Re: [Jack-Devel] query jack scaling factor?

On 05/30/11 21:03, Paul Davis wrote:
> On Mon, May 30, 2011 at 3:52 PM, Matthew Robbetts
> <[hidden]> wrote:
>
>> Just out of interest, is it possible to give a link (or list name, etc -
>> whatever is easiest) to the discussion where this argument was given? I
>> would be really interested to hear any rationale for it that wasn't
>> limited to the "easiness" of having a symmetric numerical range.
>
> this is the best place i know that catalogs the conventions used, and
> mumbles a bit about the rationale for the one that its author believes
> is best:
>
> http://blog.bjornroche.com/2009/12/int-float-int-its-jungle-out-there.html

Thanks for that - I've seen that post before, actually. While I agree
with many of Bjorn's points, I do have some issues with the arguments
and have been meaning to write up a similar blog post for a while.
Perhaps I should try and get around to that. Whether anyone cares at
this point is another matter :)

> the arguments themselves ... not so much. i've see it mostly on
> mailing lists, and it most concerns whether you honor the dynamic
> range (which is asymmetric because of the different number of positive
> and negative sample values) or the bit-values of the samples.

I would propose that the important fact is really the semantic meanings
of sample values, in terms of their being elements of a finite field. I
need to construct a number-theoretic argument formalising the point, as
I'm sure that's correct framework for this.

Certainly, as Bjorn points out, linearity has to be the key issue.
Linearity in the mean (as would be obtained using any scaling factor
with proper dither) is sufficient for most purposes, but of course is
not as strong as the honest-to-goodness semantic equality provided by
the 2^n scaling factor.

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