Richard Owlett wrote:

> I started playing with some human perceptible audio questions.
> 
> If I understand correctly, humans perceive audio levels on a log power 
> scale.
> 
> I'm starting to look a spectrum analysis problem ( intentionally vague 
> as I'm not sure of what I want to look at ;)
> 
> I wish to plot "data".
> Linear in intensity has obvious problems.
> 
> Log (intensity squared) has much history.
> 
> BUT I wish to look at a a VERY wide dynamic range on a visual plot.
> 
> I have reason to believe that plotting (log(log(intensity squared))) may 
> point out 'interesting' features.
> 
> BUT, does it have any intrinsic significance?

Significance? Dunno. Realize, first of all, that log(I^2) = 2*log(I), so
that by squaring, you simply change the log's scale. A linear plot gives
equal increments equal sizes. A log plot gives equal relative changes
equal sizes. I.e., a certain ratio corresponds to a certain distance
on the axis. Logarithmic intensity is linear dB. Your question amounts
to "Logarithmic dB is linear _____" Fill in the blank, and you answered
your own question. (It's not hard to fit the entire dynamic range of 
hearing on a note-book size graph that you can read values from.)

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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I started playing with some human perceptible audio questions.

If I understand correctly, humans perceive audio levels on a log power 
scale.

I'm starting to look a spectrum analysis problem ( intentionally vague 
as I'm not sure of what I want to look at ;)

I wish to plot "data".
Linear in intensity has obvious problems.

Log (intensity squared) has much history.

BUT I wish to look at a a VERY wide dynamic range on a visual plot.

I have reason to believe that plotting (log(log(intensity squared))) 
may point out 'interesting' features.

BUT, does it have any intrinsic significance?