Final words about increase in bit depth/sample rate?

[MatsD]

There's a lot of talk these days about the benefits of 24 bit/96 kHz recording over the old CD standard. Often there is a lack of technical knowledge and instead you are fed with final words like "There's a significant audible difference..." or "There's no audible difference whatsoever..."

Claimed benefits of recording at a greater bit depth are:
- Better dynamics/headroom - you can afford to lose a few bits here and there due to low levels and still have at least 16 used bits in all tracks when it's time for mixdown.
- Plugins who can deal internally with higher bit rates sounds better when fed with 24 bits than 16.
- A multitude of audio tracks mixed down to a final stereo track would present a higher demand in digital representation than just a few tracks. The 16 bit/44 kHz format is not sufficient to hold all this data with accuracy.

I feel comfortable with the first and second claim, but the third one I find questionable. Is it really true that it requires more digital "resources" to represent the sound of a full symphony orchestra than it requires to represent a simple sine wave? And if so, is the CD standard format not sufficient to deal with accurate representation of very complicated wave forms (like the symphony orchestra or a multitude of mixed down audio tracks)? Is there a real and for every added track increasing degradation in sound when mixing down several 16/44.1 tracks to a single 16/44.1 master? Or is this just plain nonsense? If this is true it also implies that you would benefit from mixing down a multitude of 16/44.1 tracks to a 24/96 (or at least a 24/44.1) master which would more accurately be able to hold all data from the tracks added together, provided all 24 bits are used and not just the lowest 16 bits.

To elaborate here, mixing down a bunch of 16 bit tracks within the same system (i.e. Cubase Export Audio) to a final 24 bit mix with everything at unity (master set not to go above 0 dB) would result in a 24 bit file with only the bottom 16 bits used. But if you calculate the added headroom of these 8 unused bits, you should be able to increase the levels on the master faders n dB above 0 dB (calibrated for 16 bits) and thus get a 24 bit mixdown with all bits used. Mixing down from 16 bits doesn't equal mixing down 1x16 bits but Nx16 bits, where N is the number of tracks. When mixing down to 24 bits you can allow more of these Nx16 bits to be transfered to the mix, to put it simply. In real life the equation gets a bit more complicated if we consider that some tracks are stereo and some are mono and the final mix is stereo. Then Nx16 then corresponds to the total number of mono tracks (where each stereo track is regarded as two mono tracks). The resulting mix would have 2x24 bits capacity.

My guess is that audio quality is preserved no matter how many tracks are mixed down, and this is due to the fact that every track is mixed down with only a fraction of its original amplitude. Everyone knows that the more tracks you have in a mix, the more you have to back off on the faders in order not to get a total signal above 0 dB and introduce digital clipping (provided the individual tracks are recorded at or near 0 dB level). The amplitudes for all tracks are added together and must be reduced to fit the headroom in the final mix. Less amplitude/volume means less need of number of bits in the representation, thus no significant degradation in sound.

The benefits from an increase in sample rate is more questionable. According to Nyquist 44.1 kHz can accurately reproduce frequencies up to 22.05 kHz, which is above most peoples (and certainly most ear abused musicians) hearing limit. Sufficient oversampling and good AD/DA converters is of course a must. What would be the benefits of increasing the sample rate to 96 kHz? Do you get a flatter frequency response and less distortion at the highest audible frequencies? Is the Nyquist theorem just theory and is 44.1 kHz sample rate when it comes down to dust really not enough to accurately reproduce all audible frequencies? Where does for example oversampling come into the picture or statistical quantification errors, the latter suggesting a greater accuracy for higher sampling frequencies than 44.1 kHz?

These are, I think, important questions for anyone involved in digital recording. Any facts beyond "I hear the difference" are welcome. Hints of good literature (books, web sites) that deal with these questions would also be appreciated.

/Mats D, Sweden

[iqi616]

I agree with you about those 2 facts of better-than-CD quality. In general CD quality is BETTER than most people's hearing and the environment they listen in (also many people wouldn't realize that a 16-bit 44.1 kHz recording of a good vinyl album wasn't direct to digital unless they could hear the rumble, scratches, and wow). It is only the music/equipment industry that keeps pushing us to want for more so that they can make more sales on existing intellectual property (e.g. 5.1 surround sound for anything other than movies). As far as I'm concerned, the only improvement they could usefully make to a stereo CD is to make it unscratchable.

