10.1 Unit Step Function u ₀(t)

A function is said to be discontinuous if it exhibits points of discontinuity, that is, if the function jumps from one value to another without taking on any intermediate values.

A well-known discontinuous function is the unit step function u ₀(t) ^[*] which is defined as

It is also represented by the waveform in Figure 10-1

Figure 10.1: Waveform for u ₀(t)

In the waveform of Figure 10.1, the unit step function u ₀(t) changes abruptly from 0 to 1 at t = 0. But if it changes at t = t ₀ instead, its waveform and definition are as shown in Figure 10.2.

Figure 10.2: Waveform and definition of u ₀(t ?t ₀)

Likewise, if the unit step function changes from 0 to 1 at t = ?t ₀ as shown in Figure 10.3, it is denoted as u ₀(t + t ₀)

Figure 10.3: Waveform and definition of u ₀(t + t ₀)

Other forms of the unit step function are shown in Figure 10.4.

Figure 10.4: Other forms of the unit step function

Unit...