10.5. Applications of Laplace Transform of δ(t)

Try these first

1. 1.

   What is the Laplace Transform of δ(t)?

   Hint

   Think about the special case of the Dirac Delta function.

2. 2.

   Define the sifting property.

   Hint

   Consider the integral of f(t) multiplied by δ(t-a).

3. 3.

   What is the Laplace Transform of δ(t - a)?

   • 1
   • e^{-as}
   • 0

   Hint

   Review the properties of Laplace Transforms for delta functions.

4. 4.

   The Dirac Delta function is always zero except at:

   • True
   • False

   Hint

   Reflect on the definition of Dirac Delta.

5. 5.

   Given the equation d²y/dt² + 2dy/dt + 5y = δ(t - 1), find the solution y(t).

   Hint

   Consider the impulse response of a second-order system.

6. 6.

   Explain how you would model a digital signal using the Dirac Delta function and Laplace Transform.

   Hint

   Think about transforming a series of impulses into a continuous representation.