I think one factor that is frequently ignored is that people's ears react differently to edges vs. continuous high frequencies. That is to say, ears can hear the momentary burst of high frequencies from a snare drum far better than they could hear a sine wave at 22 kHz. I don't know how that factor relates to this discussion however.

My final comment is that there will always be those audiophiles that spend more time listening to the gaps between the songs than they do listening to the music. I think that's because they enjoy the technology or the snobbery MORE than the music.

[MatsD]

What i am most interested in is if mixing down to a greater bit depth than the one used for the individual tracks has any benefits.

An example: My song is made up of four 16 bit mono tracks, recorded hot (just below 0 dB). The total dynamic content is 4x16=64 bits. When mixing down to 16 bit stereo format, I need to cut the dynamic range down to 2x16=32 bits by reducing the volume of each track. But if I mix down to 24 bit stereo format, I would have 2x24=48 bits capacity and would not need to reduce the total dynamic content of the four mono tracks as much, and that would be a real benefit. But I'm not sure this is possible in the digital domain. Perhaps you always end up with a 24 bit stereo mix where only the bottom 16 bits are used and the eight top bits are empty, which indicates that it would be useless to mixdown to a greater bit depth than the original format. Perhaps you need some software or hardware device in order to resolve n number of 16 bit tracks to make full use of the 24 bit format.

/Mats D

[BasPer]

I didn't have the stamina to read through your entire post. But this is how it is:

A 16-bit wave file is made up from sixteen-bit numbers. A sixteen-bit number is a number between 0 and 65535 (in base ten ). When you mix down a multitrack project to a stereo file what happens is - not exactly but lets say it anyway for the sake of simplicity - that the numbers for each of the tracks are added together. So mixing down 48 sixteen-bit tracks could give peaks of 48*65.535=3.145.728. And to represent that number you need log2(3.145.728) = 22 bits. And i hope that was what you were asking for, or I'll look kind of stupid.

[atomictoyz]

Originally posted by MatsD
with only the bottom 16 bits used....


According to Nyquist 44.1 kHz can accurately reproduce frequencies up to 22.05 kHz, which is above most peoples (and certainly most ear abused musicians) hearing limit. Sufficient oversampling and good AD/DA converters is of course a must. What would be the benefits of increasing the sample rate to 96 kHz?....

Usually its the first 16 bits that are kept and the last 8 are randomly truncated. Truncation is Bad!

The Nyquist Theorm is great for higher frequencies, but suffers when the lower frequencies are sampled. The number of times you quantize a wave length is directly related to the frequency. So the a 20hz signal is so long that its nearly impossible to get a good sample when compared to a 20khz signal. There is alot of ambience at the higher frequencies that the converters just are not designed to sample. There is alot more to the issue of the increase of the 24/96 movement, but when you compare it to 16/44.1, its clear there is more definition of everything. Plus everytime a process is done digitally, the recalculations change the actual signal to a different frquency.

Peace,
Dennis

[MatsD]

OK, so there is a gradual degradation from high to low frequences regardless of sample frequency but less obvious the higher frequency you use, due to the fact that lower frequencies equals longer wave lengths. OK, I buy that. You will primarily get a better representation of the lower frequencies by using 96 kHz instead of 44.1 kHz, right?

I'm still confused about the bit issue though. Why would it not be possible within the digital domain to add two 16 bit files to one 24 bit file? Mathematically this presents no problem as far as I can see. If you can add two 16 bit files together and then reduce the dynamic range to fit within the dynamic range of a new 16 bit file, why can't you add two 16 bit files together and then reduce the dynamic range (somewhat less) to fit within and fully occupy the greater dynamic range of a 24 bit file?

/Mats D

[BasPer]

None of what you two guys say in the last two posts is correct, or even make any sence. But I have to get some sleep before I cach a train in four and a half hours, so I'll wait till tomorrow setting you straight. And hopefully someone else will have explained it by then...

Oops, Sonusman alredy did it. I really have to take a speed typing class...

[skippy]

Atomictoyz wrote: "The Nyquist Theorm is great for higher frequencies, but suffers when the lower frequencies are sampled. The number of times you quantize a wave length is directly related to the frequency. So the a 20hz signal is so long that its nearly impossible to get a good sample when compared to a 20khz signal."

Regrettably, this is false. Nyquist stated the upper limit of the passband with respect to the sampling frequency, but not the lower limit.

Shannon's Sampled Data Theorem is the true basis for modern digital audio- Nyquist just kind of embroidered around the edges a little, years and years later. (;-) The fact is that Shannon's sampled data systems have no lower frequency limit, as such: they are theoretically accurate to +- 1/2lsb *right down to DC*.

