Computing a convolution usingconvwhen the signals are vectors is generally more efficient than usingconvmtx. For multichannel signals,convmtxmight be more efficient.

Compute the convolution of two random vectors,aandb, using bothconvandconvmtx. 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;forkj = 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;endt1col = [tcnv tmtx]/Nt

t1col =1×20.0008 0.0242

t1rat = tcnv\tmtx

t1rat = 31.3551

convis about two orders of magnitude more efficient.

Repeat the exercise for the case whereais a multichannel signal with 1000 channels. Optimizeconv's performance by preallocating.

Nchan = 1000; tcnv = 0; tmtx = 0; n = zeros(Na+Nb-1,Nchan);forkj = 1:Nt a = randn(Na,Nchan); b = randn(Nb,1); ticfork = 1:Nchan n(:,k) = conv(a(:,k),b);endtcnv = tcnv+toc; tic c = convmtx(b,Na); d = c*a; tmtx = tmtx+toc;endtmcol = [tcnv tmtx]/Nt

tmcol =1×20.1461 0.0786

tmrat = tcnv/tmtx

tmrat = 1.8589

convmtxis about three times as efficient asconv.