Daily outline for Mon, Nov 21, 2016 9:10 AM (5 months ago)
Fourier Transform applications
assigned today:
Due today:
planning thoughts
- audio (already talked about it)
- Quantum
- momentum and position representations
- Damped Driven
- Diffraction
Do diffraction before x/p (and only do 1d diffraction?)
in class
- Quiz on Nyquist (no change to the problem)
- had them plot two different repetitive functions with different periods
- asked them to consider which frequencies would be needed
- big idea: period goes up, frequency spacing goes down
- extended this to period going to infinity
$$f(t)=\frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{\infty}F(\omega)e^{i\omega t}\,d\omega$$
$$F(\omega)=\frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{\infty}f(t)e^{-i\omega t}\,dt$$
- Talked about how the first one is an interesting statement about how adding waves can produce anything and how it's a useless statement without the second one that tells you how to do it
- Had them calc the time derivatives of the first one to set up the damped driven stuff
- compared and contrasted to the Laplace approach
- talked quickly about the quantum stuff
edit