Using only horizontal line segments 1), the step
or staircase function is formed.
Every discrete function can be seen
as such a step function.
The function of Heaviside Ha()
has only one step: until x = a it has a value zero, above the value one. The function describes the velocity
of an object as result of a sudden force, during a infinitely small time interval. H is
the abbreviated notation for H0, what is in fact the same as the unit step function. At the place of the step the value
of the function can be set to ½.
The rectangle function P(x)
is equal to 0 outside an interval, and equal to 1 inside. It can be expressed as
the difference of two functions of Heaviside.
When taking only integer values for x, we get the discrete curves.
1) By the way, because it's the case of a function, vertical line segments are not admitted.