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[chrisj]

George, can I post a set of files to demonstrate my findings?
I ran off some experiments today and found that while white-noise didn't contain enough extreme high frequency stuff to be ABXable (when you SRCed it to .00001 away from what it was), it was possible to make pathological cases that were obvious.
The demo files I made are actually audible changes being produced through UPsampling. It works just as well to upsample from 44.099K. The reason is- DAW output can easily contain data flat-out illegal by the rules of the Nyquist sampling theorem.
The files are white noise 24db down, filtered in four ways- +1.75db/oct, +2.25db/oct, 3db/oct, and 6db/oct. The latter three are allowed to clip. Each of these are then copied, 'hacked' so they are supposedly 44.099K, and upsampled to 44.1K using two Audacity settings for sinc interpolation- the highest quality setting, and the lowest.
There's 12 files in all, and the 1.75db/oct ones should all be indistinguishable. As the level of clipping increases, and the amount of illegal content increases, the files become increasingly distinguishable. Note this isn't downsampling, and that the SRC routine is about as artifact-free as you can get (try it against sine sweeps, it's pretty flawless). What you'll be hearing is files containing increasingly illegal content, clipping the hell out of your DACs, and then the SRCed files lacking any such clipping or illegal content.
Be careful with levels! This is about as loud as sound files get, and it'll fry your tweeters if you crank it. Turn it right down so you can hear what it's doing to the DAC without other parts of the system being overloaded in turn.
So, George, can I start posting the files? Should I make a big zip maybe, or do 12 posts each with a file attached?

[Erik]

chrisj wrote on Thu, 19 August 2004 16:24

The reason is- DAW output can easily contain data flat-out illegal by the rules of the Nyquist sampling theorem.

Really, how?

Quote:

white-noise didn't contain enough extreme high frequency stuff

Really, how?

Quote:

copied, 'hacked' so they are supposedly 44.099K, and upsampled to 44.1K

Not sure how this on-disk masturbation relates to any real-world scenario.  What are you trying to demonstrate or prove?

--Erik

[chrisj]

How does almost 12 db RMS level difference grab you? People have masturbated over far far less, my dear Erik.
Here's the executive summary, and I have the files handy for when I figure out what to do with them.

Noise at -24db with a 6db/octave treble boost, grossly clipped to -0.002db RMS on average: after upsampling from 44.099K to 44.1K at high quality, -5.1db RMS on average. At low quality, -11.3db RMS on average. In each case, the difference was screamingly obvious and 16/16 ABX double-blind tested. This was the worst case, flat-out distorted and loaded with extreme high frequencies.

Noise at -24db with a 3db/octave treble boost, still clipped to -0.9db RMS:
After upsampling from 44.099K to 44.1K at high quality, signal averaged -4.1db RMS. A medium quality test was done and averaged -6.3db RMS. In both cases the sounds were still distinguishable double-blind 16 out of 16 times. Interestingly, the low quality, which averaged -9.8db RMS, was more difficult to distinguish- 14 out of 16, ABX testing.

Noise at -24db with a 2.25db/octave treble boost was still clipping, but averaged -4.89db RMS. In this case the high quality 'upsampling' was distinguishable from the original 15 out of 16 times- it was -6.6db RMS after the upsampling from "44.099" to 44.1 (note, these are exactly the same file, but the metadata was altered to make a copy pretend to be 44.099K and be SRCed up to 44.1). The medium and the low quality SRCs (this refers to the steepness of the filter- all have an ideal stopband) were -9.2db and -13.8db RMS, but neither could be distinguished from the original by ear- I got nine out of sixteen each time, proving I couldn't hear 'em in spite of the gross difference in amplitude, and in spite of the fact that I provably could hear the much closer 'high quality' version of the same thing.

