10. The Dirac Delta Function (Impulse Function)

Try these first

1. 1.

   What does the Dirac Delta Function represent in signal processing?

   Hint

   Think of signals that change suddenly.

2. 2.

   What is the integral property of the Dirac Delta Function?

   Hint

   Consider the area under the impulse.

3. 3.

   What does the Dirac Delta Function model?

   • Continuous function
   • Instantaneous input
   • Periodic signal

   Hint

   Think about the nature of sudden spikes.

4. 4.

   The area under the Dirac Delta Function is equal to:

   • True
   • False

   Hint

   Consider its mathematical definition.

5. 5.

   Given the system described by the differential equation dy/dt + 2y = δ(t-3), find y(t) using the Laplace Transform.

   Hint

   Translate the equation using Laplace Transforms and use the shifting property.

6. 6.

   How would the response of an electrical circuit differ when subjected to δ(t) vs. δ(t-5)? Explain using the concepts learned.

   Hint

   Consider the timing of the applied impulse and its effects on system responses.