ACME Volume 2 2018

I had a hard time following this section. It felt like a lot of math without a clear idea of where we were heading. While each piece makes sense, I had a hard time following all the indices and sums when I wasn't sure why I would want the result at the end. It is satisfying to find different ways to estimate functions that have different strengths than the Fourier transform.

The trickiest part of this section for me was following all the notation. It made sense, but I had to think about it sometimes to understand what was going on. I like learning another way to estimate functions using by projecting them onto an orthonormal basis. It makes the Fourier transform seem less magical and more functional. And it makes me wonder, what other useful bases could we use?

I don't understand the last "Vista" in the section. I'm not sure how you can recreate a non-periodic function from just the relatively few points k*pi/n for k in the integers. But that is pretty amazing. I liked understanding how antialiasing works. It was satisfying seeing the material from the other class apply so specifically.

I understood the math for this section, but I'm not quite sure I understand what a convolution is doing in real life. How exactly does it "average data locally"? I'm not used to learning math with applications in mind. It is interesting to have them combined.