Fourier Transformation is Simply Changing Basis
This post explains DFT and DCT from a linear algebra perspective. The note has been polished by AI based on the original learning notes of the author. When I tried to learn Fourier transformation in undergrad, I never really figured out why the formula is the way it is. I rigidly memorized the formulas through brute force to answer exam questions, then completely forgot everything two weeks after the semester ended. Almost 10 years later, I had an in-depth discussion with AI about what Fourier Transformation actually is and was fortunate to have an aha moment. ...