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`.

CONVOLUTE function
Convolution of an even number of points