Re: Re: Re: ...Yes M'Lud, the evidence...
No, we don't have half the bits for plus and half the bits for minus. We have half the quantization levels for the plus and half the quantization levels for minus. Since the quantization is 16 bits, the total quantization levels is 2<sup>16</sup> or 65,536 which gives us 32,768 levels for positive and 32,768 levels for negative.
And we have a dynamic range of 96dB peak-to-peak AND 96dB peak.
Again, the maximum quantization error will be 1/2LSB. So we have a 1/2LSB error for postitive and 1/2LSB for negative.
So if you're looking at just the peak value, the dynamic range is determined by 1/2LSB. So 32,768/0.5 = 65,536. 20 x log 65,536 = 96dB.
If you're looking at the peak-to-peak values, the dynamic range is determined by 1LSB. So 65,536/1 = 65,536. 20 x log 65,536 = 96dB.
It's no different than if you're comparing the relative levels of two sinewaves. If you're referencing the peak value of one sine wave, you have to calculate based on the peak value of the other. If you're using the peak-to-peak value of one sinewave, you have to calculate based on the peak-to-peak value of the other. If you're using the RMS value of one sinewave, you have to calculate based on the RMS value of the other.
And when you do this, the ratios remain the same and the result remains the same.
The tried and true definition of dynamic range has been the ratio of the noise level to the maximum signal level. This definition works just as well for analogue as well as digital systems.
Sure.
In audio, the dynamic range is expressed as the ratio of the noise level to the maximum signal level.
In the digital domain, the noise level is determined by the quantization error. Which again will be no greater than 1/2LSB either plus or minus.
If it makes one feel better to call it "noise" in the analogue domain and "error" in the digital domain, fine. But you're still effectively talking about the same thing.
And I've already explained why the peak-to-peak 90dB figure is incorrect so no need to repeat it here.
se
UGH! When are they going to get the HTML tags working again?
MBK said:
No, we don't have half the bits for plus and half the bits for minus. We have half the quantization levels for the plus and half the quantization levels for minus. Since the quantization is 16 bits, the total quantization levels is 2<sup>16</sup> or 65,536 which gives us 32,768 levels for positive and 32,768 levels for negative.
And we have a dynamic range of 96dB peak-to-peak AND 96dB peak.
Again, the maximum quantization error will be 1/2LSB. So we have a 1/2LSB error for postitive and 1/2LSB for negative.
So if you're looking at just the peak value, the dynamic range is determined by 1/2LSB. So 32,768/0.5 = 65,536. 20 x log 65,536 = 96dB.
If you're looking at the peak-to-peak values, the dynamic range is determined by 1LSB. So 65,536/1 = 65,536. 20 x log 65,536 = 96dB.
It's no different than if you're comparing the relative levels of two sinewaves. If you're referencing the peak value of one sine wave, you have to calculate based on the peak value of the other. If you're using the peak-to-peak value of one sinewave, you have to calculate based on the peak-to-peak value of the other. If you're using the RMS value of one sinewave, you have to calculate based on the RMS value of the other.
And when you do this, the ratios remain the same and the result remains the same.
The tried and true definition of dynamic range has been the ratio of the noise level to the maximum signal level. This definition works just as well for analogue as well as digital systems.
Sure.
In audio, the dynamic range is expressed as the ratio of the noise level to the maximum signal level.
In the digital domain, the noise level is determined by the quantization error. Which again will be no greater than 1/2LSB either plus or minus.
If it makes one feel better to call it "noise" in the analogue domain and "error" in the digital domain, fine. But you're still effectively talking about the same thing.
And I've already explained why the peak-to-peak 90dB figure is incorrect so no need to repeat it here.
se
UGH! When are they going to get the HTML tags working again?
MBK, I was implicitly referring to my previous post where I
explained to Fred that he was making the mistake of thinking
that one bit can go both positive and negative from a certain
value (presumably called 0). I then saw that you made the
same mistake in your argument and tried to point that out
in a (possibly/hopefully) humorous way. Of course, it was
a bit stupid of me, perhaps, to assume that you had read
that previous post of mine.
