In reading this article, my intuition says to me that the Burrows-Wheeler Transform (https://en.wikipedia.org/wiki/Burrows%E2%80%93Wheeler_transform https://en.

In reading this article, my intuition says to me that the Burrows-Wheeler Transform (https://en.wikipedia.org/wiki/Burrows%E2%80%93Wheeler_transform https://en.wikipedia.org/wiki/Burrows%E2%80%93Wheeler_transf...) and the Fourier Transform (https://en.wikipedia.org/wiki/Fourier_transform https://en.wikipedia.org/wiki/Fourier_transform) -- are related -- in some as-of-yet unknown to me, mathematical way... like maybe one is a specific, specialized sub-case of the other, or something like that... I don't have the mathematical ability to prove or disprove this conjecture -- but if some Mathematician in the future wanted to go down the path of either proving or disproving this, then I'd start with looking at the idea that both Transforms have reverse Transforms that preserve information, and that the Fourier Transform is basically its own reverse Transform... in other words, the Fourier Transform is sort of like an "identity" in the world of transforms... It seems that there would, or should be, in the world of Math, transform functions of "different orders", i.e., if Fourier is its own opposite, and if data compression comprises two transformation functions, one to compress data, another to decompress it -- then couldn't there also exist "Trinary Transforms" -- where you run transformation function A, get some data out of it, then run transformation function B on that resulting data, and get some different data out of it, then run transformation function C on that data -- and after running transformation function C -- you get your original data back. If those exist, then maybe N-ary Transformation Functions do too, where you run a set of data through N functions -- and you get your original data back after the Nth time... "transformation function families" -- for lack of better terminology! I don't know -- I don't have the Mathematical expertise to prove or disprove it! Disclaimer: All of the above is based on rampant speculation and conjecture -- and could be (and probably is!) absolutely and completely wrong on one or more levels -- so take with the proverbial "grain of salt"!