In practice (as we use them in digital audio), there are usually highpass properties designed into the actual converter support circuitry. But if the converter itself were to be wrapped in DC-coupled analog circuitry for one reason or another, you're good right down to DC. Example: the digital multimeter in your toolbox.

You usually don't _want_ to be DC coupled for audio, though- there's no sense having your precious few bits used up in preserving DC offsets from previous stages, when you are trying to somehow preserve the ten-trillion-to-one dynamic range of our auditory apparatus! In practice, digital is too damned _good_ at preserving LF information: most knowledgeable people will actually roll off their signals below 20Hz or so just to keep the infrasonic stuff _out_ of their mixes, because digital sampling will preserve it very nicely. But real-world woofers can't do a thing with it...

Anyway, Nyquist is silent on the lower limit of the passband in a sampled data system for the simple reason that the lower limit *is* DC, with no reduced-resolution effects whatsoever down there.

Sonusman has offered excellent advice here: the essays at http://www.digido.com should be required reading for everybody *before* the religious arguments start. This is hard stuff, but it is _science_, not art: it can be understood, you really don't need to be an EE to understand it, and the pseudoscience and misunderstandings really should be put to rest.

They never will be, probably, because a lot of this stuff has taken on the mantle of religion. And regrettably, religious-style issues are used by many people as a convenient excuse not to probe futher. But the truth is out there, and digido is an excellent place to start in achiving a _true_ understanding of resolution issues, distortion residuals, and the effects of proper dither compared to the effects of simple truncation. And learn not only that it can be heard (hell, even I can hear it, and everybody knows I'm as deaf as a post!), but _why_ it can be heard...

It's absolutely worth everybody's while to get up to speed on that stuff- and _then_, let's talk.

[MatsD]

I was not implying that 24 bits would make anything sound louder, in fact I was not stating the essence of the benefits at all. But if I am to do so, I meant that there ought to be a way of mixing down the sum of the dynamic ranges of several 16 bit tracks to fully occupy the dynamic range of a 24 bit file. What I am talking about is a better dynamic resolution, not a boost in volume. Perhaps there's a fundmental reasoning error in my suggestion, but the technical stuff from you two guys didn't make me any wiser and seems to a great extent to deal with other issues.

The practical questions remains - can there in any way be any dynamic benefits of mixing down a bunch of 16 bit tracks to a 24 bit "master"? Is the nature of the digital domain such that I, no matter what, always will be ending up with a 24 bit file where 8 bits are unused? Is it impossible to reduce the sum of several 16 bit dynamic ranges to the full resolution of a 24 bit mixdown recording?

/Mats D

[sjoko2]

sigh................

[MatsD]

All technical details about the benefits apart, you are at least suggesting that you in fact can render a 24 bit mixdown from a bunch of 16 bit tracks, which was my main issue. I'm aware of that a DSP decrease in volume is in fact a decrease in bit representation of the sound and that was in fact the reason for my question. It seems a waste to decrease the resolution of all 16 bit tracks down to fit within a new 16 bit file, if it is possible to decrease the 16 bit files bit depth less and fit them into a 24 bit file. Experiments however has indicated that mixing down from 16 bit to 24 bit has only rendered me a 24 bit file with 16 used bits and 8 bits of "air". I am mainly working with Cubase and I often mixdown within the software using Export Audio. Perhaps I must use another method to record a fully occupied 24 bit file from my 16 bit tracks in Cubase.

I will read the articles you recommend, thanks for pointing them out to me.

/Mats D

[MatsD]

OK, I think I meant that in the final mix, each track will have a reduced dynamic range compared to the range of the original tracks in order for all of them to be able to sit in the context of a new 16 bit or 24 bit file. They all suddenly will have to "share the space" of a file with the same (16 bit) or somewhat greater (24 bit) depth as they originally had each. That's why I'm interested in mixing down to 24 bit without any unused bits - to get as good a resolution as possible. Of course I can always use 24 bits all the way or even the 32 bit floating point with True Tape fake dynamic reserve, but I'm still curious if mixing down to 24 bits within the software or some other way can render me a better resolution than mixing down to a 16 bit file. If the 24 bit file contains 8 unused bits, I have acheived nothing but to occupy my harddisk space with anneccesary big files.

Thanks for taking time to explain things.

