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w = conv(u,v)
C = conv(...,'shape')
w = conv(u,v) convolves vectors u and v. Algebraically, convolution is the same operation as multiplying the polynomials whose coefficients are the elements of u and v.
C = conv(...,'shape') returns a subsection of the convolution, as specified by the shape parameter:
Let m = length(u) and n = length(v) . Then w is the vector of length m+n-1 whose kth element is
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The sum is over all the values of j which lead to legal subscripts for u(j) and v(k+1-j), specifically j = max(1,k+1-n): min(k,m). When m = n, this gives
w(1) = u(1)*v(1) w(2) = u(1)*v(2)+u(2)*v(1) w(3) = u(1)*v(3)+u(2)*v(2)+u(3)*v(1) ... w(n) = u(1)*v(n)+u(2)*v(n-1)+ ... +u(n)*v(1) ... w(2*n-1) = u(n)*v(n)
convmtx and xcorr in the Signal Processing Toolbox

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