Hi Julian,
> In your example above, *IF* your 100v and 98 v etc were AC signals (and so
> the 98V is the noise level), then the dynamic ranges are exactly as you
> disparagingly calculate them, 1.02 in the first case and 3 in the second
> case. That is correct, and that is what the definition formula says. Do
> you have any trouble with that?
Except that you can't measure a 2V value with 98V of noise! If the noise
level were 98V, your effective "resolution" is 98V...
> Now if I change my way of thinking to DC signals, then I can see why you
> say what you are saying, but you then have made life extremely complex for
> the more usual situation and ruined a perfectly good definition, and then
> had to make up your own.
I am using equations and definitions straight out of a book, AND have shown
that what I've been saying is identical to what the ISO proposal contains.
I really don't know why you say what you say.
> I have no problem with any of this, except that
> you HAVE made up your own definition to get rid of offsets, and
> this is not
> only irrelevant to signal theory, it is slightly inaccurate.
Well, no, I did not make up any definition, much less to get rid of
offset...
> The
> definitions in the books are AC signal based or assume no offset, which
> seems to me to be self-evident.
Scanner CCDs don't put out AC, they put out DC, same with audio...yes, with
audio, the signal IS a sine wave...but it's measurements ARE DC...A/D
converters take DC in (or current, depending on the design, but all I've
used, except one, is DC). The equations and examples in my reference books
have no reference to AC or DC. At a moment in time, the A/D takes the DC
measurement of the input signal...that's it!
> The REASON
> that signal theory assumes AC signals is precisely because it is concerned
> with noise,
Er, I thought you said dynamic range had nothing to do with noise??? You
say:
"What I actually say is dynamic range is based on largest possible
signal and smallest possible signal."
And best of all:
"Dynamic range is a RANGE, this idea that it
is "divided by noise" is just strange."
But yet now, you are using "noise" as the DIVISOR in your DR equation! Hum
;-)
> and noise is by definition, a varying signal and therefore
> AC.
Yes, noise is a varying signal, and of course, not constant...hence, +-1/2N
is the accuracy of any measurement.
> This is also what makes it so easy to remove offsets,
> because it is so
> easy to distinguish between the non-varying part of a "minimum
> signal" (the
> offset) and the varying part (the noise).
I don't understand the hang-up on offset here. The important piece is the
overall signal range (max signal level - min signal level...min signal level
is what you are now calling "offset") and noise. It doesn't matter to me
which you use, just so we agree on what the term you are using means.
> ??? You have made up an entire lexicon to support an unusual view of
> dynamic range!
Again, absolutely not true. "smallest discernable signal" is RIGHT out of
the Higgins book. As well as "largest"...as well as that "smallest
discernable signal" is the same as noise...
> I THINK I see what you are doing in all this, I just don't
> know why,
I am merely repeating (and trying to explain and clarify ambiguous terms)
the terms used in the reference material. I haven't "done" anything, but
try to clarify something that appears most people have a confusion about.
> IF you want to allow DC offsets within your
> calculations, then you need these definitions I agree. But it is much
> easier to just remove any DC offset first,
But it doesn't matter, it comes out to the exact same thing whether you use
(maximum signal level - minimum signal level) or absolute signal "range" or
what ever term you want to use...as they are completely interchangeable.
> then use the book definition of
> dynamic range.
What book definition?
> And it gives you the right answer, not a slightly
> incorrect
> answer.
I don't see ANYTHING in any of my answers that is even slightly incorrect.
>
> TWO EXAMPLES
> *********************
> EG1) Use your "DC" example of 98 min signal to 100 V max signal. Say the
> noise is 100mV.
> **********************************************************************
> CASE 1 - doing it your way.
> First: what is your smallest discernable signal, and what is the smallest
> signal level? I'm damned if I know.
Did you not READ the definitions I spent the time to write up to clarify
these things? If you did, then you would know EXACTLY what was what.
Obviously, 98V is the smallest signal level, and 100mV is the smallest
discernable signal (or noise).
> If 98 is the minimum POSSIBLE level,
> then the minimum SIGNAL level must be 98+noise = 98.1V.
No, noise is taken into account in the divisor...you do NOT do anything to
the largest signal level or to the smallest signal level, simply take them
as they are.
> Then putting the
> correct values into your (incorrect) formula
It's not MY formula, nor is it incorrect...but it appears your use of it is
incorrect.
> gives(100-98.1)/0.1 =
> 19.
> Unfortunately for my ease of discussion, putting in the INCORRECT
> value into the (incorrect) formula in this case gives the right answer
Well, ALWAYS using the numbers as you did below (correctly) will give you
the correct answer! Funny how that is...