/Mats D

[sjoko2]

Ed - I'm so busy at the moment trying to catch up it would be wrong for me to promise anything. But, if you want to write it, I will respond to you direct with any details you might need, suggestions for edits etc.

However, I think any article like that will need to start from te absolute basics, as from glancing through the questions raised, and opinions rendered, a lot of people seem completely unaware of what bitrate or clockspeed actually is or does.

[skippy]

While Ed and Sjoko2 are working on the definitive article about resolution and accuracy, allow me to regale you with an old-fart story.

I'm old enough (just barely) to have done a significant portion of my engineering education with a slide rule. Programmable calculators became cheap enough to be viable even for a destitute college student during my academic career, but when I started out the weapon of choice was the good old slipstick. And as a result of that, I learned a certain level of respect for numbers that seems to be missing in the digitally-driven education process these days.

When you do extensive calculations with a slide rule, you learn very quickly that you can only work to a certain level of precision. All your results come up with a limited number of decimal places that are actually meaningful, because the slide rule compares logarithms with limited accuracy. So, to take a quick and easy example, when you calculate the area of a circle, you'd measure the radius (let's say I measured it as 1.05 feet), square it (easily done on a slide rule) and multiply by pi (3.14). And that'd give you a result of 3.46 square feet. It was easy to keep track of the *precision* of your calculation, because it was very effectively limited by the means of the calculation.

Now, let's do that on my modern high-zoot calculator here. I'll just punch in (((1.05)**2)*pi), and it says right here that the answer is 3.4636590058....

Which is wrong, given the *precision* of my measurement of the radius! The *right* answer in an engineering sense is 3.46 +- .03 (accuracy and tolerance), because that's all the precision I made the basic measurement of the radius with. Just because the calculator gives me that _resolution_ (that many digits), doesn't mean that all those digits are correct! I used to love watching the people who could afford calculators get dinged on tests for reporting too much "accuracy": the fact is, it ain't accurate. Really.

Here's why. When I measured 1.05, that implies an accuracy of +- 1/2 of my least significant digit. My eyes are old and tired, so I don't read that ruler too well any more- that "1.05" could *actually* have been any value between 1.045 and 1.055, and I just couldn't tell the difference because my measurement system (ruler plus eyes) is no better than that. Assuming that the value really *meant* 1.050000000000000 is *absolutely* incorrect! Fact is, below that "5", we have no freakin' clue what's going on: the rest is just noise. In every measurement, there is uncertainty, you see. So If I plug in the limits of that measurement and report all those digits, look what happens:

(((1.045)**2)*pi) = 3.43069771754.....
(((1.055)**2)*pi) = 3.49667116326.....

So 3.46 is a reasonable *estimate*, and we'll divide the error band (the difference between those limits) in two and say that it's 3.46 +-.03. Which is true, and correct. Because of the (relative) inaccuracy of the initial measurement, the result *could occupy any value in that range*.

This is a great example of why you want your initial measurement to have as much _precision_ (read: resolution) as possible: if we could have measured that circle's radius more precisely as 1.0453 feet, the right answer for its area would be somewhere between (((1.04525)**2)*pi) and (((1.04535)**2)*pi), or 3.43233... to 3.43299..., or 3.4326 +- .0003, if you wanna get pedantic about it. We measure with 2 decimal places more *precision*, we get results with two decimal places more *accuracy*. Period. End of statement.

And that's why you got dinged on the test if you reported results to 10 decimal places: you were reporting _noise_ as fact.

Now, the application of this to digital audio and the 16-versus-24-bit problem may be a little less obvious. But the first thing that you must do is free yourself from the idea that all those digits/bits are meaningful, just because they're _there_. Unless you take great pains to make your measurements with unerring precision, and do your math with the _correct level_ of precision, some of that measurement uncertainly will show up in your result- and it is noise, dammit!

And for the other engineers lurking out there: yes, I *know* that the error bands here are actually (1/2LSD)**2, or .025 and .00025 in these examples- I'm trying to keep it simple, and focus on the behavior of the errors as extracted from the results, and not get hung up on the exact derivations of them or their exact values. Please bear with me for simplicity's sake- if it got any nerdier than this, nobody'd read it!

Hope that helps, anyway. Now, I'll turn it over to Ed and Sjoko.

[atomictoyz]

Originally posted by skippy
Atomictoyz wrote: ...Blah Blah...

While at work on a Monday that started bad and got worse. Im left handed and dyslexic, so ignore everything I typed that day... Heh heh...no excuses though... I have no idea what Im talking about.

