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,
b, using both
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 0.0006 0.0164
t1rat = tcnv\tmtx
t1rat = 29.6496
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 0.2212 0.0629
tmrat = tcnv/tmtx
tmrat = 3.5192
convmtx is about three times as efficient as
h— Input vector
Input vector, specified as a row or column.
n— Length of vector to convolve
Length of vector to convolve, specified as a positive integer.
h is a column vector of length
the product of
A and a column vector,
n is the convolution of
h is a row vector of length
the product of a row vector,
x, of length
A is the convolution of
A— Convolution matrix
Convolution matrix of input
h and the vector
x, returned as a matrix.
convmtx uses the function
toeplitz to generate the convolution matrix.
convmtx handles edge conditions by zero padding.