Noise at -24db with a 1.75db/octave treble boost, upsampled at low and high quality SRC, could not be distinguished from the original at all. Seven out of sixteen on the ABX comparator for each. In spite of this, the original was -12.1db RMS, the high quality conversion was -13.2db RMS, and the low quality conversion was -19.3db RMS. These are major changes, but they are happening at too high a frequency to hear. The 1.75db treble boost version barely clips ever- I believe if you tuned it so it never quite clipped, and used an arbitrarily high-quality sinc interpolation SRC, the RMS loudness would be entirely unchanged.

Program content averaging -4.89db RMS loudness is extreme but not unheard of. My point is just this: program content rich in high frequencies and averaging -12db RMS is still hot enough to be illegal content that is distorting the DAC and would be eliminated by a high quality SRC (even one from the 'same' sampling rate upsampled to a microscopically higher one). High-frequency program content that's as high as -4.89db RMS, at ANY moment, is hot enough to be audibly distorted and obviously different when you filter out information that's beyond the Nyquist limit. High-frequency program content as hot as -0.9db RMS is just blatantly, obviously trashing the DAC and can be distinguished every time from the same thing filtered to let through only frequencies below Nyquist- hell, you can't HAVE high frequency content hotter than about -5db RMS without trashing the DAC in a provably obvious way. Just because the samples can be represented as 16 bit words doesn't mean squat.

So be warned.

How's that for 'prove'?

Files will be coming up as soon as I figure out what to do with 'em- there's about 3500K but I might just throw out the 'medium' interpolation examples and the 6db/octave ones, which are so obvious they're a waste of space.

[George Massenburg]

Chris,

It turns out that we can't do file sharing on this site.  Do you have an FTP site that you can upload fiiles to?

George

[chrisj]

Well, all right then-
The files are in a zip at
http://www.airwindows.com/analysis/MicroUpsampling.zip
I figure that's as good a name as any, for taking a file, cheating the metadata so it claims to be 44.099K and 'upsampling' it to 44.1K.
The files are 16 bit AIFFs.

[Erik]

Ok, now you've posted files on a website.  Impressive.

Can you please describe what you're proposing, or point me to a description of what you're trying to demonstrate?  There seems to be quite a few variables here and I'm not sure what your point is.

Beyond that, this relates to 456 and tape machines how?

--Erik

[chrisj]

Yeah. Gawrsh, this internot thingy sure is complimakated!
I know how to work e-mail too
Okay. The specific aspect of the 456 thread that I branched off with was a bit where I said, you could 'fix' certain things about certain over-hot DAW mixes by resampling- even if you were just 'bumping' the resampling a bit. Specifically, you can even upsample and kill a bunch of information IF it isn't really supposed to be there in the first place.
In other words- if you mix on an analog console, or master through analog gear, AND resample at pretty much your final output level, you are guaranteed to not have this type of distortion, because a properly working sampler WILL NOT encode information beyond the Nyquist limit. If it's working right, no matter what you put into it, you're not going to get anything out that'll clip the DACs. I think this is part of the reason Brad Blackwood can get really hot and lively treble without it being grating- he may be doing some of that in analog and resampling at 44.1K. In so doing, it guarantees he's not generating illegal data.
If you work in a DAW or otherwise all-digital, nothing is protecting you from putting on treble or gain sufficient to overload the DACs. Certain types of sound will be
(a) grating and obnoxious
(b) technically not legal within the constraints of a Nyquist-observing sampling system.
That's in spite of the fact that the actual samples can be represented within that system. The files that I submitted? Every one could be stepped down one LSB less than full scale, which would mean that technically the data would not 'clip'. Yet the result is still totally illegal within the theoretical system- represents values that can not be arrived at through correct sampling of an input waveform, no matter what input waveform you chose. It could only represent a waveform way hotter than the maximum theoretical limit of the sampler- and on playback, this of course distorts horribly.
I'm demonstrating that the danger point for this, when handling really hot high-frequency sound, is at least 4db down from full scale. That's worse than I expected, though I am using pathologically difficult sounds akin to hi-hats cranked through raw digital clipping- but these types of very high frequency transients are common in DAW mixes, I just made examples where it's impossible not to notice what happens.

