Hi Julian,
> Previously you promoted a definition of Dynamic Range by saying:
> "the Dynamic Range equation out of "Digital Signal Processing in VLSI":
> DR (dB) = 10log10(largest signal/smallest discernable signal) " ..Eq(1)
>
> I have called this ... Equation(1) or Eq(1)]
>
> You quoted this, and you agreed with it. I too agree with this and it is
> standard in textbooks.
>
> 1) Do you still agree with this?
Of course.
> Removing the logs we get
>
> DR (ratio) = largest signal/smallest discernable signal ...Eq(2)
>
> 2) Do you agree with Eq(2)?
I tend to use that for shorthand, but it makes some assumptions...as you
said, it's not in log form, and therefore can't be treated as such.
> We were subsequently discussing a little example as follows:
>
> >Julian: This example system for some reason has a noise of 1V,
> a smallest
> >discernable signal of 2V and a largest signal of 10V.
>
> You often tell me that noise and smallest discernable signal are not
> necessarily the same thing and I agree with you.
No, that is a misinterpretation of what I said. I have said that the
smallest signal level and noise are not the same thing. The smallest
discernable signal and noise ARE the same thing. What you mean is "smallest
signal" or "smallest signal level" or whatever you want to call it, is 2V,
NOT "smallest discernable signal", as you have already defined noise as
being 1V, so you are using two terms that mean the same thing and assigning
them two different numbers.
> In this example they are
> different to make clear the distinction between all these values.
>
> Now, could you please substitute the relevant figures from our
> example into
> Eq(2)?
>
> I'll do it here:
> DR = largest signal/smallest discernable signal
> = 10/2
> = 5
>
> That is, the dynamic range of our example system is 5.
>
> 3) Do you agree with this?
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.
You are also confusing "smallest DISCERNABLE signal" with "smallest signal
level"..as you are using the "smallest MESURABLE signal" where you should be
using noise (and noise IS the same thing as smallest discernable signal).
Your proper numeric equation should be:
DR = (8-2)/1 or 8.
> In responding to this example in a previous post, you said:
>
> Austin:
> >DR = ((max - min) / noise)
> >The absolute range is 10-2.
> >so... (10 - 2) / 1 or 8 is the dynamic range.
>
> You calculated a dynamic range for the same example of 8.
>
> 4) Do you agree that 8 is different from 5?
Of course.
> Your new equation for Dynamic Range that you used here is:
>
> DR = ((max - min) / noise) ...Eq(3)
>
> 5) Do you still agree with this?
I don't know why you call it new....but that's the correct equation for DR,
and it can be differently written substituting a single term "maximum
absolute signal" for "(max - min)".
> 6) Do you agree that Eq(2) and Eq(3) are different?
No, what is different is YOUR interpretation of the terms. The dynamic
range equation even as ISO has used them COMPLETELY agree with my use of the
terms. Your equation (2) does NOT use noise, yet all the definitions of
dynamic range (ISO included) include noise...
> 7) If you agree they are different, then this explains why you say the
> example dynamic range is 8 and the definition that is used by everybody
> else uses gives a dynamic range of 5. And thus you are agreeing that you
> are using a non-standard definition of dynamic range.
Well, no. It's the interpretation of the TERMS in your equation that is
non-standard. My use of terms IS the standard.
> 8) If you do not think they are different, will you please rewrite Eq(3)
> using the terminology that is used in Equation (2) - that is, rewrite your
> equation (3) in terms of the two quantities "largest signal" and "smallest
> discernable signal"? Do you agree this cannot be done?
Again, it's YOUR believing "largest signal" means the highest level the
signal achieves, when it REALLY means the overall absolute range of the
signal, and that "smallest discernable signal" is the minimum level the
signal achieves, when that term really means noise.
> 9) Do you agree that the definition of dynamic range in the book (Eq(1))
> does NOT contain any mention of value "noise"?
No, I do not agree. "smallest discernable signal" IS noise. See the
diagram I provided that clearly shows this:
> 10) Do you agree that your personal definition of dynamic range (Eq(3))
> DOES contain the value "noise"?
It is NOT my "personal definition" of dynamic range. THE equation for
dynamic range IS based on noise, and all respectable references HAVE said
exactly that.
> 11) Do you agree that the definition of dynamic range in the book (Eq(1))
> means that Dynamic Range is, in the general case, independent of noise?
No.
> 12) Do you agree that your definition (Eq(3)) is always dependent
> on noise?
I agree that THE equation for dynamic range IS ALWAYS based on noise.
> 13) Do you agree that your definition (Eq(3)) is quite different from the
> book definition?
Again, no. It is YOUR interpretation of the terms that is incorrect, if you
interpret them correctly, then it would come out to the same thing.
> I look forward to your response which must surely flush out where and why
> we have this very fundamental difference.
It is VERY easy to show your interpretation of terms simply makes NO sense:
Largest signal - 100V
Smallest signal - 98V
Overall range 2V
By your interpretation of terms, the dynamic range would be 100/98 or 1.02.
Largest signal - 3V
Smallest signal - 1V
Overall range 2V
Again, by your interpretation of terms, the dynamic range would be 3/1 or 3
How can that be? They both have the SAME overall range of 2...one is simply
offset by 97V.... They SHOULD have the exact same dynamic range, why not?
Again, they are BOTH of the same overall range, merely offset...and offset
should not effect dynamic range, as it is merely an offset...and if you
believe offset should, then please explain of what use that would be?
IMO, your interpretation of terms provide a conclusion that is simply not
useful, and the terms as I have used them DO provide VERY useful information
about the characteristic of a signal.
Austin
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