> thus: DR = (100-98) / O.1 = 20.
But, that is NOT the incorrect value, nor is it an incorrect formula. By
definition, 100 IS the "largest signal level", and 98 IS the "smallest
signal level". NO WHERE does it say to add or subtract noise to either
signal. You to simply USE THOSE VALUES AS STATED!!! You are changing the
meaning of the terms, and applying your mistaken terms here. No wonder you
get a wrong answer, you're using the wrong numbers!
> CASE 2 - Use normal definition
> Remove the offset by subtracting the offset DC component of 98V from the
> upper and lower limits. Then the max signal is 2V, the min signal is 100mV
> (i.e. noise) and DR = max/min = 20.
Sigh.....
> In this example, as I said, your formula is incorrect but by using an
> incorrect value as well, you get the right answer.
Well, you are wrong about that. You are mistaken by adding noise as you
did. No where does it say to do as you mistakenly did.
> EG2) Example using AC signals:
> **************************************
> Say noise = 100mV = "min" (= minimum signal = minimum discernable signal),
> and Max signal = 2V = "max". (Note that under AC conditions
> minimum signal
> and minimum discernable signal are the SAME, always. Minimum discernable
> signal and noise are the same, NEARLY always).
Yes, but minimum signal level and noise (minimum discernable signal) are NOT
the same, though they MAY be the same value, but in this case ARE NOT.
> CASE 1: DR by your definition = (max-min) / noise = 1.9V / 100mV =
> 19.
Wrong. Your use of the equation is entirely incorrect. You should NOT add
noise to the minimum signal level, noise is taken into this equation in the
divisor, and your application incorrectly changes the equation. The CORRECT
equation use is:
minimum signal level = 0
maximum signal level = 2
noise = .1
DR = (2-0)/.1 = 20
> This is unfortunately just plain wrong again
Yes, what YOU wrote IS wrong, but because you are misapplying the equation.
NO WHERE does it say to subtract noise from the minimum and maximum signal
levels!!! YOU are changing the equation here. The minimum signal level
(what you call "min") is ZERO, not .1V.
> CASE 2: DR by book definition = max/min = 2V/100mV = 20.
>
> Now I KNOW you will object here and say that "max" should be "max absolute
> signal" or something, but it just isn't true.
No, what you did here is fine, and correct. "max" as you have used it here
IS the max absolute signal, since maximum signal level is 2, and minimum
signal level is 0, the max signal as you are using it IS 2. What you did in
"CASE 1" is just plain wrong.
> There is no range involved
> in that figure of "max", it is just a level.
That's fine. I never said there is a "range involved", the over all signal
range IS what is used for your term "max".
> There is no
> justification for
> using this difference,
But it doesn't matter if you do or don't, IF you use the equation correctly
that is.
> and it is not supported or mentioned in tests.
Er, huh??? Tests???
> It
> also gives you the wrong answer!!!
It ONLY gives you the wrong answer if you MISAPPLY it...as you did.
> Heck, please take a moment to think
> about this.Take a look at the books, the numerator in this equation is NOT
> a range, it is a straightforward level.
Well, it is DERIVED from a range. Look at the diagram I provided. It
CLEARLY shows how it is derived from a range. I hardly believe that's
difficult to understand!
> The dynamic range is the ratio
> between two levels, that's all it is. It is not a ratio between a range
> and a level.
Correct, I never said any differently, but (largest signal level - smallest
signal level) GIVES you a level, NOT a range. It's called "equivalence", a
mathematical principle, I am sure, you easily understand.
> The DR in this example is definitely 20, and not 19.
You are correct, and I agree, but the equation I've shown ALSO give you 20,
if you USE IT RIGHT.
> I don't know how to get you to accept that your calculation of DR is
> incorrect, but here's three attempts.
Well, because the equation for DR that I've used IS ABSOLUTELY CORRECT, it's
YOUR misuse of it that is NOT correct. MY use of it matches what you claim
is the correct answer. Funny that is.
> First,
> ******
> I'd say please read the book definitions critically. Look at the
> definition of DR and see that they are NOT saying that the numerator is
> something minus something else. They say, exactly, that the numerator is
> the "largest signal". This is NOT the largest signal minus the smallest
> signal, it is just the largest signal.
HEAVY SIGH. Are YOU saying there is a difference between what YOU call
"largest signal" and the term "(maximum signal level - minimum signal
level)"???? BECAUSE THERE IS NOT.
