The Myth Of Dynamic Range

ullanta

ullanta

Veteran
Hey, dudes! I'm tired of hearing about 24-bit audio having more dynamic range than 16-bit. Just went through the whole argument in the RED Camera section. I thought I'd move some of the pertinent details over here... Can we make this a sticky?

Basically, digital audio (except for a few exotic compression schemes) has a fixed dynamic range (from 0 to 1). From absolute silence to whatever clips. We determine the clipping point with gain/trim/padding.

The different bit depths determine RESOLUTION of that range. Now, the smallest discernable difference of sound levels (e.g., resolution) determines the smallest sound level representable. People are using "the smallest sound level representable" interchangably with "dynamic range". So, for 16 bits, the smallest sound representable is 1/65536 of 0dB (or, full scale, FS). 1/65536 of full scale is the same as -96dBFS.

Some math to compare 16 and 24 bit encoding of digital audio:

IN 16 BIT AUDIO - each "step" is 1/65536 of FS
---------------
20 * log (1/65536) = -96.3 dBFS
20 * log (2/65536) = -90.3 dBFS (1 "step" between -96 and -90 dB)

20 * log (32768/65536) = -6 dBFS
20 * log(65536/65536) = 0dBFS (32768 "steps" between -6 and 0 dB)


IN 24 BIT AUDIO each "step" is 1/16777216 * FS
---------------
20 * log(1/16777216) = -144.5 dBFS
20 * log(2/16777216) = -138.5 dBFS (1 "step" between -144 and -138 dB)

20 * log(256/16777216) = -96.3 dBFS
20 * log(512/16777216) = -90.3 dBFS (256 "steps" between -96 and -90 dB)

20 * log(8388608/16777216) = -6 dBFS
20 * log(16777216/16777216) = 0 dBFS (8388608 "steps" between -6 and 0 dB)


Resolution of 24 vs. 16 is 256 times greater throughout the range.

Remember the math. The decibel scale is logarithmic. The absolute size of a decibel relative to FS approaches 0 as the magnitude of the negative decibel numbers increases. So the six decibels between -144 and -138 dB represent a range that is about 16 million times smaller than the 6-decibel range between -6 and 0 dB.

It is ONLY the difference in resolution that extends the dynamic range! 16 bits can't provide the granularity to encode a factor of 16 million, so the smallest "step" possible is about -96dBFS. EVERY step from 0 to 65535 (or "full scale") is -96dBFS. In 24 bits, EVERY step is -144 dBFS. As the math shows, 65536 * -96dB = 1; and 16 million or so * -144 dB = 1. So every extra bit doubles the resolution, and in doing so allows representation of steps half as large. Thus, the smallest representable value becomes half as large - thus the 6dB extension of dynamic range. But that is the least-significant 6dB on the scale, and pretty tiny.

I think ysomeconfusion stems from the fixing of the top end of the scale at 0dB. These are negative logarithmic values. If numbers are positive, dynamic range does indeed double with every added bit. But as negative values, the amount of extra dynamic range (in linear terms) added by each new bit approaches 0. 24 bits gives 256 times the resolution of 16 bits. It increases dynamic range by 1/256 (-48 decibels). That is, dynamic range of 24 bits is about 1.018 times the dynamic range of 16 bits.

However, this isn't REALLY a difference in dynamic range at all. In digital audio, the smallest number is used for "-inf" (that is, basically, 0). The "dynamic range" discussed is the ratio between the smallest representable level and the highest. And all the systems can represent 0. So the range is fixed. What they are really talking about is not range but PRECISION... that is, how precisely can we specify very small values?

Now, practically, there are some benefits related to dynamic range. If we record at 16 bits, with average levels at -12, we're really using only 14 bits, and that can start becoming ugly due to the low resolution of the effective 14-bit data. With 24 bit sampling, we can leave a LOT of headroom (48dB) and still have the same resolution as 16-bit audio [though, of course, the noise floor would make such an extreme case problematic. Certainly leaving 20dB of headroom when necessary is a very useful]. So, in fact, the benefit of higher bit depth is to get more out of a SMALLER dynamic range (e.g., 0 to -20dBFS, what we're left with after leaving more headroom than we'd be happy with in a 16-bit system).

