Question

What is a unit step function?

Is the value U(0) = 1?

Ex. when t=20 and equate to U(t-20)=U(0)=1???

Answer 1

In many engineering applications, we often encounter functions whose

Value changes abruptly at specified values of time t. One simple example is when a voltage is switched on or off in an electrical circuit at a specified value of time t.

The value of t= 0 is usually taken as a convenient time to switch on or off the given the voltage.

The switching process can be described mathematically by the function called the Unit Step Function (Otherwise known as the Heaviside function)

Definition: The unit step function, u(t), is defined as

u(t) = 0, when t<0

       = 1, when t>0

That is, u is a function of time t, & u has value zero when time is negative(before we flip the switch) & value one when time is positive(from when we flip the switch).

2. Shifted Unit Step Function:

In many circuits, waveforms are used at particular intervals other than t=0. Such a function may be explained using the shifted unit step function.

A function which has value 0 up to the time and thereafter has value 1, is written:

U(t-a) = 0 if t<a

          = 1 if t>a

E.g. f(t) = u(t-3)

(2)

U(0) = 0

It depends on what kind of convention we are using. If we considering that t is a discrete variable, then the value is 1. else, if we are using the half maximum convention, then the value is 0,5.