I suppose I can turn around and ask a question in return. Within your understanding of digital audio, and given that it is possible to upsample digital audio with arbitrary degree of accuracy (assume perfect upsampling) and given that you have sample values that are not actually in excess of full scale- can you have information in a waveform that goes away when you UPSAMPLE? If so, what is it?

I have just proved that you can have information, easily generated through DAW processing, that does go away. I am proposing that this information is 'illegal' and could not be arrived at through direct sampling- and for that reason, it breaks the playback system of the DAC and reconstruction filter- and that this is undesirable, sounds awful and needs to be avoided.

If you're not cranking the treble and pushing levels to upwards of -5db RMS level in your mixing and mastering, you don't have to do a thing, as only serious DAW abuse causes this. However, I think that is more common than uncommon these days... you yourself may be doing it.

If you do- you could fix it completely, just by changing the sample rate of your stereo master to 44.099 and using high quality (such as sinc interpolation) SRC to resample it to 44.1K, which SHOULD be an imperceptibly insignificant change, not even a downsampling, but can clear the glare right up if you're causing it.

And that's where I came in- that is exactly the assertion I made in the other thread. It happens to be true- and the difference can be as extreme as 12db of 'illegal' energy removed, if you're really over the top with it. This can be measured. I measured it.

Another way this relates to tape machines is, tape machines also guarantee you won't have this problem- both by not having it in the first place, and by tending to roll the extreme highs where the problem would manifest. That's not a given, though- you can get illegal 44.1K content even off _vinyl_ if you sample at a very quiet level and then amplify. There's plenty of vinyl records that have information that would have to be restricted to fit onto CD. If you sampled them directly, the input filters get it- but if you sample them at greatly reduced volume, and normalize, you can end up with illegal data that overdrives the DACs even without having individual samples clipping.

[Erik]

I think you're mixing up a bunch of stuff here.  There's nothing at all "illegal" about any 44.1 file.  And there's nothing you can do in a DAW to create energy in that file that's "illegal."

If you process audio through a non-linear process, it's not going to generate higher frequency stuff than is supported by the sample rate in the file.  It will simply alias, and that energy is reflected downward, not upward.  Because, well, there's nowhere 'up' to go.

Likewise what you're talking about isn't a 'treble' phenomenon anyway.  Generate a 21kHz sine wave full scale.  Do your upsample trick.  Check for level and distortion, also check post DAC if you have the gear.  Having removed some variables, what does that tell you?

--Erik

[chrisj]

You are mistaken, at least three times.
It's trivial to create an 'illegal' 44.1 file, and to do it through DAW processing of a 'legal' file. Sampling theory assumes a finite peak amplitude, normally considered as digital full scale. If that is 32767 to -32768, you can take a long series of samples at -32767 and insert one that is 32766 in the middle, and the reconstructed waveform implied by this data is wildly beyond full scale and cannot be directly sampled by a properly designed converter. Hence, 'illegal'.
It's also trivially easy to produce this stuff in a DAW, like it or not, by treble boosting and amplification, particularly if you are permitting digital clipping.
Your one good point here is that doing this does not generate higher frequency stuff- if you tried to represent the DATA accurately it'd force you to go to a higher sampling rate, but within the context of a sampling system the illegal data do not represent higher frequency content- it represents higher AMPLITUDE than permissible.
Here's a question for you about the sine wave. When you generate a full scale 21 or 22K sine wave- where are the actual data points, the sample values? Because the sine is full scale, does that mean the 16 bit data are at 32767 and -32768? I submit that in a properly designed signal generator they are not, and if you have a wave done properly (with the data points REPRESENTING a correct waveform post-reconstruction) there will be no change at all from a SRC 'bump'.
Doesn't change the fact that there's loads of stuff out there which would be changed by such a process, that you can generate it trivially easy by EQ and amplification, and that it breaks the sampling system and contributes to distortion and bad sound.
I actually have not once said that processing could generate frequencies higher than Nyquist within a sampling system- just looked over my previous comments to be sure. I am saying that there can be illegal INFORMATION. The fact that applying a brickwall filter to 22.050K removes this information does not mean that the information is over 22.050K. It happens to be information at or just below 22.050K... that has an amplitude you can't have in a Nyquist sampling system. It's just good fortune that the same process is capable of addressing both problems.