Also Originally posted by skippy
Regrettably, this is false.......

Reaallly!.........no regrets? I regret posting it....When I read your response Skippy I didn't recognize what I had typed as my own...This BBS needs some clutter nulling DSP...Im sure sonusman would approve :0)


Peace,
Dennis

[skippy]

No, don't regret it: none of us was born knowing this stuff, and it is a hard topic- usually clothed in nerdy verbiage like the stuff I spewed above. But if we all play this right, we can all learn something new: this is a developing field, and the stuff I learned in the 70's and '80s has been expanded on, and in some cases obsoleted outright.

Remember when I first showed up here about a year and a half ago, talking about A/D conversion? Hell, I used to design DSP signal paths for audio *for a living* back in the mid-80s, and thought I had a very good handle on it. But then I got completely out of the pro audio industry for 10 years. And while I was asleep, the industry moved forwards, and the introduction of cost-effective oversampling/digital filtering converters changed the nature of the conversion process is a very fundamental way (with the demise of brickwall antialiasing filters, for example). So all my cherished old hard-won knowledge, while not exactly _wrong_, was instantly revealed to be just a historic curiosity. Shoot, we don't _do_ stuff that way anymore. Coulda knocked me over with a feather. I'm still amazed every time I walk into the studio.

That's why I said "regrettably". I don't want to attack the messenger, because *I've* been wrong before, and I will be again, and getting attacked ain't fun. I do want to attack the _concepts_ that are wrong, though, so we can all improve the breed...

No sweat! I'm looking forward to the collaboration that Ed proposed: a "readable-by-the-non-nerd explanation" would be a true service to the industry.

[barefoot]

Simply mixing a bunch of 16 bit tracks down in 24 bit does have some minor signal to noise ratio benefit, but processing is where the true power lays.

Here is a VERY SIMPLE example to illustrate the point:

Take a 16 bit recording of a hand clap peaking at 0dB and apply a simple delay echo to it. Each echo has worse and worse signal to noise ratio as the volume drops off. The echo decays to about -92dB until it gets completely washed out in the noise floor.

Now take that same 16 bit recording and convert it to 24 bit, then apply the delay. The echo drops off -48dB before it sees any degradation in signal to noise (its original 92dB) then finally gets lost in the noise at about -140 dB.

Now if that's not a good example of the power of extra bits, I don't know what is.

In a 24 bit mix of 16 bit tracks there is obviously always noise down around -92dB. But other signals like delay and reverb tails don't get lost just because they are mixing with noise. If that were true you wouldn't be able to understand your wife/girlfriend saying "Turn that off!" when the TV cable goes out. Just by adding the very basics, delay or reverb, you dramatically increase the signal to noise ratio of your final mix.

Hope this helps.


barefoot

[barefoot]

The attached image shows a graphical representation of what a delay or reverb tail from a 16 bit track does in a 16 bit mix versus a 24 bit mix.

barefoot

7KB attachment

[TexRoadkill]

Mats- Hard drives are cheap now. Start recording in 24bit and get on with your life

[barefoot]

The noise floor of 8bit is clearly audible, so it makes for a good listening example of the point I tried to make earlier. And 16bit has 256 times the resolution of 8bit, just as 24bit has 256 time the resolution of 16bit. So, 16bit is to 8bit as 24bit is to 16 bit.
Make sense?

I took an 8bit hand clap file and added delay. Here is the result:

73KB attachment

[barefoot]

Now I took the same 8bit file, converted it 16bit first, then added the same delay processing. Any questions?

73KB attachment

[barefoot]

Finally, here is the processed 16bit file dithered back down to 8bit.

73KB attachment

[NYMorningstar]

There wasn't much difference between the 8bit or 16bit but the 8 bit did seem to trail off faster at the 3rd echo. The dithered file noticably had less quality with a definite hiss throughout. Does dithering always add this hiss? Is it less noticable dithering from 24bit to 16bit?

[sjoko2]

Originally posted by NYMorningstar
There wasn't much difference between the 8bit or 16bit

yeah aha right I see

[barefoot]

Originally posted by NYMorningstar
There wasn't much difference between the 8bit or 16bit but the 8 bit did seem to trail off faster at the 3rd echo. The dithered file noticably had less quality with a definite hiss throughout. Does dithering always add this hiss? Is it less noticable dithering from 24bit to 16bit?

NYMorningstar,
You must be listening through the cheapest computer speakers known to man.

barefoot