#273 overall
EE261 The Fourier Transform and Its Applications
Stanford University
2 recommenders · 2 threads · recommended in 2 years, 2014–2017 · score 1.8
EE261 is Stanford's introductory course on the Fourier transform and its applications, taught by Brad Osgood, covering Fourier series, the transform, and their use in signal processing and related fields. The course reader is available as a free PDF.
Commenters praise Osgood's lectures and course reader for clear, rigorous definitions and an intuitive grounding in the Fourier transform.
Mathematicsintermediatefreevideo lectures#fourier transform#fourier series#signal processing#osgood#linear algebra
Recommendations by year
20062026
Brad Osgood's lectures are phenomenal. He was trained as a mathematician, so his explanations are crystal clear in terms of definitions and where physicists sweep mathematical formalisms under the rug. After watching his entire lecture for this course, and spending a lot of time reading the course reader, I learned a lot about how to decrypt the kind of mathematical nonsense that physicists tend to say (as well as learning about the real foundations, c.f. tempered distributions and others).
That being said, a lot of these lectures can be summarized in a few sentences if you already have a strong foundation in linear algebra. For example, the fact that complex exponentials form an orthonormal basis for periodic functions is the content of the first handful of lectures, and deriving the Fourier transform is only slightly messier to explain in terms of linear algebra (this is not because of the linear algebra but because Fourier transforms are inherently a little messy).
What do you mean, not much intuition for Fourier transforms? Sure, sometimes you get weird results and need to work with fairly generalized versions of functions, and a bit of background in functional analysis is helpful, but a strong intuition about the Fourier transform is both extremely useful, and not that hard to develop.
For starters, I'd recommend the course notes to Stanford's EE261 (https://see.stanford.edu/materials/lsoftaee261/book-fall-07....) - well written, very funny, a nice level of rigour, etc...