On 4 February 2015 at 11:05, Sturla Molden <sturla.mol...@gmail.com> wrote: > On 04/02/15 06:18, Warren Weckesser wrote: > >> By "discrete form", do you mean discrete time (i.e. a function defined >> on the integers)? Then I agree, the discrete time unit step function is >> defined as > > It is the cumulative integral of the delta function, and thus it can > never obtain the value 0.5. The delta function is defined to have an > integral of 0 or 1. > > Sturla
There are several definitions. Abramowitz and Stegun (http://people.math.sfu.ca/~cbm/aands/page_1020.htm) assign the value 0.5 at x=0. It can also be defined as: H(x) = 1/2 * (1 + sign(x)) Where sign(0) = 0, and therefore H(0) = 1/2. Actually, Heaviside function is better seen as a distribution instead of a function, and then there is no problem with the value at 0, as long as it is finite. _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
