conv - Convolution and polynomial multiplication
Syntax
w = conv(u,v)
C = conv(...,'shape')
Description
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:
full | Returns the full convolution (default). |
same | Returns the central part of the convolution of the same
size as A. |
valid | Returns only those parts of the convolution
that are computed without the zero-padded edges. Using this option, length(c) is max(length(a)-max(0,length(b)-1),0). |
Definition
Let m = length(u) and n = length(v) .
Then w is the vector of length m+n-1 whose kth
element is
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)
See Also
conv2, convn, deconv, filter
convmtx and xcorr in the Signal Processing Toolbox
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