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.

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.