So... in conclusion, 24 bit provides for better recordings, but because of increased precision, NOT increased dynamic range:

1) The difference in dynamic range between 24 and 16 bits is tiny, because it's in dB on the least-significant end of the scale, way, way below the noise floor.

2) The difference in dynamic range isn't really a difference in dynamic range, since dynamic range is always 0 to 1.

3) In 24-bit recording, the practical benefit is in being able to get better sound using LESS dynamic range (more headroom)... not more!
 
Last edited:
So, since I have more headroom, don't I then have more dynamic range? I have a larger range to work my volume within?

Also, I can hear the difference between 16 bit and 24 bit, especially when recording sound FX, or dialogue that goes form soft to loud quickly. So, even though your post is very thorough, what really matters is real world application.

It's like when people start touting off specs on mics and recorders, and crap....that's all well and good, but how does it really work in the real world? That's what matters.

-Dave
 
Interesting - Good read.

Recording 24bit 48Khz isnt that much different from 16bit 48khz. But, you get an extra 10bits per sample (1/48000). When you are cramming analog information into any digital medium less bit compression is perferred. Thats why sound programs do 32bit float processing.

I remember reading that when you use 44Khz or 48Khz recording, something accounts for the real performance of the recording to represent half that number becoming 22Khz & 24Khz. Since human hearing is 20-20Khz this usually works. But for some types of sounds in the high freq, they can distort. Recording 24bit 96Khz is much better than 16bit 48Khz. And dont forget all the other AD/DA's, amps, electronics that are much better in a device that does 24bit 96Khz.
 
Dave_Fisk said:
So, since I have more headroom, don't I then have more dynamic range? I have a larger range to work my volume within?

** sort of depends on wfrom where you look (or listen). If you don't use the full dynamic range, (by allowing too much unused headroom) you're still down in the noise floor.

Also, I can hear the difference between 16 bit and 24 bit, especially when recording sound FX, or dialogue that goes form soft to loud quickly. So, even though your post is very thorough, what really matters is real world application.

It's like when people start touting off specs on mics and recorders, and crap....that's all well and good, but how does it really work in the real world? That's what matters.

-Dave
Click to expand...

** Right. 24-bit sounds better to me than 16-bit.

Regards,

Ty Ford
 
Dave_Fisk said:
So, since I have more headroom, don't I then have more dynamic range? I have a larger range to work my volume within?

Also, I can hear the difference between 16 bit and 24 bit, especially when recording sound FX, or dialogue that goes form soft to loud quickly. So, even though your post is very thorough, what really matters is real world application.

It's like when people start touting off specs on mics and recorders, and crap....that's all well and good, but how does it really work in the real world? That's what matters.

-Dave
Click to expand...

I'm not arguing against 24 bit recording, Dave! (and Ty!) I highly recommend it. It's better. It's just that it's not more dynamic range that's the benefit. It's more precision. The extra "dynamic range" itself is not a great benefit since it's below -96dB... well, well, below the noise floor.

As for headroom - it comes OUT of the 0 to 1 range of digital audio. Headroom is "the unused portion of the dynamic range you leave for emergencies".... so the more headroom you leave, the less dynamic range you're planning to use. That is, if you leave 12 dB of headroom, that's 12dB you're hoping not to use, right?

Now, in preamp terminology, headroom is something different... it's how much over a nominal signal level the preamp can take before distorting, and indeed extends the dynamic range of acceptable input signals. But in the digital realm, there's nothing above 0dBFS, and headroom has to be cut out from under there.
 
Last edited:
As I understood it you can record at a genuine -20 db if you're in 24 bit and bring it up to the desired level cleanly... and trying the same thing at 16 bit just doesn't work without introducing a lot of noise. I think I've been incorrectly calling this increased dynamic range... although in practical use I don't know exactly what else to call it. I think if I said it was increased resolution that most guys wouldn't get a handle on the point I'm trying to make. Analog recordings can usually be cleanest at the lowest levels... lower input signal usually means lower noise through the analog chain... digital wants the highest levels just short of clipping. Isn't that correct? So when one system of digital recording allows me to utilize an extra 20db of usable "dynamic" range... what does that mean?

