[vorbis] Description of MDCT

[Keith Wright]

The Vorbis audio format, uses something called the Modified
Discrete Cosine Transform (MDCT).  I was interested in how this
worked, but did not know where to start.  Is this the name of a
particular algorithm, or does it just mean something like a
cosine transform, but not quite right?  So I asked the Vorbis
mailing list.  Nobody answered.

It was not a high priority, so I did other things for about a year.
I got interested again, so I did a Google search for MDCT.
I got just a few hits, one of which was my own mailing list question
from a year previous.  

I can almost hear you saying that you are tired of people whining
about lack of documentatation, but this is not a complaint, it is
an announcement that I did something about it.  I searched the
local library and the internet, came up with a few definitions,
removed the errors and differing sign conventions and worked out
the details.

This doesn't count as research; it is, of course ``well known'' in
the mathematician's sense.  Nevertheless, my experience leads me
to believe that it is not perfectly trivial to actually become one
of those who know.

Abstract
--------
Assuming only basic trigonometry, we define the Modifed
Discrete Cosine Transform (MDCT), and prove its basic properties.
The dread words ``it can be shown'' do not occur.

This document is not complete, but I am releasing the draft
because there is enough here that it may be useful to someone.
Comments and suggestions for improvement are welcome, especially
if you know the answers to any of the questions at the end.
It can be found at http://www.free-comp-shop.com/vorbis.html


-- 
     -- Keith Wright  <kwright at free-comp-shop.com>

Programmer in Chief, Free Computer Shop <http://www.free-comp-shop.com>
         ---  Food, Shelter, Source code.  ---
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