Dynamic Range and Noise floor question.

you aren't necessarily missing anything... a lot of folks, manufacturers included, have made a real mess of specifications!

Noise level - that's meaningless without a specified bandwidth, although at least they told you they were using a filter (A-weighting). We also do not know how the device under test is configured, but that's a separate gripe<G>!
 
Dynamic Range - again, there isn't enough information here - dynamic range with respect to what?
 
So let's guess that their noise floor number is just that - wide band noise passed through an A-weighting filter. And we'll also guess that the dynamic range is with respect to the noise floor - which is not entirely valid, but it's all we got. So that means that that the device distorts 112.5 dB above the noise floor, which would be a pretty bad specification if it were qualified. But we don't know if they are talking about dBu or dBV or dBFS or dBwtf<G>!
 
There are so many characteristics, and I think you need to know them all in order to understand what they are trying to tell (sell) you...
 
You need to know if measurements are made in the analog or digital domain.
You need to know the nominal operating level - 0VU = +4 dBu for example.
You need to know the maximum operating level, and exactly how it was determined.
You need to know what the noise floor sounds like - is it equal energy across some specified bandpass?
 
Then you need to define S/N or dynamic range...
 
S/N ratio is usually the difference between the nominal operating level and the noise floor at a specified frequency or frequencies. Sometimes it is taken as the difference between a single tone at nominal operating level and the total noise across the band pass.
 
Dynamic range is the actual usable range, and it extends from some maximum operating level (3% THD used to be the magic number, but it is difficult to reach that anymore, so usually the designer will simply measure the THD when the signal swings from rail to rail) to somewhere at, or maybe even below the noise floor, because it turns out we can hear stuff even if it is in the soup.
 
All of this gets even muddier when working within the digital domain, where the maximum level is 0 dBFS because, well, because you can't exceed "all ones". The problem is that too many chip and device designers just assume that if they have x bits they have 2^x bits of dynamic range... and that is not always true.
 
It gets even uglier, since dB is, by definition, an RMS measurement, and digital measurements are, again by definition, peak measurements. So there is some additional math required to make sense of that...

There is are excellent application notes on specifications at the Rane and Audio Precision web sites, among others. I'd suggest a little time with your favorite browser to help clear this up.
 
I spent the entire evening fighting with my computer, so if this is all a bit fuzzy let me know and I'll try to clear it up.

if you are measuring the instantaneous value, e.g. the value if a single sample, then it is a peak measurement, even if it is not the peak value... which I know sounds ridiculous, but it is what we have to work with<G>. It is, of course, possible to make RMS or even average measurements, over time, but so few people seem patient enough to wait<G>!!

wst3
if you are measuring the instantaneous value, e.g. the value if a single sample, then it is a peak measurement, even if it is not the peak value

 
You can't have a "peak" unless you are comparing it to something. And if you want to compare it to itself, then it's also the minimum - and the average. 
 
And measuring the difference between samples is not a peak measurement unless you deliberately choose samples to result in a peak. I think the confusion is that digital measurements are very often taken this way whereas this is not the case in analog.
 
And of course in the real world, the "instantaneous" sample value we are considering will often be the result of doing calculations using a number of values measured over time at a lower bit depth and a higher sample rate. But that isn't particularly important, as the result still can be regarded as an instantaneous measurement (even if it wasn't measured that way).
 
 
 
The point is to understand exactly what a specification refers to. 

mike_mccue
 
Does a spec like this make sense?
 
Noise level, dB (A): -114.9
Dynamic range, dB (A): 112.5
 
I'm having trouble imagining how a device's noise floor can be measured beyond the device's dynamic range.
 
Maybe I'm missing something?
 
Thanks.
 
 
The loop includes the analog output and input stage, but presumably the measurements are being made in the digital domain, and I assume involve comparing the original digital data that is fed to the DAC to the resulting digital data that is collected after the return through the ADC.

Without knowing exactly what or how they're measuring it's hard to know, but assuming they are using RMS measurements and measuring the noise with no signal present relative to 0 dBFS and using a sine wave to test the DR, the maximum digital sine wave equals -3 dBFS RMS, which would put the DR at a 3dB disadvantage, no?

mike_mccue
I had thought about that as a possibility. I guess I've been imagining dynamic range in a digital domain as being an absolute limit and so imagined that a noise floor would be lower than 0dBFS by a fraction of the possible range between *digital silence* and full splat.
 
For example; If a CD player has a theoretical or potential range of 98dB I'd expect to find that the noise floor of the appliance was something like 80dB below full output. That's just a *from the hip* expectation but it leaves me wondering how a spec such as I listed in the OP can seem descriptive of what a user will experience.

