10.1. Definition

Try these first

1. 1.

   Define the Dirac Delta Function.

   Hint

   Consider its integral property.

2. 2.

   What is the integral of the Dirac Delta Function over its full range?

   Hint

   Think of the area under the impulse.

3. 3.

   What does the Dirac Delta Function represent?

   • A continuous function
   • An instantaneous impulse
   • A sinusoidal function

   Hint

   Think about the context in which it's used.

4. 4.

   True or False: The integral of δ(t) over the entire real line is 1.

   • True
   • False

   Hint

   Recall the definition of the delta function.

5. 5.

   Assume a system described by the equation dy/dt + 2y = δ(t - 1). Solve for y(t).

   Hint

   Transform the left side first, and then isolate Y(s).

6. 6.

   Given that δ(t - 10) is the input to a system modeled by dy/dt + 5y = δ(t - 10), derive the system's step response.

   Hint

   Find the transformation and apply the inverse transform step.