# convmtx

Convolution matrix

## Syntax

## Description

## Examples

### Efficient Computation of Convolution

Computing a convolution using `conv`

when the signals are vectors is generally more efficient than using `convmtx`

. For multichannel signals, `convmtx`

might be more efficient.

Compute the convolution of two random vectors, `a`

and `b`

, using both `conv`

and `convmtx`

. The signals have 1000 samples each. Compare the times spent by the two functions. Eliminate random fluctuations by repeating the calculation 30 times and averaging.

Nt = 30; Na = 1000; Nb = 1000; tcnv = 0; tmtx = 0; for kj = 1:Nt a = randn(Na,1); b = randn(Nb,1); tic n = conv(a,b); tcnv = tcnv+toc; tic c = convmtx(b,Na); d = c*a; tmtx = tmtx+toc; end t1col = [tcnv tmtx]/Nt

`t1col = `*1×2*
0.0022 0.0122

t1rat = tcnv\tmtx

t1rat = 5.6655

`conv`

is about two orders of magnitude more efficient.

Repeat the exercise for the case where `a`

is a multichannel signal with 1000 channels. Optimize `conv`

's performance by preallocating.

Nchan = 1000; tcnv = 0; tmtx = 0; n = zeros(Na+Nb-1,Nchan); for kj = 1:Nt a = randn(Na,Nchan); b = randn(Nb,1); tic for k = 1:Nchan n(:,k) = conv(a(:,k),b); end tcnv = tcnv+toc; tic c = convmtx(b,Na); d = c*a; tmtx = tmtx+toc; end tmcol = [tcnv tmtx]/Nt

`tmcol = `*1×2*
0.1384 0.0850

tmrat = tcnv/tmtx

tmrat = 1.6273

`convmtx`

is about three times as efficient as `conv`

.

## Input Arguments

`h`

— Input vector

vector

Input vector, specified as a row or column.

**Data Types: **`single`

| `double`

`n`

— Length of vector to convolve

positive integer

Length of vector to convolve, specified as a positive integer.

If

`h`

is a column vector of length`m`

,`A`

is`(m+n-1)`

-by-`n`

, and the product of`A`

and a column vector,`x`

, of length`n`

is the convolution of`h`

and`x`

.If

`h`

is a row vector of length`m`

,`A`

is`n`

-by-`(m+n-1)`

, and the product of a row vector,`x`

, of length`n`

with`A`

is the convolution of`h`

and`x`

.

## Output Arguments

`A`

— Convolution matrix

matrix

Convolution matrix of input `h`

and the vector
`x`

, returned as a matrix.

## Algorithms

`convmtx`

uses the function`toeplitz`

to generate the convolution matrix.`convmtx`

handles edge conditions by zero padding.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

## Version History

**Introduced before R2006a**

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