# Increased headroom vs resolution with 24bit audio recording

I've been doing a bit of reading on 16bit vs 24bit audio and came across this article that claims 24bit/192kHz playback is basically pointless (but, that's not what I'm hear to discuss).

What I found surprising was the fact that moving to a 24bit recording process doesn't result in a higher resolution per sample, but rather a wider dynamic range.

I would have assumed this to work in a similar way as digital images. If you are using 8 bits per channel and look at the red channel, a value of 0 corresponds to black and 255 corresponds to the reddest of the reds. If you increase this to 16 bits, you don't get a redder red than what you had with 8 bits. Instead, a value of 65535 now corresponds to the reddest red and you can represent more shades of red between black (0) and red (65535).

Back to audio: Let's say you have an analog signal of a sine wave coming out of a preamp and into a 16bit ADC and the peak of this signal corresponds to a value of 65535. If you now swap out the ADC with a 24bit one, wouldn't the peaks of same signal now correspond to 16 million something? I understand with the extra bits that we can now represent a much quieter signal (relative to our original signal) and I guess this kind of explains the wider dynamic range thing. But, aren't we still representing the same range of input voltages?

I'm clearly missing something and would appreciate some enlightenment.

First, I'd like to take a moment to point out that that article only argues that 24bit sampling is useless for end user playback. I'm also not 100% convinced by the article personally, but that's neither here nor there.

As for the dynamic range, yes, the 24 bits expands the dynamic range in the same way that it does for a camera. For both audio and cameras the extra bits go to both expanding the absolute range and also to make more values between those absolutes. It can cover both a wider set of signal levels as well as more detail in the signal. (If you think about it, this is kind of obvious as an increase in 8 bits would be 256 times louder if the same scale was maintained and that is uselessly loud. In fact, 1 bit more would be more than we could use in that case.)

The reason that the article argues that it isn't useful is that the extra resolution is below the limit of what the ear can distinguish. This is similar to the foolishness of the DPI wars in the smartphone industry since beyond a certain point, the eye can't physically resolve the resolution that is being displayed.

So for purposes of recording, where algorithms CAN work on the extra resolution, it is worth storing in 24bit, but when it comes to final mixed down audio, the article argues it won't add much since people won't be able to tell the difference.

The only error in your question is this as far as I can tell: -

What I found surprising was the fact that moving to a 24bit recording process doesn't result in a higher resolution per sample, but rather a wider dynamic range.

In fact 24 bits provides more resolution in the same analogue voltage range AND this means more dynamic range.

Yes, a 24bit device probably works on the same range of voltages but consider a song that is being mixed....

Maybe there are 16 channels of audio comprising the mix; each one is a different instrument and, when played together, at some point in the "mix" the peak signal is reached i.e. it's just on the verge of clipping. No problem so far I hope?

Each of the 16 individual tracks cannot be the same amplitude as the "mixed" track and you could say the amplitude of each individual track was 16 times smaller in amplitude and, if this was a 16-bit digital mixer, each individual track would be only utilizing the lower 12 bits (ensuring keep the "mix" remains within 16 bits).

Because of this, an individual track has quite a poor resolution (12 bit) and will be a little grainy but, with a 24 bit system, each track would be able to be defined within 20 bits and therefore much better than a rendered CD (16 bits).

• Sorry, this is just wrong or at least irrelevant. There are no "16 bit mixers" nowadays, all modern digital audio processing is done with floating-point samples for which the whole dynamic-range issue doesn't really apply at all. So if you were to just lower the volume of each track so the mix doesn't clip, it would rather mean the effective resolution of each track is increased, because the volume reduction makes the gaps between the possible values smaller. Unfortunately... – leftaroundabout Sep 9 '13 at 22:08
• ... it doesn't quite work this way: individual tracks are often not only not reduced below 0dB, but in fact boosted quite a lot higher, via compression and other nonlinear effects, and generally altered through effects like EQing, all of which can make quantisation artifacts more audible. That's why you should record in 24 bits. – leftaroundabout Sep 9 '13 at 22:11
• @leftaroundabout you misunderstand me dude. I was using a hypothetical 16-bit mixer as an idea to help the guy asking the question. I'm not trying to justify recording in 16 bits or 24 bits. That's not what my answer is about. – Andy aka Sep 10 '13 at 7:07

# All Digital Audio Articles are Flawed.

I've been doing a bit of reading on 16bit vs 24bit audio and came across this article that claims 24bit/192kHz playback is basically pointless (but, that's not what I'm hear to discuss).

There is endless online debates on virtually all aspects of digital audio, and articles as the one you have cited are common triggers.

The reason is that all these articles are flawed and incomplete. There are 3 reasons for this:

• Digital audio theory is complex - I've been teaching digital audio for years, and can assert that it takes about 60 frontal hours of teaching to only cover the topic on a fundamental level. Authors of articles can not provide such vast amount of information, thus the explanations are always incomplete.
• Authors are often biased and pointing - Most authors try to argue a certain thing, but they choose not to show the cases which will object their arguments. Authors can guard their argument by carefully picking terms, so the argument itself is reasonable and logical. But you can easily be misled to believe A also means B, but B was never actually mentioned. For instance, it may justified to say that it is pointless recording at 192kHz, but only if the audio is never to be processed in the digital domain (there are benefits processing at higher sample rates and higher bit depths). The point is that "recording" does not mean "processing", so the statement "it is pointless to record at 192kHz" is reasonable, but it still doesn't mean there are no benefits in doing that.
• There's an undetermined gap between theory and practice - People's opinion is often subdivided on the theoretical and practical levels. The theorists will claim that any issue, audible or not should be accounted for; The practical ones claim that issues should only be accounted for if audible and distinguishable. The problem is that whether or not issues will be audible depends on countless variables that change on a case basis - so whether or not 16 bit will be audibly distinguishable from 24 bit depends on the signal being processed, amount and nature of the processing, the monitoring setup, to name a few. So it's anyone's guess really.