> Using the second of the above
> examples (2V, 100mV, AC), if you had a meter, you'd stick it on the output
> and read 2V when the thing was limiting. That's what you'd read, and
> that's what you'd put as the numerator of the equation. If you
> removed the
> signal source so you were looking at noise on the output, you'd
> read 100mV,
> and that's what you'd put as the denominator. It is really that simple.
It IS simple. So far, you appear to be in complete agreement with
everything I've said, except for some reason, you are having trouble with
the mathematical concept of equivalence...
> Elsewhere you say:
> >Absolutely not, as it is wrong. You are confusing the absolute largest
> >signal (as in //, like absolute numbers) with highest signal level. The
> >"largest" signal (as in absolute) is (max measured signal - minimum
> >measured) signal or 10-2 or 8.
>
> No!!! This "absolute largest signal" is TOTALLY your creation.
Sorry, it's EXACTLY the same thing YOU are calling "largest signal". And
"largest signal" IS an ambiguous term. It can mean two entirely different
things...the highest "voltage" a signal reaches, OR the largest amplitude a
signal reaches. They ARE two different things.
> Here again is the formula (YOUR QUOTE) you are referring to:
> DR (dB) = 10log10(largest signal/smallest discernable signal)
>
> I am not confusing highest signal level with "absolute largest signal",
> simply because I'm not even MENTIONING "absolute largest signal"! I don't
> even consider "absolute largest signal" and neither does the
> formula. There is no need to put it anywhere, to write it down, think
> about it, or to consider it in any way. This "absolute largest signal" is
> your creation which you require to get rid of offsets, but you do NOT need
> to use it even for DC offset situations, and you CERTAINLY don't
> need it in
> AC situations where it is not just wrong, it is meaningless - and
> confusing.
Well, again the term YOU use "largest signal" is entirely ambiguous. I have
had to come up with unambiguous terms to try to explain this VERY simple
concept to people who have misunderstood dynamic range because ambiguous
terms have been used.
> The "largest signal" in the definition
> is just that - the largest signal, or what you called "max measured
> signal".
But again, BOTH terms are ambiguous there. Whether you LIKE my terms or
not, I have defined them COMPLETELY, and there should be NO mistake as to
their meaning. If YOU want to define your own set of terms, please do...but
using terms that are ambiguous is not going to get anyone anywhere.
> I know that this does not agree with your thinking because this
> interpretation does not give the same answer as your own personal formula
> does.
Well, funny enough, as shown above quite a few times, "my thinking" gives
the exact same result (WHEN APPLIED CORRECTLY and not misused by changing
the meaning of the terms), as YOUR "understanding".
> The problem is with your own
> formula.
The problem is with your MISUSE of the formula.
> As a cross check - another reference of **YOURS** defines DR in the
> following terms: DR = "maximum level RMS" / "noise level RMS". (see the
> actual formula at
> http://members.austarmetro.com.au/~julian/filmscanners/filmscanners). In
> this case too, the maximum level is just what it says, it is NOT a
> difference between two levels.
Again, why is this now an issue, as it is a COMPLETELY IRRELEVANT issue,
unless you really don't believe the simple principle of equivalence...that
the "difference between the two levels" and the "maximum level" are EXACTLY
the same thing the way we are using it. I've said this all along, and you
are now harping on it for what reason I can not fathom! As I said, either
term works, and which ever is used is simply irrelevant.
> The only
> answer is -
> to make the book definition of DR fit with your personal definition.
Well, my understanding AND definition AND everything I've said, completely
agrees with the reference books I've cited AND the ISO proposal, so I fail
to see how this is "my" personal definition. I have ALSO discussed the ISO
dynamic range use, and shown that it COMPLETELY agrees with what I've said.
I'm simply snipping the rest because if you apply the DR formula the way it
was STATED, DEFINED and INTENDED, it matches your accepted understanding.
So, I do not see this as an issue any more.
It appears that there is only one issue that we do not agree on and that is
that (maximum signal level - minimum signal level) is the same as what you
call "largest", and since it just simply is, I believe we are now in
complete agreement.
As far as this goes:
> As a PS I need to say that I only introduced min discernable signals that
> were different from noise in yesterday's post to accommodate what I
thought
> you were saying. I agree that almost always min discernable signal and
> noise are the same thing and everything I have said today assumes min disc
> signal = noise. It *IS* in fact perfectly possible for a device to have
a
> different noise from it's smallest discernable signal,
I agree. I also believe that for the purposes of our discussion, as we
agree on this, that using "noise" and "smallest discernable signal"
interchangeably works for both of us.
Austin
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