No such edit war ensued until you started it!
The page before the "edit war" was adequate, and proved (up to a point) why the DFT was involved. Whilst it may not have been perfect, it was certainly better than the update, which offered no such "proof", was badly-formatted, and contained unencyclopedic phrases such as "This decomposition of C has got loads of practical applications" and "The greek letter ρ is called rho so it's good for denoting rhotation operations".
If you want to see the article move towards a matrix-style notation, please do it properly; any edits should be an improvement, not making the article worse.
P.S. computers don't love matrices any more than they love convolution. Claiming that "the linear systems approach of the electrical engineers is computer-unfriendly, obtuse, meritless, and dowdy" is completely unfounded. I hope that this won't cloud any further edits to the article that you may choose to.