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# convmtx() - Signal Processing

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### Example

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A = convmtx(h,n) returns the convolution matrix, A, such that the product of A and a vector, x, is the convolution of h and x.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.convmtx handles edge conditions by zero padding.

A = convmtx(h,n)

Efficient Computation of ConvolutionOpen This Example It is generally more efficient to compute a convolution using conv when the signals are vectors. 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 time 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 t1rat = tcnv\tmtx t1col = 0.0006 0.0599 t1rat = 94.6975 conv is about two orders of magnitude more efficient.Repeat the exercise for the case where a is a mutichannel 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 tmrat = tcnv/tmtx tmcol = 0.2961 0.0884 tmrat = 3.3487 convmtx is about 3 times as efficient as conv.