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Ramp and step are important signals for understanding some interesting
properties of the impulse signal, which will be described in the next
section. The step signal is zero for negative input and one for
positive. Thus, it is defined by

(3.1) 
The Step signal can be interpreted as a ramp of width zero, when
the ramp is defined as follows

(3.2) 
As can easily be seen, if w tends to zero the ramp becomes a step
signal. This relationship is important because we cannot differentiate
a step signal because it is discontinuous. However, the ramp signal is
continuous and therefore differentiable, its differentiation is a box
function (see Fig. 3.1).
Figure 3.1:
On the left the step is function depicted, in the middle the ramp,
and its derivative (the box function) on the right. The smaller
w gets the higher and narrower the corresponding box function gets
(until it reaches the impulse signal in the limit).

Next: The impulse signal
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