Learning Goal:
To understand the relationship between the step and impulse functions and use the sifting property of the impulse function to calculate the integral of a function that is the product of some function and the impulse function.
The impulse function, δ(t)δ(t), is defined by the following two equations:
∫∞−∞Kδ(t)dt=K∫−∞∞Kδ(t)dt=K
δ(t)=0δ(t)=0 for t≠0t≠0
The first of these equations tells us that the area under the impulse function is a constant; the second equation tells us that the impulse is zero everywhere except where the argument of the function is zero. An impulse occurring at t=at=a is written δ(t−a)δ(t−a).