I read the explanation and it's great in scientific terms... but what I mean is when you have an extra 20db of "bandwidth" on which to record (okay maybe it's an extra 10 or so actually)... but anyway... how would you explain that? Would you still call it resolution?
 
Actually, in analog, you want hot levels to avoid hiss and tape noise. In digital, you can record with low levels and usually be ok. Digital has better signal to noise over analog.
 
MattinSTL said:
Analog recordings can usually be cleanest at the lowest levels... lower input signal usually means lower noise through the analog chain... digital wants the highest levels just short of clipping. Isn't that correct? So when one system of digital recording allows me to utilize an extra 20db of usable "dynamic" range... what does that mean?
Click to expand...

All systems S/N ratio benefit from hotter signals. Analog devices just generally handle overloads more gracefully. When I used multitrack reel, I would routinely push the signal to +3 or +6 with no obvious distortion (assuming you were using the right tape). All systems have noise and the hotter the non-noise signal you are pumping thru, the more it will mask noise.

ullanta has already pretty much summed up the practical benefits of 24 bit recording.

a) You can record at lower average levels without having to worry about loss of resolution or quantization noise

b) Huge benefits when summing multiple signals together.
 
MattinSTL said:
As I understood it you can record at a genuine -20 db if you're in 24 bit and bring it up to the desired level cleanly... and trying the same thing at 16 bit just doesn't work without introducing a lot of noise. I think I've been incorrectly calling this increased dynamic range...
Click to expand...

Indeed, it's decreased dynamic range, with more resolution. Exactly the point... you can do a lot more with it (eg, bring it up to a higher level as you've said) than you can with 16 bits.

The noise floor of the "real world" remains the same. The quantization noise (an effect of the AD conversion) is much lower at higher bit depths. And, to throw into the mix, 24-bit equipment likely has (on average) better self-noise properties than 16 bit equipment of the same general quality level. But assuming NO "real world" noise or analog self-noise (a big assumption!), you can crank a 24 bit signal up 48 dB (that is, take a level that's almost imperceptible on the meters to full scale) and get the same quality as an optimally recorded 16-bit signal.
 
To put it simply: In digital audio recording this "resolution" is nothing more than S/N ratio, or dynamic range. Each one bit added to the bit depth pushes the quantization noise 6 dB down, if we record the max levels at 0 dBFS.

With 16 bit recording the quantization noise is 96 dB below maximum levels, in 24 bit 144 dB below maximum level. It this is not dynamic range, what is? This is exactly the dynamic range we can record cleanly on each system. Ask any AUDIO engineer about this and this is the answer you'll get, those creatures apparently do not visit an amateur site like this, alas.

What we quantizise in audio recording is not the VU meter, we quantizise the voltage fluctuation representing the audio pressure wave. When the amplitude of the wave doubles, we need twice as many numbers to describe the wave. Twice the amplitude means 6 dB more in the logarihmic system and one more bit in binary numeric representation.

Let's look at 16 bit recording first: at the floor level (-96dB on the meter) the smallest waves might trigger a number to be generated, or not. This means that the resolution is truly bad: we have a lot of noise. If we double the loudness level to -90 dB, we have twice as many numbers to play with; random noise stays at the same level but the signal is cleaner with two possible values. Not good, but better. Each doubling of the loudness doubles the size of the available number, untill we get to the limit with 16 bits: 16^2=65536. Yes, the last 6 dB on the VU meter carries as many possible samples as all the 90 dB below it combined, is it resolution or what? Yes and no; what it amounts to is that the wave can be measured more accuratelly, which in audio is called LESS NOISE! And indeed, the noise floor is 96 dB away. Now you might say what about the lower level signals that are present in tha same loud waveform. They get no resolution advantage from the loud signal, signals say, 60dB down are getting exactly the same treatment they would get alone. Riding piggyback a loud wave does not make the small waveletts any bigger, they get the number values they deserve. Remember; all complex waves are but a sum of different sinusoidal waves at different amplitudes.

In comparing the 16 and 24 bit recordings it is better to start from top down. First the max loud signal, which gets the value of 16777216. -6dB down gets 8388608, -12dB gets 4194304, and so one. When we run out of numbers we arrive at -144dB point. Thus we can cleanly record a dynamic range of 144dB with 24 bits.

