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
0.0002 0.0063
t1rat = tcnv\tmtx
t1rat = 36.2662
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
0.0538 0.0387
tmrat = tcnv/tmtx
tmrat = 1.3884
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 lengthm
,A
is(m+n-1)
-by-n
, and the product ofA
and a column vector,x
, of lengthn
is the convolution ofh
andx
.If
h
is a row vector of lengthm
,A
isn
-by-(m+n-1)
, and the product of a row vector,x
, of lengthn
withA
is the convolution ofh
andx
.
Output Arguments
A
— Convolution matrix
matrix
Convolution matrix of input h
and the vector
x
, returned as a matrix.
Algorithms
convmtx
uses the functiontoeplitz
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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