Digital BW, The Print

> > In our multitude of discussions, I never considered assuming
> > all the steps would be the same.  And I think your
> > extensive audio experience lead you to assume there
> > was "some" fixed step size.  Actually, more accurately, all
> > the formulas that you brought over had the fixed step
> > size builtin long, long ago -- no need to ever worry about
> > variable size steps in audio.
>
> Thanks for putting that into a useful perspective Roy. That spoke to the
> concept on linearity vs non-linearity I kept referring to, but I
> don't think
> I ever explained it in an understandable way. You did.
>
> Todd

Todd,

We discussed this a number of posts ago:

"> You also did not speak to my premise that I think that a calculation of
> tones from DyR is only possible if linearity is assumed, which is not
> something I would take for granted in a silver print.

You don't need linearity at all.  Noise can be calculated using calculus,
and integrated over the entire range of the print...  Knowing math is not
your strong point?  I am guessing you don't know what integration is, in a
mathematical sense?  I can explain if you like."

And between you and I:

"> It would seem to me that those
> calculations work well for a system that produces a full and linear
> placement of tones between your dmin and dmax,

You are correct.

> but when those
> conditions are
> not met it would yield an inaccurate tone count. If I'm wrong
> please explain
> why.

You are absolutely right, and I'm happy that you have an understanding of
this to make such an observation!  Bravo!

This is where calculus comes into play.  It is a way of taking into account
the variability of the noise throughout the system.  Here's the deal.  The
noise "change" could be deterministic (possibly linear), which means it's
predictable.  If that is true (and I believe it is), then taking some number
of points (what ever are warranted by the type of equation that defines the
noise over the range, and if the noise is a simple gain, as in it's linear,
two points would do) in the "middle" will give you enough information to
derive the dynamic range.  Let's not talk about what that "result" or
equations would look like yet..."

Characterizing a non-linear system is just no big deal, it's done all the
time, and I've done it a number of times my self...

Regards,

Austin