BTW, what do you think of the Zobels now after a few days?
explained to Fred that he was making the mistake of thinking
that one bit can go both positive and negative from a certain
value (presumably called 0). I then saw that you made the
same mistake in your argument and tried to point that out
in a (possibly/hopefully) humorous way. Of course, it was
a bit stupid of me, perhaps, to assume that you had read
that previous post of mine.
BTW, what do you think of the Zobels now after a few days?
MBK: Not my definition, the standard one, the ratio between the largest and smallest encodable signals. I'm sure Steve or Christer or someone else with an electronics library to hand will be happy to give you an exact quote. I think that your difficulty is that you inappropriately ascribe something special about the 0 volt level. That's an easy trap to fall into (believe me, I know!) and a harder trap to get out of.
Say this slowly, three times:
The system is not constrained to be symmetric about a particular value. All values are equally valid.
Say this slowly, three times:
The system is not constrained to be symmetric about a particular value. All values are equally valid.
Don't know if it helps anybody but one of the things that have
bothered me a little, but which I finally managed to answer
myself is that it was not obvoius to me that it is fair to think
of the quantization error as a noise floor in the same sense
as for analog, since if we have no input we have no quantization
error and hence noise exists only when a signal is present.
(Do I get the prize for longest sentence of the day?
).
However, this was obviously wrong, in retrospect, since that
presumes we know if there is a signal or not. If all the data is
zero, we actually cannot know if this is because there is no
signal (well, 0V DC is a signal too, in a sense) present, or if
there is a very low level signal that just happens to be
lost in quantization error. That is, there is no observable
difference, so the quantization error is the noise floor even
when no signal is present.
bothered me a little, but which I finally managed to answer
myself is that it was not obvoius to me that it is fair to think
of the quantization error as a noise floor in the same sense
as for analog, since if we have no input we have no quantization
error and hence noise exists only when a signal is present.
(Do I get the prize for longest sentence of the day?
).However, this was obviously wrong, in retrospect, since that
presumes we know if there is a signal or not. If all the data is
zero, we actually cannot know if this is because there is no
signal (well, 0V DC is a signal too, in a sense) present, or if
there is a very low level signal that just happens to be
lost in quantization error. That is, there is no observable
difference, so the quantization error is the noise floor even
when no signal is present.
Christer,
no offended, was just confused.
Actually I wasn't toggling the bit between -1 and +1 for a third dimension but assuming just one-zero. But my error was that I introduced the reference value at ground, but only for the maximum signal level, not for the minimum level. I think I got it now.
Zobels: Ha! Yet again the KISS principle strikes. The Zobels did improve the sound but maybe 2/3 of the disturbance remained. Today I now found that I had made an illogical grounding path in my chip amps. This created a ground loop which previously didn't matter since all paths are short im my amp ... but... but ... some weeks ago I added an output resistor to signal ground of my dipole EQ (to get balanced output impedances). I found out by chance of course. And as a result the signal return promptly must have gone to power ground. I believe this created the main fuzz in the system but I can't test before tomorrow (neighbors, police, blah blah .
). That explains of course why headphones sounded much better...
Conclusion, never touch a running system.
no offended, was just confused.
Actually I wasn't toggling the bit between -1 and +1 for a third dimension
but assuming just one-zero. But my error was that I introduced the reference value at ground, but only for the maximum signal level, not for the minimum level. I think I got it now.Zobels: Ha! Yet again the KISS principle strikes. The Zobels did improve the sound but maybe 2/3 of the disturbance remained. Today I now found that I had made an illogical grounding path in my chip amps. This created a ground loop which previously didn't matter since all paths are short im my amp ... but... but ... some weeks ago I added an output resistor to signal ground of my dipole EQ (to get balanced output impedances). I found out by chance of course. And as a result the signal return promptly must have gone to power ground. I believe this created the main fuzz in the system but I can't test before tomorrow (neighbors, police, blah blah .
). That explains of course why headphones sounded much better...Conclusion, never touch a running system.
MBK said:Zobels: Ha! Yet again the KISS principle strikes. The Zobels did improve the sound but maybe 2/3 of the disturbance remained. Today I now found that I had made an illogical grounding path in my chip amps. This created a ground loop which previously didn't matter since all paths are short im my amp ... but... but ... some weeks ago I added an output resistor to signal ground of my dipole EQ (to get balanced output impedances). I found out by chance of course. And as a result the signal return promptly must have gone to power ground. I believe this created the main fuzz in the system but I can't test before tomorrow (neighbors, police, blah blah .
