The Unreasonable Effectiveness of the Fourier Transform

Summary

The Unreasonable Effectiveness of the Fourier Transform Notes from Joshua Wise's talk at Teardown 2025. New: You can now watch a recording of my talk on my YouTube channel! Or you can just click "play" below, I suppose. VIDEO Here are a few resources from my talk. Here is a PDF of my slides, if you wanted to refer to anything in specific. Here is the Jupyter notebook that I used to produce all of the zillions of plots. I do not claim that it is good code, but it is code. The OFDM patent is US3488445A, filed in 1966, expired in 1987. Here is Eugene Wigner's original discussion, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". There are many good follow-ons to this, too. Here is the paper on how to estimate both carrier offset and time offset at the same time. I implemented it by typing in the algorithm, and it worked, but if you understand it and can explain it to me please let me know. Here is the DVB-T decoder that I wrote. I do not claim that it is the right way to do any of these things, but it is a way to do these things. Finally, here is an absolutely fantastic video that breaks down the implementation of the Fast Fourier Transform algorithm. I watch it every year or two. Thanks so much for coming! Please let me know if you have feedback on this. I'd love to hear what you thought.