[filmscanners] Re: Density vs Dynamic range

["Julian Robinson" <jrobinso@pcug.org.au>]

Austin,

> > No!!!!!   I don't!!!!!  Please read.  I say it is "usually" determined by
> > noise, because noise is what USUALLY determines the smallest possible
> > signal.  WHat  I actually say is dynamic range is based on
> > largest possible
> > signal and smallest possible signal.  I thought that was pretty
> > straightforward.  Sheesh.
>
>OK, your clarification straightened me out...that your belief is still not
>right...darn, I thought we were getting somewhere ;-)

This makes it pretty hard to ever convince you of anything!  However, you
have agreed that you were wrong about what I said the first time.  I didn't
give you a clarification, I just repeated what I said the first time.  So
this little milestone illustrates that you are actually capable of making
an error in interpretation - at least once in your life.  Can you concede
that it is therefore POSSIBLE that it might have happened another
time?!!  If yes, that there is just the tiniest chance, a 'one grain of
sand amongst the sands of all the beaches of the world' chance, that you
have an incorrect interpretation of what dynamic range is?!

******************************************************
The dynamic range is NOT a resolution definition, it is a signal range
definition.
******************************************************


>So, you are saying that my reference material is entirely incorrect?  I KNOW
>that isn't the case.

Everything I have seen that you have quoted from a book I agree with.  But
what you show from the books is NOT what you use yourself!  You change the
meaning of the numerator to derive a new formula.  And you use noise
instead of "min discernable signal" because they nearly are always the same
thing, but from a definition point of view, they are NOT the same.  Please
think about this.    If a reference shows "maximum signal" or words to that
effect on the top of the equation, it means what is says, "maximum signal",
NOT ("maximum signal" - "minimum signal").  Pleeeeeease show where each of
your references state that the top of the equation is what you call
"absolute range".  And please show references that use your actual formula.

> > Once again, if you want me to describe such a box where the "smallest
> > discernable signal" is NOT determined by noise, just say so .
>
>But that would be a mis-use of terminology.  Again, for the 100th time,
>"smallest signal level" is NOT the same as "smallest discernable signal".
>"Smallest discernable signal" IS noise, and as my references have defined
>it.

OK here's an example.  It is a simple box that has a smallest discernable
signal which is different from the noise signal.

It is a detector circuit.  A very basic one.  Actually a peak detector.

The input goes to a full wave rectifier - a diode bridge, followed by a
capacitor and then an op-amp feeding the output.  The op-amp has a high
enough input impedance so the peaks are preserved for a while, and it has a
gain of 1 i.e. it is a buffer.   Now ... you feed the input with a variable
amplitude  ac signal and at the output you get a DC signal which is kind of
proportional to the peaks of your input signal.    The noise comes from the
diodes, the capacitor and the op-amp.  Let's say the noise is 1
millivolt.   The thing saturates for an input signal of 10V peak to peak,
i.e. at an output of 8.4V.

OK, so start at 0V ac on the input, and start winding up the wick while you
watch the output. What happens?  At first nothing.  We'll assume the diodes
have a sharp forward knee, and a 0.7V drop.  More signal, more
signal.  Still, nothing - all we see is 1 mV of noise at the
output.  Suddenly, when the input gets to just above 1.4V p-p, you just
start to see something at the output.  At 1.41V p-p you see 0.01 V DC at
your output, well visible above the noise.  From there on, as you crank up
the input, the output follows the input linearly.

But, do you see, the minimum discernable signal was just above1.4V - about
1.401 in fact.  You can not discern anything at 1.39 V, nothing at all.  At
1.41V your meter starts registering a solid 10mV.  So your smallest
possible signal that is discernable at the output is 1.401V.  The dynamic
range of this box, is DR = max signal / min signal = 10V / 1.401V = 7, near
enough.   I repeat, the smallest input signal it can register is 1.401V
(i.e. this is the min discernable input signal), the largest it can handle
is 10V.  The dynamic range of the box is 7.

That is a legitimate and useful dynamic range calculation, it gives the
information you want about the range of signals this detector can detect.
It does NOT tell you anything about resolution.  Let me emphasise this:
dynamic range usually  DOES tell you something about resolution, because
systems are USUALLY linear,  but in this case it does not.

