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 =

    0.0014    0.0591


t1rat =

   42.1445

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 =

    0.7146    0.1917


tmrat =

    3.7283

convmtx is about 3 times as efficient as conv.