Another impressive piece by Monty. I really enjoy his articles. Just the right mix of text, graphics and formulas.

He also made a few videos:

https://www.xiph.org/video/

And the audiphile's "favorite" topic: "24/192 Music Downloads ...and why they make no sense"

http://people.xiph.org/~xiphmont/demo/neil-young.html

Interesting bit of context from his blog post that introduces this document:

"Even better... while I was documenting TF for posterity, I spotted a possible improvement. So, I've tossed in documentation of a brand new technique as well!"

and

"I literally discovered the second stage while writing the demo page about the 'regular' TF we used in Opus. Working two-stage TF is about six days old."

http://xiphmont.livejournal.com/60856.html