Not sure how you're getting 80dB there.
 
Assuming no dither, noise shaping or weighting and ignoring any analog noise in the converter, the average quantization error should be within ~3dB of the LSB.
 
If you are taking a weighted measurement, the result will be lower as a portion of the noise will be attenuated by the weighting filter. And if you add noise shaping, the noise shaping will move most of the noise where the weighting filter will attenuate it.

My (overly simplistic) view:
Any piece with a noise-floor of -115dB is pretty darn quiet.
As a result, I'd expect it to have pretty wide dynamic range.

drewfx1You can't have a "peak" unless you are comparing it to something. And if you want to compare it to itself, then it's also the minimum - and the average. 

Not trying to be difficult, but can you explain that please? As far as I know it is absolutely possible to make peak, average and RMS measurements without comparing it to anything other than the scale (e.g. volts, spl, etc). And if you compare it to itself then what's the point? I'm really missing something in your statment...
 

drewfx1And measuring the difference between samples is not a peak measurement unless you deliberately choose samples to result in a peak. I think the confusion is that digital measurements are very often taken this way whereas this is not the case in analog.

 
There are differences in measurement techniques between the analog and digital domains. But I"m not sure what that has to do with measuring the difference between samples, or why that would be considered a peak measurement.
 

drewfx1And of course in the real world, the "instantaneous" sample value we are considering will often be the result of doing calculations using a number of values measured over time at a lower bit depth and a higher sample rate. But that isn't particularly important, as the result still can be regarded as an instantaneous measurement (even if it wasn't measured that way).

 
So I am definitely missing something here... please elaborate. To me any given sample is an instantaneous value, that is what sampling is all about... measuring the instantaneous value at time "t". Bit depth and sample rate have nothing to do with the level, except that for a given word length there will be a finite number of possible values.
 

drewfx1The point is to understand exactly what a specification refers to.

Well this is certainly true! And probably the biggest stumbling block the audio and MI marketplaces face.

wst3

drewfx1You can't have a "peak" unless you are comparing it to something. And if you want to compare it to itself, then it's also the minimum - and the average. 

Not trying to be difficult, but can you explain that please? As far as I know it is absolutely possible to make peak, average and RMS measurements without comparing it to anything other than the scale (e.g. volts, spl, etc). And if you compare it to itself then what's the point? I'm really missing something in your statment...

 
Peak implies "highest" or "maximum", no? "Highest" compared to what? Simple as that. 
 

 

drewfx1And measuring the difference between samples is not a peak measurement unless you deliberately choose samples to result in a peak. I think the confusion is that digital measurements are very often taken this way whereas this is not the case in analog.

 
There are differences in measurement techniques between the analog and digital domains. But I"m not sure what that has to do with measuring the difference between samples, or why that would be considered a peak measurement.
 

 
I didn't really write what I was getting after very well.
 
In digital, when we are talking about a "peak" we are generally referring to the highest (positive or negative) valued sample compared to all the other samples in the period of interest. Is there any other definition of "peak"?
 

drewfx1And of course in the real world, the "instantaneous" sample value we are considering will often be the result of doing calculations using a number of values measured over time at a lower bit depth and a higher sample rate. But that isn't particularly important, as the result still can be regarded as an instantaneous measurement (even if it wasn't measured that way).

 
So I am definitely missing something here... please elaborate. To me any given sample is an instantaneous value, that is what sampling is all about... measuring the instantaneous value at time "t". Bit depth and sample rate have nothing to do with the level, except that for a given word length there will be a finite number of possible values.

 
OK, say our ADC is outputting 24 bits at 48kHz. Given that oversampling - often at a higher rate and a lower bit depth - is common, that means our instantaneous sample value output by the ADC at 48kHz at time "t" is a calculated value based on the values of many samples over a period of time - perhaps a thousand samples or more. The point is that the calculation does not involve taking the peak value of all the input samples, so why would we call it a peak measurement?
 
 
It's not a big deal. I just don't understand why you would want to call each sample a peak measurement.

drewfx1Peak implies "highest" or "maximum", no? "Highest" compared to what? Simple as that.  

I think you are mixing domains a bit here, and that leads to poor use of terms, which can lead to confusion.
 
Peak voltage refers to either the maximum point in a periodic waveform over one cycle, or the maximum voltage of a non-periodic waveform over some defined period of time. These are definitions that are agreed upon by standards bodies, much like the SI measurement system. Sure, there are folks that try to re-use them for other purposes, but that leads to confusion. In both cases there is no reference, the comparison is to all other values during the measurement period.
 
