|5|c|Table 1: Functions and discontinuities|
All these functions have one general property in common: a discontinuity (a jump of derivatives) at the point t=0. The simplest example of a discontinuity is given by the step function H(t) (Figure ). It has a discontinuity of order 0. We observe the same discontinuity for the second function . One can find the orders of the discontinuities of the other functions in column 2. In columns 3 etc., the amplitudes of derivative jumps are given:
Definition: The function f(t) has a discontinuity of order r at the point t=0, if for all and for .Values are called amplitudes of order k.