This paper appears to speak to many of the issues discussed in this thread:
<>
It seems quite authoratative, which puts it over my head, but something
tells me both sides will claim it supports them. I'd be interested to hear
how any of you interpret it in the context of our discussion.
However, one thing did jump out at me which I think appears to be in direct
conflict with Austin's approach.
There is a diagram in sec. 3.1, fig. 5, which illustrates DyR as a range
between the "noise floor" and "distortion region". To my eye it bears a
strong resemblance to the portion of Higgins diagram Austin has cited many
times:
<>
Below is Austin's text which explains how he (Austin) interprets the
diagram. (Note that it is Austin who is suggesting how we should relate this
diagram to his terminology, but the author himself (Higgins) does not go so
far (see below):
"largest" is shown on this diagram to be the maximum signal level minus the
minimum signal level, and is the largest range or absolute range that the
signal can go from <=> to. Example, maximum signal level is 5, minimum
signal level is 2, the absolute range/largest range is (5 - 2) or 3.
"smallest" is shown as the noise. It is the same thing as "smallest
discernable signal", which means the smallest change that can be detected.
Where the signal is at it's lowest point, is what I am calling "minimum
signal level".
Where the signal is at it's highest point, is what I am calling "maximum
signal level".
The dynamic range equation is, using these terms, and the provided diagram,
can be either of the following:
DR (dB) = 10log10 (largest/smallest)
DR (dB) = 10log10 ((maximum signal level - minimum signal level) / smallest)
You can substitute "smallest DISCERNABLE signal" for "smallest" in these
equations. Do NOT confuse "smallest"/"smallest discernable signal" with
"minimum signal level", they are not the same thing, though in some
circumstances they MAY have the same value.
Now, if you are using log values for "largest" and "smallest", then you have
the following equation:
DR (dB) = largest(in dB) - smallest (in dB)
------------------------------------------------------------------------
I actually dislike that version of the diagram since it's out of context.
This is the diagram (almost) in full:
<>
Note that when seeing the entire diagram with accompanying text we notice
that Higgins may or may not agree with Austin's interpretation of him. We
also see that Higgins did not intend his diagram to be an illustration of
how DyR is defined or calculated, but simply to show that the DyR of a
source needs to be mapped to fit the DyR of the medium that will hold it in
order for the smaller signals not to be lost to noise, and the larger
signals lost to clipping.
That's not to say there was anything wrong in Austin's use of the diagram,
it's just to point out it is Austin's interpretation, not the Author's per
se.
------------------------------------------------------------------------
Note, there are at least two critical differences between The Higgins
diagram with Austin's terms, and the Analog Devices white paper figure 5.
1). What Higgins calls "Largest", and Austin defines as, "the maximum signal
level minus the minimum signal level, and is the largest range or absolute
range that the signal can go from <=> to"...
This range is what Austin uses as the numerator in his DyR equation...
In figure 5 this range is called: Dynamic Range - The difference between the
loudest and quietest representable signal level, or if noise is present, the
difference between the loudest (maximum level) signal to the noise floor.
2). Austin has claimed that if Higgins had meant for the numerator to simply
be what Austin calls "maximum signal level" he would not have illustrated
the concept of "Largest" with a double sided arrow which spans the range
between noise and clipping (what fig 5 calls DyR).
However, in figure 5 we clearly see them point specifically to the highest
signal (Peak Level) as a single point where anything greater would be in the
"distortion region". In fact they define it as the clipping point. This is
the value they use as their numerator.
Remember, their definition of DyR is:
Dynamic Range = (Peak Level) - (Noise Floor)
Austin, I never count you out buddy, but this Analog Devices diagram and
text looks to be in clear opposition to your interpretation of Higgins. Your
comments are most welcome.
Todd
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