Vorbis - Nov 2009 - Floor1 doubts...

Hello,

I've read in a thread from this mailing list (
http://lists.xiph.org/pipermail/vorbis-dev/2009-September/020019.html) that
the usage of FLOOR1_fromdB_LOOKUP table is to convert Floor1 values from a
dB scale to a linear scale. In a dB scale, given a reference value, the
other dB values are obtained from it, normally dB_value = 10log(p1/p0),
where p0 is the reference value. Supposing p0 is a fixed value, both
10log(p1/p0) => p1/p0 and 10log(p1/p0) => p1 are dB to linear conversions,
so, my doubt is: which one of the conversions is done, p1/p0 or p1? Besides,
given that the maximum value of FLOOR_fromdB_LOOKUP table is 1, my deduction
is that the conversion which is made is 10log(p1/p0) => p1/p0. The
alternative would be converting to p1, chosing arbitrarily 1 as the maximum
value (in which units?). As I haven't been able to find any reference to
this, I tend to believe that the conversion is made to p1/p0...

In the other hand, in "Improved Noise Weighting in CELP Coding of Speech -
Applying the Vorbis Psychoacoustic Model To Speex", it is said that the
floor is a superposition of the tonal and noise masks. So, given my previous
supposition of converting to p1/p0, and given that the maximum value in
FLOOR1_fromdB_LOOKUP is 1... then, which is the reference value used? I
first thought of the ATH (2e-05 Pascals), but, if so, the maximum value for
the floor would be the ATH itself, and it seems to me a bit unlikely for the
masks to be always lesser than the ATH... So if my supposition of converting
to p1/p0 is right, then the alternative must be that p0 is not a fixed value
in FLOOR1_fromdB_LOOKUP and it varies somehow.

So, I see here two options: that all my suppositions are right, and then p0
varies, in which case, how does it vary? Or, which I think will be the most
probable option, I've made some wrong deduction or supposition, but, as much
I think of it, or as much I look for any kind of info in the spec, the web,
articles... I'm not able to find any answer...

I really need to understand this, so, any kind of help will be much
appreciated.

Thank you very much.
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On Tue, Nov 10, 2009 at 9:44 PM, Eldhelrim <eldhelrim at gmail.com>
wrote:
> Hello,
>
> I've read in a thread from this mailing list
> (http://lists.xiph.org/pipermail/vorbis-dev/2009-September/020019.html)
that
> the usage of FLOOR1_fromdB_LOOKUP table is to convert Floor1 values from a
> dB scale to a linear scale. In a dB scale, given a reference value, the
> other dB values are obtained from it, normally dB_value = 10log(p1/p0),
> where p0 is the reference value.
[...]

This mostly restates the same idea several different ways that are
equivalent and I'm not sure where you're confused.  So let's step
back
a second...

The floor encodes a continuous function and the values of that
function are meant to be used as multipliers/ratios.  Linear floor
multiplied by residue gives you a spectrum.

The floor is encoded on a logarithmic scale (not actually decibels in
fact, but decibels are easy to understand, so the spec discusses this
in terms of decoding the encoded floor to decibels, then doing a
decibel->linear conversion).  Unitless decibels are just ratios.  1 =0db, 2
== 6dB, 4 = 12dB. The coversion is a simple 20log10(linear).

Is that helpful?

Monty