convmtx

R2026b

Convolution matrix

Syntax

A = convmtx(h,n)

Description

A = convmtx(h,n) returns the convolution matrix, A, such that the product of A and an n-element vector, x, is the convolution of h and x.

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

    0.0002    0.0032

t1rat = tcnv\tmtx

t1rat = 
16.5482

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

    0.0398    0.0275

tmrat = tcnv/tmtx

tmrat = 
1.4487

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™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

The convmtx function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced before R2006a

R2026b: Use thread-based environments

You can use convmtx in thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.