This one bit = 6dB dynamic range rule is written in stone, as we are measuring waves where twofold amplitude increase needs twice as big a number (in binary sytem we need one more bit). There is no other way to do it. For this reason the so called "resolution" always boils down to S/N ratio, which in this context is the same as dynamic range.

The Myth is upheld...
 
Last edited:
soarprod said:
Actually, in analog, you want hot levels to avoid hiss and tape noise. In digital, you can record with low levels and usually be ok. Digital has better signal to noise over analog.
Click to expand...

Or, put another way, digital has a wider usable dynamic range.

Ty Ford
 
Petrus said:
This one bit = 6dB dynamic range rule is written in stone, as we are measuring waves where twofold amplitude increase needs twice as big a number (in binary sytem we need one more bit). There is no other way to do it. For this reason the so called "resolution" always boils down to S/N ratio, which in this context is the same as dynamic range.

The Myth is upheld...
Click to expand...

Oh, Petrus, you're confusing your math concepts on the negative numbers. You really need to sit and grasp the fact that this is a NEGATIVE logarithmic scale. Everything you say is completely correct for a system where the BOTTOM of the range is fixed and the largest representable number can grow infinitely with added bits. But it does not apply to digital audio where the TOP of the range is fixed.


Think of it this way: In a normal, BOTTOM-FIXED system, If we start from 0 and add dB, indeed every 6 dB doubles the range. If we start from -96dB, and add dB, every 6 dB doubles dynamic range. If we start from -96dB and provide 144dB of range, we get a range from -96 to +48dB. Yes, 256 times greater dynamic range than -96 to 0.

But in digital audio, in moving to a 24-bit system, we don't add 144 dB above -96 to get 256 times the dynamic range. We have to shift everything down so that the maximum level is still one. WE ARE PINNED AT THE TOP OF THE SCALE TO A VALUE OF 1. So adding bits AT BEST has a decreasing dynamic range benefit. Adding a bit to a 16-bit system doesn't double dynamic range, it increases it by about 1/128000.
 
Petrus said:
With 16 bit recording the quantization noise is 96 dB below maximum levels, in 24 bit 144 dB below maximum level. It this is not dynamic range, what is? This is exactly the dynamic range we can record cleanly on each system. Ask any AUDIO engineer about this and this is the answer you'll get, those creatures apparently do not visit an amateur site like this, alas.
Click to expand...


Hey, I'm an audio engineer. And it's not really effective to bash the site in trying to make a point.

Just tell me, what's the difference in absolute terms between -96 dB and -144dB in your calculations? That is exactly the difference in dynamic range between 16 and 24-bit audio (if you don't count 0 and just consder the dynamic range fixed).

Simple question. One answer. Give it a shot.
 
When it comes to recording, doesn't the dynamic range really depend on the analog side of thngs? When doing the A/D conversion, all you're doing is mapping a range of analog voltages to a digital scale of so many bits. If the min/max range of voltages on the analog side is limited to 64db, for example, it doesn't matter whether you map that range to 16 bits or 24 bits, you still only have 64db of real world dynamic range, right? I'm really asking here; not making statements from any expertise.

So as I see it, assuming both sides are properly matched, the analog electronics would dictate what your true dynamic range is and the number of bits would dictate how well you resolve that range. If the two sides are not properly matched, the number of bits may only just be marketing hype.

-Dan
 
Well, in the great sheme of things his whole discussion is just quantization noise.

I make no calculations, I try to explain how digital audio recording works, why adding bit depth just adds more dynmic range and does not add "resolution", unless you want to call better S/N ratio "resolution". And using a minus sign in front of dB makes no mathematical difference in this context, as any mathematican knows. It is just the way we like to build our VU meters, as it is more logical and can be used the same way with all bit depths.

And I am a railroad engineer...

But, an example (I really do not fully understand your question, my mother tonque is Finnish):

We are recording an orchestra. The maximum level it puts out is about 120 db (loudness). We use 16 bit recording. We set the levels so that the highest levels hit -2dB on the meters. The lowest possible PPPPPP is at 120-94 dB loudness level (we had 2 dB safety margin). That is 26 dB loudness. In theory there could be some sound detail even more quiet that we miss because we hit the quatization noise floor at 26 dB loudness point (not in real life, tough).

