MATH416 Applied Harmonic Analysis: An Introduction to Signal Processing

What does it say on Testudo?

Introduces students to the mathematical concepts arising in signal analysis from the applied harmonic analysis point of view. Topics include applied linear algebra, Fourier series, discrete Fourier transform, Fourier transform, Shannon Sampling Theorem, wavelet bases, multiresolution analysis, and discrete wavelet transform.

Why did I take this class?? Should I have taken this class???

Looked interesting from the description. I also needed another class, and didn't think of anything else. I was planning to also take COMM107 but not at Zoom University. Probably shouldn't have taken it and taken PHYS270 instead.

Review

Very boring class. I attended all Zoom meetings during the first month or so, but eventually realized it wasn't even worth it. The first month is basic linear algebra review then principal component analysis and Laplacian eigenmaps. This stuff sounds so much more fancy than they actually are. I think about a month was spent on the discrete Fourier transform and the fast Fourier transform. I mean the FFT seems useful for \(O(N\lg N)\) algorithms but I don't think we needed to go that slow.
The last month was spent on the discrete Haar transform and other filtering transforms. I stopped attending most lectures at this point, but the material was pretty easy to pick up just by reading the notes. The main takeaway from this class seems to be that orthogonal transforms are nice since they're easily invertible.