8.1, due on November 27

Theorem 8.1.7 explains a sufficient condition for the Fourier series of a function to converge to it pointwise. I guess what it's saying is that at a discontinuity the function needs to be equivalent to the average of the two limits on either side. That seems intuitive.

I'm confused by Example 8.1.8, in the part where the Fourier series of the function is given. I don't see how we made the jump from calculating c_k to getting the infinite series that we got. No calculations were given.

From the reading it looks like Fourier transforms are to signal processing as eigenvalues are to other areas of engineering. They have lots of application in various fields. I'm personally interested in signal processing when applied to phonetics and speech processing, because that's a very interesting field that still has many unsolved problems.

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