and another column vector x of length n is the convolution of c with x.

A = convmtx(r,n)

where r is a length m row vector returns a matrix A of size
n-by-(m + n-1). The product of A and another row vector x of length n is the convolution of r with x.

Example

Generate a simple convolution matrix:

h = [1 2 3 2 1];
convmtx(h,7)
ans =
 1    2    3    2    1    0    0    0    0    0    0
 0    1    2    3    2    1    0    0    0    0    0
 0    0    1    2    3    2    1    0    0    0    0
 0    0    0    1    2    3    2    1    0    0    0
 0    0    0    0    1    2    3    2    1    0    0
 0    0    0    0    0    1    2    3    2    1    0
 0    0    0    0    0    0    1    2    3    2    1

Note that convmtx handles edge conditions by zero padding.

In practice, it is more efficient to compute convolution using

y = conv(c,x)

than by using a convolution matrix:

n = length(x);
y = convmtx(c,n)*x

Algorithm

convmtx uses the function toeplitz to generate the convolution matrix.

`conv`	Convolution and polynomial multiplication.
`convn`	N-dimensional convolution (see the online MATLAB Function Reference).
`conv2`	Two-dimensional convolution.
`dftmtx`	Discrete Fourier transform matrix.