My takeaways: >"This is known as the Walsh matrix. It essentially consists of square waves running at different speeds, although with some complex symmetries t

My takeaways: >"This is known as the Walsh matrix. It essentially consists of square waves running at different speeds, although with some complex symmetries thrown in. And yes: every multiplier is just a +1 or a -1, so the computation boils down to flipping some signs in the input data and then summing the results. The matrix looks fairly trivial, but its design is involved. To capture all frequency and phase information, the rows have increasing sequency — that is, each next row has just one more sign flip than the one before. Further, the pattern is carefully engineered to ensure orthogonality — the fragile input-output symmetry that allows seamless conversions back and forth between the frequency representation and the original time-series data. [...] >"Hadamard [Matrices]: At a glance, the plot looks chaotic, but it’s simply a reordering of the Walsh layout. For example, rows #1 and #8 are swapped; the same goes for #1 and #15. And unlike Walsh, this fractal-esque pattern is actually fairly easy to create from scratch." I did not know any of this before! Anyway, an excellent article! (Applications of Walsh & Hadamard Matrices in Physics and in modern technology -- are too numerous to count!) Related: https://en.wikipedia.org/wiki/Walsh_matrix https://en.wikipedia.org/wiki/Walsh_matrix https://en.wikipedia.org/wiki/Hadamard_matrix https://en.wikipedia.org/wiki/Hadamard_matrix