******************************************************
The dynamic range is NOT a resolution definition, it is a signal range
definition.
******************************************************

In this case, DR MUST be expressed in terms of the input voltages because
this is a non-linear system, so to specify the dynamic range of the BOX,
you have to use the input voltages.  (But to determine what the minimum
discernable signal is, you obviously have to watch at the output, just as
you have to watch at the output to determine when the thing is
limiting).  The dynamic range is, as the definitions say, the ratio of the
largest signal to the smallest signal.  In ****THIS**** case, it has
nothing to do with the noise, in this unusual case.

A man comes to buy an ac peak detector from me.  I ask him what range of
signals he wants to measure, he says "ah, from 1V to 10V".  I show him this
box and a 10x amplifier and say "this will do the trick, this setup has a
range of 0.14V to 10V - you put the amp (which I have here, on special
today) in front of the detector, select 10x or 1x gain, and Bob's your
uncle".

He goes away and comes back next day saying - "what a crock of s*** - to
measure 1V I have to turn the amp gain up, then I can't measure 10V any
more because it saturates!"  "Oh" I say, "you want to measure 1V and 10V at
the same time, without changing your settings?"  "Sure he says, of
course.  I wanted a *Dynamic Range* of 10:1".  "ah", I say, "why didn't you
say so?"

--
Now there is another bit of info about this box that might interest some
people, and that is the RESOLUTION of the thing.  What can it
resolve?  That is a good question, and I would answer it by saying "let's
see now, the output range is, um,  8.6V-0V = 8.6V and the noise at any
level superimposed on that is, um 1mV, so let's see now, there are
8.6/10^-3 = 8,600 meaningful levels I could measure.  This is close to what
you would call the dynamic range (you would say 8,599).  Unfortunately, it
is not the box dynamic range, it is the number of meaningful levels to
which I can resolve the range of this box.  It *IS* the dynamic range of
the ***OUTPUT***, but not of the whole box, not of my  PEAK DETECTOR.  The
output stage does have a dynamic range of 8,600,  But the whole box has a
dynamic range of 7.  This is a characteristic of non-linear systems -
linear systems OTOH  have the same dynamic range measured input or output.

Another man comes in to see me for a peak detector, and I show him this
box. He says "what is the resolution of this device?" and I say "It
resolves to 1mV, but it only covers the range 1.4 to 10V and he says
"that's fine, I only want to measure between 5 and 6 V but I need it
accurate to 5mV". ("accurate" is loosely used here, we'll say he can
calibrate the thing against something else).  He buys one.

Neither of the people so far needed to know anything about the 8,600 figure.

But then a rare and endangered species, a woman with a technical bent,
comes in and says I want one of those peak detectors over there, but I want
the output digitised, and I want the digitisation such that it doesn't
throw away any significant information, in other words, don't compromise
the performance".  I say "no problem, it'll be ready next week".  Then I
think to myself - what sort of A/D do I need? ah let's see now, 8,600
levels or better, that means 14 bits, wow, that's an expensive A/D for my
little shop.  And off I go and build her a digitised peak meter.

There are two ways I could have calculated that 8,600 figure...

Julian's method
******************
First, remove any DC offset at the output. There are none, so that is ok.

Then... number of levels available at output
         = max / noise
         = 8.6V/1mV (because 8.6 V is the MAX VALUE of the output, it is
not an "absolute range", it is the max value because that is what this box
saturates at ---- 8.6V (corresponding to a 10V input)
         = 8,600.

Austin's method
******************
Substitute the figures relevant to the output in Austin's formula:

Austin's number = (max - min)/noise
         = (max-noise)/noise     [here]
         = 8,599/1
         = 8,599

What this actually gives you is the number of STEPS you want from your A/D,
which is one less than the number of LEVELS.

Neither of them DEFINE dynamic range, they are simply aiming to calculate
the number of resolvable levels.  It happens that the calculation for DR is
max/min, and the calculation for num resolvable levels is max/noise, so it
doesn't take a genius to see that if min = noise, these are the same
calculations.  It is tempting therfore to say that because min always
equals noise in a linear system, then I'll just blur the boundaries a bit
and, well, max/noise defines dynamic range.  It is not so!  It IS so in any
system in which you STATE or PRESUPPOSE that the min signal is equal to
noise, but it is NOT so in the general case.

******************************************************
The dynamic range is NOT a resolution definition, it is a signal range
definition.
Furthermore, calculation of resolution is NOT necessarily the same as
calculation of dynamic range
******************************************************

----Another attempt to explain and demonstrate----------------------------
I will now demonstrate that the book definition of dynamic range will give
you the number of levels when the noise determines the min discernable
signal, and that your formula will not give the right answer. I do this by
choosing an extreme but very possible and meaningful example. It is not
related to the previous example.

