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8.8

I did read the entire section. I didn't think it was too bad, it explained using change of basis a lot more clearly than the DFT section did - or maybe I just feel more comfortable with it now. I didn't really follow the FWT fully, or understand how the rescaling from [0,1) to [a,b) works, but I think I understood the overall picture. Naturally, this reminded me of the DFT pretty heavily, but seemed to be a lot simpler due to it just being a bunch of step functions, or maybe I'm just more exposed to the idea of it and it makes more sense. I think this also ties in really nicely to Banach integration we're doing in Volume 1, which shows a continous function is a limit point of a sum of step functions.
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8.7

I did read the entire section, and I think I understood the overall picture, but got lost on some of the details. I understood Haar sons and using them as a approximation tool pretty well, but got a little lost on the details of the daughters and combining them with the sons in approximations. For some research I'm doing with the EE department, I'm building and training neural networks, and using wavelet and fourier series have reminded me a lot of them. These Haar sons/daughters while not exactly the same, remind me a lot of relu's and leaky relu's I use in my neural networks.
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8.6

I did read the entire section. I didn't feel it was too bad again - still feel it was on a shaky foundation, but the aliasing and Nyquist frequency stuff wasn't too bad. I feel like this section helped connect Fourier Series with the DFT for me a bit, but I still need to look into it more. This reminded my of error approximation for Taylor Series quite a bit. The only difference, from my understanding, is the Taylor Series Error was good for any function, whereas this stuff is for limited band functions. And I actually have the use of this one explained to me a lot more.
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8.5

I did read the entire section. I did the lab on convolution a little early, so I had dipped my toes in a little bit, so I didn't think the section was too difficult. As always, concrete examples will help more than anything. I feel like I'm building on a shaky foundation again since I don't think I 100% get all the Fourier stuff yet. This reminds me a lot of the stuff we're doing in my circuits class, which is all very similar, but rather than doing the math then showing the applications, we have the applications, then the circuit, then the math for it. It's interesting to see how it all connects though.
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8.4

I did read the entire section. I didn't feel it was too bad, since I'm a little ahead on the labs, I've done some stuff with the DFT and understood most of what was going on. Maybe it's silly, but I didn't get what the w_n^k's were, just something about roots of unity, but some explicit examples would be nice. Also I didn't follow the proof of the FFT like at all either. In my circuits class currently, we're just starting to make circuits that act as high and low pass filters, and the Fourier Transform seems to fit in their pretty nicely. We've been doing it with the Laplace transform thus far, but I'm excited to see how the Fourier stuff fits in with everything. 
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8.3

I did read the entire section. I didn't think it was too bad, given I understood the first section well, nothing seemed to be too big of a leap. I didn't follow the proof entirely at the end of the section, but that can probably be attributed to exhaustion. I am still confused about how to construct a Fourier Series given it includes T and w though. This feels like a cross of Laplace transforms and Taylor Series. It has the approximations properties that come from Taylor Series, but it also has some of the transforming that I remember doing w/ Laplace transforms in DifEq and in my circuits class.
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8.1

I did read the entire section. I thought it actually made a lot of sense, but maybe that's just in contrast to all the probability stuff we wrapped up. Fourier series didn't seem too hard to me (they reminded me of taylor series to some extent), but it definitely wouldn't hurt to see a few concrete examples of it done. My emphasis is actually signal processing, so this is the stuff I'm starting to get into in my concentration classes. We actually did build a filter the section mentions for an audio amplifier, but we largely glossed over the details unfortunately.
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