Hence,

(III.9)

Delayed function : , i.e .f(t) is delayed by seconds

(III.10)

Now, let us take , hence . At and at . Thus,

(III.11)

Hence,

(III.12)

Pulse function : See Fig. III.1(c) for the schematic of an unit pulse function. The area under the pulse is 1. The duration of pulse is T and hence it achieves maximum intensity of . Thus the function is defined by

It can also be defined as the “addition” of two step functions which are equal but with opposite intensity, however, the second function is delayed by T .

Hence, it is evident that is equal to in intensity however it is delayed by time

Thus, . Since is a step function of intensity , the following expression will hold.