# Resolution in Digital Audio

What I found surprising was the fact that moving to a 24bit recording process doesn't result in a higher resolution per sample, but rather a wider dynamic range.

The term `resolution` is nearly always misused in the context of digital audio. Digital audio books use the term to describe "the amount of information" we have on something. This may apply to the resolution of frequency spectrum analysis, which can be done at lower or higher resolutions.

But if applied directly to digital audio, the word means "the amount of information we have on the signal". In that context, it is perfectly correct to say (from The Scientist and Engineer's Guide to Digital Signal Processing):

"An analog signal formed from frequencies between 0Hz and 10 kHz will have exactly the same resolution as a digital signal sampled at 20 kHz."

Perhaps surprisingly, sampling theory does not account for dynamic range - the theory states that as long as a signal is sampled at equal intervals at least twice as fast from the highest frequency present, the signal representation is perfect and complete - that is, we have all the information we need to recreate the signal.

But what about dynamic range you may ask? By the sampling theorem, digital audio has infinite sampling range. However, the practice of rounding (quantising) continuous analogue voltage to discrete digital values yields an error, and this error translates to noise, and this noise determines the signal to noise ratio of the system, which most people consider the dynamic range of the system (which is not perfectly correct as depending on the frequency content we can hear sounds below the noise floor; it depends whether you define dynamic range as physical or perceptual phenomenon).

Now could you say that a digital audio with a higher bit depth has more resolution? It is certainly tempting, but here is the catch:

A 1 bit ADC at very high sample rates will yield a higher Signal-to-Noise ratio (thus dynamic range) than 24 bit ADC at very low sample rates.

In fact, nearly all modern ADCs are built with 1-bit Delta Sigma converters in them. Whether you choose 16 or 24 bits, and whether you choose 44.1 or 192kHz, the converters first sample with 1 bit at high sample rates, only then convert it to your choice of format.

So what is `resolution` really? Nika Aldrich brilliantly explains it in his book Digital Audio Explain for The Audio Engineer:

Until now the term "resolution" has not been used in conjunction with bit depth of digital recordings in the book... The term "resolution" implies a subjective measure of quality... There are, however, only four characteristics of a waveform.. "Resolution" is not one of them.

# Digital Audio is not Digital Photography

I would have assumed this to work in a similar way as digital images.

The analogy between the two is intuitive, in fact it would be weird if people didn't make it. But digital audio and photography are not the same, not in the core at least. In fact, the analogy to camera sensors is a prime reason to why people fail to grasp digital audio.

Digital sensors involve 1 sample (of varying intervals) of a matrix of pixels - otherwise, one sample with many measurements. Digital audio involves many samples of equal intervals over time, each made of a single measurement. The process is not the same.

Resolution in digital photography equates the number of pixels per image. But higher resolution (more pixels) in digital images does not necessarily mean higher quality - higher resolution sensors mean the matrix is made of smaller pixel sensor, so less photons hit each pixel sensor, which yields more noise. This is what Apple is trying to convince people:

Digital audio does not conform to the same principles. More bits to describe a sample simply mean less rounding, so less noise. But this is not the same as the noise we talk about with photography.

You are correct making the comparison between colour depth (8 or 16 bit per channel), to bit depth in audio. But neither noise or resolution is part of this.

# Dynamic Range in Digital Audio

To begin with, all ADCs are calibrated to a specific window of input voltage. For simplicity, lets consider the range to be -1V to +1V. Regardless of the sampling bit depth (24 bit, 16 bit, or 1 bit - which is what is actually used internally) the voltage measurements are always taken for the same voltage range.

Now imagine you have to map 1 bit into this range. You have two step (quantas) - `0` and `1`. It would be sensible to put these at -0.5V (`0`) and +0.5V (`1`).

Now if you pick arbitrary input values and round them to the nearest step, you'll see the error will never be higher than 0.5V. For instance, an input of +1V will be rounded to +0.5V. This rounding generates noise, and the noise highest peak can be at +0.5V (the maximum rounding error).

If we now use 2 bit sampling, we get four quantisation steps: -0.75V (`0`), -0.25V (`1`), +0.25V (`2`), +0.75V (`3`).

This time the maximum rounding error is 0.25V, so the quantisation noise highest peak will be at 0.25V - half of that with 1 bit conversion.

So every time you add a bit, the quantisation noise level halves.

As previously explained, we consider the signal to noise ratio as the dynamic range of the system.

• Your section "Digital Audio is not Digital Photography" is comparing apples to oranges. Bit depth in audio of course isn't the same as image resolution, it's the same as visual bit depth -- the number of bits per channel for each pixel -- which is what the OP is using as an analogy (Actually it's not an analogy, it's exactly the same process, just with light, instead of sound). You're confusing the two. Dynamic range in imagery has nothing to do with image resolution (which is really more analogous to audio sample rate). – naught101 Sep 24 '13 at 1:11

The sample rate has nothing to do with the bit depth. It's true, you allow for more precise measurements with a higher bit depth. If your synthesizer is outputting 16-bit digital audio, then a 24-bit processor will essentially leave it at 16-bit, but if you do any processing to the audio itself in 24-bit, the end result will be more accurate at 24-bit resolution.

More bits = more bit depth, as you mentioned. It's really the accuracy, although 8-bit vs. 16-bit is a rather large difference perception-wise.