Chief amongst the points of confusion is the fact that when you start making measurements in the digital domain you have so many new possibilities!!! I mean you have the whole dang thing stored for starters!! It's almost enough to make one's head spin.
 
For example, in the analog domain the common ways to measure distortion involve either the use of a really sharp filter to remove the excitation, or a swept filter. Neither of these involves storage because, historically, about the best we could do for analog storage was a long persistence phosphor<G> (and yeah, they were fun to read! Towards the end of the analog era there were instruments that combined really sharp band stop filters with really sharp band pass filters that were adaptive, but mere mortals could not, generally, afford such toys.
 
Once we have digitized the signal it becomes a simple matter of math. You want total harmonic distortion, or would you like to break it down by harmonics? And trust me, the latter is far more informative if you are designing or troubleshooting.

drewfx1In digital, when we are talking about a "peak" we are generally referring to the highest (positive or negative) valued sample compared to all the other samples in the period of interest. Is there any other definition of "peak"?

 
Which is pretty much what I said. There is no reference other than the measurement period.
 

drewfx1OK, say our ADC is outputting 24 bits at 48kHz. Given that oversampling - often at a higher rate and a lower bit depth - is common, that means our instantaneous sample value output by the ADC at 48kHz at time "t" is a calculated value based on the values of many samples over a period of time - perhaps a thousand samples or more. The point is that the calculation does not involve taking the peak value of all the input samples, so why would we call it a peak measurement?

 
We call it a peak measurement because we simply do not care about the calculations. We care about the word as presented to the DAC, or the word generated by the ADC. You are right about over sampling, and single bit converters, but these things do not matter with respect to audio specifications. Audio is analog, and it always will be as along as our ears are analog. (OK, our ears are not analog, but we treat them as such because there is so much we still don't understand about the ear-brain system... but that's drifting way far off track!)
 
We care about a LOT of different things when it comes to audio, I didn't even bring up crest factor, for example, because that tends to cause even more confusion. Crest factor is defined as the peak to average ratio of a periodic waveform, but we use it to describe pink and white noise sources all the time. These are supposed to be random, which kind of kills the whole periodic bit, except that they are not random at all. They can be generated from a semiconductor junction, or even a resistor, but over time we discover that even these are not truly random. Forget about MLS based noise generators, they can't be random... but all of these can be random enough for use as excitation signals for audio tests. And we can, if we are very careful, talk about the crest factor of the noise source. We have to if we want to characterize an audio system.
 
And that's the last piece of the puzzle - are we looking at a component, a circuit, or a system? And are we talking about analog or digital or both?
 

drewfx1It's not a big deal. I just don't understand why you would want to call each sample a peak measurement.

Actually, it is a big deal. There is a remarkable amount of misinformation out there. Some of it is well meaning, some of it is meant to mislead consumers. All of it makes it that much more difficult for the good guys to develop and provide high quality devices and systems.
 
If that makes any sense...

Jeff - good point, and in fact the dynamic range of an audio recording, or performance, is a very different thing.
 
But Mike's original question was specifically about a device specification!
 
Specifically, he asked if the following made any sense:
Noise level, dB (A): -114.9
Dynamic range, dB (A): 112.5
 
And in fact it doesn't, this is a silly, and meaningless specification because it does not provide enough information.
 
We can guess all day long, and the most reasonable guess is that the noise floor, across the usable bandwidth of the device, is 114.9 dB below some specific reference level, sadly we do not know what that level is.
Further, we can guess that the clipping point (also not specified) is 112.5 dB above that noise floor, but we don't know whether it was measured at a single frequency or across the entire usable bandwidth.
 
In this case, if the noise level is measured with respect to the nominal operating level then the clipping point falls somewhere below the nominal operating level - that would be pretty bad!
 
If, instead, the specification is using full scale output as the reference then the clipping point occurs approximately 2.4 dB below 0dBFS, which is still bad, but I've certainly run across designs that clip in the analog domain before they clip in the digital domain.
 
And, in fact it really makes no difference whatsoever how narrow or wide the dynamic range of a performance or recording might be if the equipment can not handle it! So I guess I think it is important to measure the medium. I've certainly attended more than enough live performances that far outstrip the capabilities of all but the very best recording chains in terms of dynamic range, so if I were recording such a performance I'd want to know what the medium is really capable of.
 
It really is not sufficient to say that a converter chip has 24 bits of resolution - some of the lowest order bits are going to be in the noise floor, and therefore of no real use to anyone. And, as in the example Mike provided, if the upper most bits cause the analog circuit to clip, well, then they aren't much use either.
 
Poor use of terminology only serves the marketers!
 
OK, rant over, time to go back to yard work...