Step and Delta Functions Haynes Miller and Jeremy Orlo 1 ...

Step and Delta Miller and Jeremy Orloff1 The unit step DefinitionLet s start with the definition of the unit step function,u(t):u(t) ={0fort <01fort >0We do not defineu(t) att= 0. Rather, att= 0 we think of it as in transitionbetween 0 and is called the unit step function because it takes a unit step att= 0. It is sometimescalled the Heaviside function. The graph ofu(t) is (t)We will useu(t) as an idealized model of a natural system that goes from 0 to 1 veryquickly. In reality it will make a smooth transition, such as the (t) is an idealized version of this curveBut, if the transition happens on a time scale much smaller than the time scale ofthe phenomenon we care about then the functionu(t) is a good approximation. It isalso much easier to deal with of our main uses foru(t) will be as a switch.}

We will use u(t) as anidealized modelof a natural system that goes from 0 to 1 very quickly. In reality it will make a smooth transition, such as the following. t 1 Figure 1. u(t) is an idealized version of this curve But, if the transition happens on a …

Tags:

  Very

Information

Related search queries