Nov 14
We explored the work that Greg did, discussing the intuition behind the formulas, and getting more comfortable with complex numbers (angle, magnitude), Gaussians (how to create a function like that), and how/why the x=[0,0,1,0,0,0,0] spike turned into something with a power spectrum which was constant. (Answer: equal amplitude sinusoids of all frequencies, with phases such that the oscillations all align at the spike)
We also discussed what a lambda function is in python, and looked at numpy's fromfunction() matrix creation thingy.
Attached is the stream-of-consiousness typing that Jim did into Greg's notes, which may be useful as a reminder of what we did.
We ran out of time and finished in a somewhat unsettled state.
The assignment
- Do more of this sort of work, taking transforms and inverse transforms of things and getting more intuition and comfort.
- The fourier transform has frequencies arrange in a funny pattern (for example with N=8 the k index runs = [0, 1, 2, 3, -4, -3, -2, -1] with the highest frequency in the middle), so to plot it you'll want to chop the array and swap the sides to put 0 in the middle rather than at the left edge.
- Do show that a transform followed by an inverse transform restores the original.
For the end of the semester: get a real sound file, make plots of its spectrum (including correct units), and write a paper discussing how that works and how it all fits together. We only meet two more times, once before and once after thanksgiving.