Conclusion, never touch a running system.
Good to hear. So whether real improvement or imagined, it
was a cheap and easy tweak that was interesting to try.
Now if only some more people with possible RFI problems
would try it, to see if there seems to be some correlation in
the results. Well, this is getting off-topic, so that's it for now,
I guess.
Hi kids. This flamefest is roaring along nicely. And none of you need worry about my educational background. "I was born a poor black child."
I don't think there is any fundamental disagreement here. If the minimum signal is +1-to-0, the dynamic range is 96dB, and if it is +1/-1, it is 90dB.
I'd have to ask how you got a 1/0 signal out of an AC-coupled ADC, but that's not my line of business.
I don't think there is any fundamental disagreement here. If the minimum signal is +1-to-0, the dynamic range is 96dB, and if it is +1/-1, it is 90dB.
I'd have to ask how you got a 1/0 signal out of an AC-coupled ADC, but that's not my line of business.
Hi,
Si senor.
And you'll find that the entire archive has also taken on the current state.
Better safe than sorry but it's a PITA.
LOOK HERE FOR THE WHY.
Cheers,
Si senor.
And you'll find that the entire archive has also taken on the current state.
Better safe than sorry but it's a PITA.
LOOK HERE FOR THE WHY.
Cheers,
Christer said:Don't know if it helps anybody but one of the things that have
bothered me a little, but which I finally managed to answer
myself is that it was not obvoius to me that it is fair to think
of the quantization error as a noise floor in the same sense
as for analog, since if we have no input we have no quantization
error and hence noise exists only when a signal is present.
(Do I get the prize for longest sentence of the day?
However, this was obviously wrong, in retrospect, since that
presumes we know if there is a signal or not. If all the data is
zero, we actually cannot know if this is because there is no
signal (well, 0V DC is a signal too, in a sense) present, or if
there is a very low level signal that just happens to be
lost in quantization error. That is, there is no observable
difference, so the quantization error is the noise floor even
when no signal is present.
Yes.
But the salient point to this discussion, which goes back to Kuei's original claim that nothing below -90.3dB can be recorded, is that any signal that's equal to or greater than 1/2LSB (or +/-1/2LSB for bipolar encoding) DOES get recorded. And the error between the signal's actual value and its quantized value is effectively the "noise" which can be no greater than +/-1/2LSB which gives us a 96dB dynamic range.
se
SY said:
Please enlighten me. I am not well-read up on the topic, really.
My, hopefully correct and reasonable, explanation was merely
meant for those, who like, me do not know all the theory and
concepts in digital audio and related areas. Well, we did have
a course on time-discrete systems, but that was one the courses
I had the most difficulties with. Should probably reread that
book some day, or month, or year, or ...
Steve Eddy said:
Yes.
But the salient point to this discussion, which goes back to Kuei's original claim that nothing below -90.3dB can be recorded, is that any signal that's equal to or greater than 1/2LSB (or +/-1/2LSB for bipolar encoding) DOES get recorded. And the error between the signal's actual value and its quantized value is effectively the "noise" which can be no greater than +/-1/2LSB which gives us a 96dB dynamic range.
se
Seems you verified my reasoning, then. Good.
I didn't write it with intent of referring to kuei at all, I just
was somewhat puzzled before as to whether the
quantization error could really be thought of as a noise floor
in the usual sense, and assumed this might puzzle others too.
BTW, I still don't get it how kuei can get differenc dynamics
for peak and RMS values?
While discussing noise floors, as far as I understand, we do
have one fundamental difference between analog and digital
noise floors. In digital a signal essentially gets lost when it
gets under the noise floor (not taking statistics, dithering etc.
into account). In analogue, though, we can still have a signal
well down in the noise floor, which is to some extent recoverable,
given sufficient resolution of the analogue system, of course.
In a sense the signal modulates the noise, which is random
"data". However, I guess this is perhaps essentially no different
from making the various digital tricks of adding noise etc. to
make more information recoverable. Am I still reasonably on
track here?
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