8.1, due Nov 26

Difficult:
I had a hard time distinguishing between k and c_k. As far as I understand, the c_k's are Fourier coefficients, but k's are the index...? I'm not sure. Some extra explanation on that would be helpful.

Reflective:
I can already see how powerful this could be. Anywhere you see a periodic signal, a Fourier transform will give extremely valuable information. I saw an interesting application of this in my deep learning class, where the position of a word in a sentence was encoded by modulating its input embedding with a certain frequency, based on the position of the word. The neural network then learned to perform a Fourier Transform to use the position of the word as a feature in its learning.

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