Convolution of an odd number of points
Suppose the blurring vector b
, the second argument,
contains an odd number of points. Let N be the length of
b
, and let M be the length of the data vector,
y
. The convolution of y
with b
is:
for . References to subscripts out of range
of
y
are not summed. The blurring vector is
normalized to 1
to insure that the integrals of the the original data and the
convolution result are identical. This normalization is internal, the blurring vector is
returned unchanged.
To ensure proper convolution, y
should be padded at
it's upper and lower ends with zeros so it's length is at least the minimum of the non-zero
length of b
and one-half the length of b
.
Note that the lengths of b
and y
can differ. To avoid centroid
shifts in the output, center the blurring vector properly. For example, suppose that
b
has 2N-1
elements containing a Gaussian, then its peak should
be at N
.