12.9. Delta Function in Fourier Transforms

Try these first

1. 1.

   What is the Fourier transform of the Dirac delta function?

   Hint

   Think about what it means for a signal to be constant across frequencies.

2. 2.

   How does the Dirac delta function behave at points other than zero?

   Hint

   Recall the properties of the delta function.

3. 3.

   What is the Fourier transform of the Dirac delta function?

   • 0
   • 1
   • ∞

   Hint

   Consider the definition of the delta function in frequency analysis.

4. 4.

   True or False: The inverse Fourier transform of a constant signal is a delta function.

   • True
   • False

   Hint

   Think about how signals reconstruct through Fourier analysis.

5. 5.

   A signal is modeled as a sum of delta functions representing impulses at various times. How would you express the Fourier transform of this signal?

   Hint

   Consider the linearity of Fourier transforms.

6. 6.

   Demonstrate how a delta function affects the response of a linear time-invariant system when suddenly excited.

   Hint

   Think about integration in engineering dynamics.