This one is a conventional ac coupled amplifier, the gain doesn't matter
because it is linear, so we can measure at output or input.  At the output,
the max signal is 2V RMS.  The noise is high at 1V RMS (you can use peak
values if you want, it doesn't matter).

What is the dynamic range of this box?  Simple, it is max/min = 2.  That is
following the book definition.  (and also, I might point out, the common
sense definition, as in: "this thing can handle from 1Vmin to 2Vmax; so it
has a range of 2:1.  Hmm...since this can be handled by the circuit without
changing any parameters like gain, that must be the *dynamic range* too").

That calculation also accurately gave the number of levels you can resolve
to --- 2.

But using Austin's equation, we have:

Dynamic range = (max-min)/noise
         = (2-1)/1
         =1

Ouch.

This is not a meaningful dynamic range, nor is it the correct number of
resolvable levels.

The situation becomes even worse if you reduce the max signal to 1.5V,
still perfectly possible, and still a circuit capable of carrying a limited
amount of useful information. Then the Austin formula gives a dynamic range
of less than one, which is totally meaningless, and thus a log dynamic
range which is negative. This is obviously wrong.

It doesn't matter much in the real world, because the noise is usually much
less than the max, but it matters a great deal when you are talking
definitions.


---one last informative example--------------
We have a log amp.  It has a minimum input signal that you can just resolve
at the output amongst the noise of 1mV.  At this point the output is 1mV
too.  It saturates for an input of 1000mV, when the output is 3V.  So we
have a log amp with an output of about 1V per 20dB of input.

This is straightforward and used all over the place.

Question 1: Now, what is the dynamic range of this thing?

Julian's method
******************
DR = 1000/1 = 1000

Austin's method
******************
DR = (1000-1)/1 = 999

So we all agree the DR is around 1000?

Question 2: What is the resolution of the output?  i.e. how many A/D bits
do I need to capture ALL of the significant information in this signal?

Is it the same as the DR = around 1000 levels, so we need 10 bits? NOT AT ALL!

Is it calculated by your formula (max-min)/noise?  NOT AT ALL.

******************************************************
The dynamic range is NOT a resolution definition, it is a signal range
definition.
Furthermore, calculation of resolution is NOT necessarily the same as
calculation of dynamic range
******************************************************
IN fact, to do this accurately, you need to know a bit about where the
noise comes from, because the system is non-linear.  If all the noise
originates in the front end, then it is independent of output level, and
will be 1mV at all output levels.  That means the discernable noise step at
the bottom will be very big, about 0.2 volts - very rough because of the
nature of log signals.  But at the top end, 1mV input noise translates to
only 0.4 mV compared with the 3V total range, if I did my maths right
(because of compression of the log scale). So to maintain the same
resolution at the top end, you'd need an A/D with 3000/0.4 = 7500 levels,
or 13 bits.

OTOH, if all or most of the noise was generated in the output log amp, then
you'd get an entirely different figure for the necessary resolution.  The
point of this labored discussion is only that...

****************************************************************
Calculation of resolution is NOT necessarily the same as calculation of
dynamic range
****************************************************************
Do you agree?

>Austin said:
>My point is to try to get you to understand that you are
>mis-using terms, and are missing the concept of dynamic range.  It is
>reasonably clear to me that you want to believe what you believe...and don't
>want to change your belief.

Actually I have changed my ideas many, many times in my life as new
evidence comes to light, or a good argument is presented.  I am PERFECTLY
willing to agree with you if you demonstrate why.

>... I know you
>aren't going to convince me your understandings are right,

Now THAT is a problem for a discourse!

>I have too much
>reference material, too many people and too many years of experience with
>this subject to be convinced that everyone, every reference and every bit of
>work I've done on this for 20+ years is simply wrong.

So, I ask again, please show me the reference material that supports your
equation/definition for dynamic range!    This one - the "(max -
min)/noise" equation.

>So, unless you are
>willing to accept the terms and concepts that the reference material
>provides

I do, and I have used the equations that YOU have provided from references,
throughout.  I agree with them.  But - I do NOT agree with your own derived
versions of those same equations.

>(and I have been using and trying to explain), I don't believe we
>can go any further.

Well I hope you don't pull out now...

Julian

----------------------------------------------------------------------------------------
Unsubscribe by mail to listserver@halftone.co.uk, with 'unsubscribe 
filmscanners'
or 'unsubscribe filmscanners_digest' (as appropriate) in the message title or 
body