Fourier Transform of a Delta Function
Highlights of the activity
- This small group activity is designed to use the Fourier transform and see its general properties for a simple case.
- Students work in small groups to find the Fourier transform of the normalized Dirac delta function.
- The whole class wrap-up discussion emphasizes that all frequencies are represented in the Fourier transform of the delta function.
Reasons to spend class time on the activity
Fourier transforms are very important for analyzing wave behavior in both classical and quantum mechanics. Students need help with both the mathematical computation of Fourier transforms and with interpreting the result in the frequency domain. This activity gives practice with both finding the Fourier transform and using the integration properties of the delta function, and it also provides an extreme example of narrow functions transforming into broad ones.