[music-dsp] Re: Ogg Vorbis windowing function

Bob Grove music-dsp at musemagic.com
Thu Mar 2 14:28:14 EST 2006

beyond meeting the criteria for a resultant window function equal to 1 (in
order to do the aliasing of the overlapped MDCT that's needed) the real
they are selecting that particular window is they are trying to get around
the many patents on windows in both MPEG-x and AC-3.
Some of these window coefficients were literally "hand tweaked" to cancel
the artifacts and then patented (MPEG-AAC) and they are trying to obtain the
same results and avoid a lawsuit.

(below is dead on as far as I can tell on the technical side) 

-----Original Message-----
From: Sampo Syreeni [mailto:decoy at iki.fi] 
Sent: Thursday, March 02, 2006 11:11 AM
To: music-dsp
Subject: Re: [music-dsp] Re: Ogg Vorbis windowing function

On 2006-03-02, Emanuel Landeholm wrote:

> But I still can't find a motivation for the window function selected.
> http://en.wikipedia.org/wiki/MDCT
> describes the window function in Vorbis.

The Vorbis window is a bit flat-topped, and has properties between the basic
half-sine and Kaiser-Bessel Derived windows. It is an algebraically simple
de novo design, so unlike KBD, it's in the public domain and easy to derive
algorithmically. However, similarly to KBD it has high stop band
attenuation. This is a tradeoff which favours energy concentration for
steady state harmonic signals at the expense of temporal accuracy while
coding transients, and passband frequency resolution. It makes sense because
the interaction between transform block length and the critical bandwidth
makes frequency selectivity less of an issue for general signals, window
switching already takes care of time resolution, and because the energy
concentration properties of KBD type windows lead to fewer supra-masking
threshold coefficients for strongly harmonic signals and so ease the strain
on the quantization/entropy coding cascade (in practice arguably the weakest
link in the chain, which is why all this other stuff exists around it
despite vector quantization theoretically being all that is needed for any

I don't know how the Vorbis window was originally derived, but I think it's
reasonable to treat it as the free KBD, with similar benefits and tradeoffs.
Sampo Syreeni, aka decoy - mailto:decoy at iki.fi, tel:+358-50-5756111
student/math+cs/helsinki university, http://www.iki.fi/~decoy/front
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