On 4 February 2015 at 11:05, Sturla Molden <sturla.molden@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.