With 24 bit system we could set the max levels at even safer -12dB on the meters. That would give us the lowest recordable sound level at -12dB loudness (clearly there would be nothing to record 12 dB below the treshold of hearing!). Thus we could safely capture everything that the orchestra could thow at us.

Dynamic range is the difference between the loudest and the quietest sound recorded, or the loudness range the system is capable of recording/transmitting. Expressed in dB, a logarihmic unit. Simple.
 
TeleDan said:
When it comes to recording, doesn't the dynamic range really depend on the analog side of thngs? When doing the A/D conversion, all you're doing is mapping a range of analog voltages to a digital scale of so many bits. If the min/max range of voltages on the analog side is limited to 64db, for example, it doesn't matter whether you map that range to 16 bits or 24 bits, you still only have 64db of real world dynamic range, right? I'm really asking here; not making statements from any expertise.
Click to expand...


Hi Dan!

It's actually a bit more complicated, but what you're saying seems sorta a reasonable way to look at it. I mean, in general, the analog circuitry is indeed the major factor in sound quality; and even if a particular converter chip quotes spectacular performance, how it's connected to everything else often outweighs this. That's why marketers have such an easy time with specs; they pretty much can quote specs for whatever subsystem sounds best, though reputable equipment producers use more reasonable (full-system) specs.

However, the user pretty much chooses the dynamic range of the analog circuitry using gain controls and such. This is also a complicated process (called "gain staging" or "gain structure"), especially when lots of analog components are chained together. The last stage has to be matched to feed the A/D converters.

Now, Signal-to-noise ratio dictates that you want the peak levels as close to 0dBFS as possible. The risk of digital clipping dictates that you want to leave as much headroom as possible. In some situations (say, typical pop music), the dynamic range of the source is relatively small, while in others (say, classical music), dynamic range is relatively large. In classical, a singer might have one passage that sustains a level 30 dB higher than anything else in the piece... which means, your average level will be around -30 dB. So while for pop music the average sound level is close to the max sound level (meaning you can set your gains so almost everything is in the high-res top of the dB range), in classical music most material will be far below the top of the range, and thus be recorded at lower resolution per dB. This is why classical music afficionados are usually so much more demanding of equipment quality - the material really needs it more. 24 vs 16-bit resolution really makes a difference here, because there's even a lot of dynamic range in the material averaging -30dB, and you want resolution even at that low level to capture it well. In recording operas, I can tell you, there's a lot of important material that looks close to a flat-line in the waveform. At 24 bits, you have a lot more leeway to raise these up to a reasonable level with nice sound than you do at 16 bits. But if you set your levels higher during recording, and get digital clipping, it's not recoverable.

So as I see it, assuming both sides are properly matched, the analog electronics would dictate what your true dynamic range is and the number of bits would dictate how well you resolve that range. If the two sides are not properly matched, the number of bits may only just be marketing hype.
Click to expand...

Right. With the caveat that the user is part of the process... that is, the user generally has a hand in determining the analog dynamic range. Of course different mics, preamps, processors, etc. have dynamic range limitations of their own, but their combinations and gain staging play a major role. So "properly matched" is often a creative/craftsmanlike decision - one can use, e.g., compression to modify dynamic range, one can leave different amounts of headroom depending on knowledge of the material and performers, etc. One big part of this process in digital recording is not just balancing S/N and headroom issues, but keeping in mind resolution issues. 16 vs. 24 bits doesn't affect dynamic range, real-world or analog equipment noise floor, etc. It does effect, however, how far down the scale you can get adequate resolution. So, not quite hype, but sometimes outweighed by other factors. But in general, the increased resolution is indeed a BIG plus, and allows one to leave more headroom.
 
Petrus said:
And using a minus sign in front of dB makes no mathematical difference in this context, as any mathematican knows.
Click to expand...

Of course, the minus sign makes no difference. As I've said, it's pinning the top end of the scale (rather than the bottom end) that makes a difference.

Just tell me, what's the difference in absolute terms between -96 dB and -144dB in your calculations? That is exactly the difference in dynamic range between 16 and 24-bit audio (if you don't count 0 and just consder the dynamic range fixed).
Click to expand...

