Thu Jan 6 14:28:24 EST 2011

Delta Operator

Called divided difference as it's defined as:

       d x[k]   =   x[k+1] - x[k] / T

I.e. the differences are taken relative to the sampling period T.

In most cases where T is fixed this can be normalized to T=1 by moving
the scaling to the coefficient end, i.e. coefficients will become
small when T approaches 0.

However, in the exposition of [1] explicit mention of T is desired to
be able to take the limiting case of T->0 to make the bridge to the
continuous case, and the cases with different T.

See also fixed step integration[2], Time Scale Calculus[3].

[1] md5://3e41deebd80a5b988de09b645c036e57
[2] http://en.wikipedia.org/wiki/Eulers_method
[3] http://en.wikipedia.org/wiki/Time_scale_calculus