The difference between -96dBFS and -144dBFS is precisely .00390625 FS (FS/256). The added dynamic range is about 0.4%. The precision is increased 256 times. There's no getting around it. You said somewhere, "adding a bit doubles the size of the largest representable value". THIS IS NOT TRUE IN DIGITAL AUDIO. The largest representable value is always 0. Adding a bit REDUCES the size of the smallest representable value, and thus doubles precision without doing much for dynamic range.
 
Last edited:
ullanta said:
The difference between -96dBFS and -144dBFS is precisely .018 FS (FS/256). The added dynamic range is about 2%. The precision is increased 256 times. There's no getting around it. You said somewhere, "adding a bit doubles the size of the largest representable value". THIS IS NOT TRUE IN DIGITAL AUDIO. The largest representable value is always 0. Adding a bit REDUCES the size of the smallest representable value, and thus doubles precision without doing much for dynamic range.
Click to expand...

Your mixing your scales. The largest representation in 24 bit is 2 to the 24th power, a lot bigger that 2 to the 16th power (16 bit). The zero you keep talking about is FS (full Scale). It is not a fixed number it is what ever the largest number the system can handle. You seem to mixing this up with 0dB, which is also not a fixed value but a referenced one, and it is an analog one. You can put your "zero" wherever you want to. So if you keep the same output level for FS then you would kind of have a point, but there is no good reason to do so. One could just as easily make FS significantly higher set the 0dB below FS and create headroom, and still have higher resolution below 0dB.
So in one scenario you are right but in the other you are not. To find out you have to do a lot of research into the specs of the various pieces of equipment. And then do a bunch of testing because they tend to use different standards so the specs are often misleading at best.

Or you could just go record and use what sounds best and not worry about it.

SK
 
Noiz2 said:
Your mixing your scales. The largest representation in 24 bit is 2 to the 24th power, a lot bigger that 2 to the 16th power (16 bit). The zero you keep talking about is FS (full Scale). It is not a fixed number it is what ever the largest number the system can handle. You seem to mixing this up with 0dB, which is also not a fixed value but a referenced one, and it is an analog one. You can put your "zero" wherever you want to. So if you keep the same output level for FS then you would kind of have a point, but there is no good reason to do so. One could just as easily make FS significantly higher set the 0dB below FS and create headroom, and still have higher resolution below 0dB.
Click to expand...

dbFS means "decibels relative to Full Scale". Full scale is indeed a fixed number. It has a varying relationship to dBSPL that you adjust with gain and trim controls. Digital audio therefore represents only the negative decibel range, that is, numbers in the range of [0, 1]. This means the largest number representable is 1, and the smallest non-zero number representable is 2 to the -24 for 24 bit, or 2 to the -16 for 16 bit. The largest number either can represent is the same. It's only the smallest representable number that's affected by the sample size.

FS doesn't have input levels or output levels, it's a purely digital and data-based representation of numbers ranging from 0 to 1.
 
Last edited:
Dudes -

Dig this - one of the most important principles in computer science is that a bunch of bits is a bunch of bits and nothing more. You can treat it as data. You can try to execute it as code. You can take 16 bits and call it a signed integer, an unsigned integer, 2 characters, 4-5 packed decimals, big-endian or little-endian, an opcode, an address, whatever.

Noiz2 - The largest representation in 24-bit is therefore not 2^24. The largest representation of a 24-bit unsigned integer is 2^24 - 1. The largest representation in a 2's complement 24 bit integer is 2^23-1. There are 24-bit floating point formats (albeit rare) where the largest representation is much larger. As character data the largest numerical representation would be 999. "24 bits" doesn't give you full information.

The representation used for most digital audio represents the range from 0 to 1. Full Scale, the numerical 1, is always the largest number representable. 0 is always the smallest number representable. Adding bits increases the number of steps between 0 and 1. "Dynamic Range" is generally measured as the ratio between the smallest representable number and the largest. Since more steps - more resolution - means the smallest representable number is smaller, the dynamic range extends a bit with each increase in resolution. But the largest number is always 1. NOTHING you can do, no matter how many bits you add, will make the largest representable number larger on the dBFS scale. It's 1. Always 1. Never anything but 1. You can write "1" as 0dB. Or 0dBFS. But it's 1. Just 1. Always 1.
 
You must log in or register to reply here.
Back
Top