[Erik]

When you use the term "bumping" in relation to tape machines and tape, I assume you were talking about head bump.

Likewise with all the references to "Nyquist" I thought you were talking about frequency.

There's nothing illegal about any of the data you mention.  And you're oversimplifying the DAC reconstruction "issue" as well.

What you're really talking about is amplitude, not frequency, and that has nothing to do with Nyquist/Shannon.

You're really talking about a Fourier transform.  Because you're reconstructing the signal it's generating new signals.  Variations in amplitude caused by this are both simpler and more complex that what you're talking about above.  I assume you're generally interested in this stuff (which is why I bother) so I suggest you read up on Fourier and write a little code, with various filters, to explore and learn.

But your current scheme is basically to use SRC as a gain drop and a smoothing filter without understanding all the tradeoffs involved.

To the extent the goal is to reduce the level of the file to prevent the alleged "DAC clipping" problem, I'd say you're much better off just applying trim than going through these gymnastics.

And, repeat: there's nothing illegal in the files or the data you mention.

--Erik

[chrisj]

*sigh* and heavily limited high frequency material can be loaded with 'illegal' data that clips DACs because it represents a legitimate waveform that is considerably higher in amplitude than digital full scale.
I'm honestly sorry if I've erred in interpersonal ways here- thought I was being very nice. I'm quite sick this week and my fiance has been so sick that she cannot eat, causing me to be very worried. It's possible that the force of this tangent is driven by such personal reasons, and in other situations I might have entirely let it slide.
The content stands. I'll get a page about it added to my website (still desperately in need of updating) and be done with it.

[Erik]

Paging Nika... cleanup aisle three.

--Erik

[chrisj]

Nika will only confirm the existence of 'illegal' data in a 16 bit file that's supposed to be used for digital audio reconstruction. So has Pricey- I've just established differences of up to around 12db RMS, not less than a db. This is not MY idea, it's well known in the field- you'd find discussions about it under the term 'Gibb Effect'. This refers to a reconstructed waveform going beyond the power supply rails. All I've done is quantify it and ABX double-blind test the audibility of the effect using a pathological case or three. That's _all_ I've done.
Did come up with a page about it (linking to the files) at http://www.airwindows.com/analysis/MicroUpsampling.html. It says nothing that hasn't been said in this thread.

[bobkatz]

I think the problem here is Chris's definition of "illegal data"! As Eric is trying to point out, there's nothing illegal about the data in Chris's examples. The fact is that you can put out a CD of square waves at full scale and it will be legal. Anything you can put onto a redbook CD is by definition legal. If it fits in 16 numbers, it's legal, by definition.

However, what Chris is trying to talk about, and if he didn't use the words "are illegal", he'd be fine, is the fact that music can contain levels which "should" be illegal. Levels which when fed through a reconstruction filter such as in a DAC, or nearly any kind of filter, such as an SRC, or and MP3 encoder, or a broadcast chain (get my point!!!!)----will produce overload distortion because they produce output levels (generally, in the analog domain) which are higher than 0 dBFS.

It's as simple as that, and I do intend to cover this area in more detail in my book's second edition, though Paul Frindle covers it to a reasonable extent in his recent post: "When tracking or mixing, If all you have is a standard digital peak meter, it is advisable to keep your levels below -3 dBFS." This is a very safe level. Leave it to the mastering engineers to screw it up beyond that.

And Thomas Lund covers it in great detail at http://www.tcelectronic.com/media/nielsen_lund_2000_0dbfs_le .pdf

Hope this post helps!

BK

[Nika Aldrich]

Erik wrote on Sat, 21 August 2004 17:23

Paging Nika... cleanup aisle three. --Erik

Erik,

Sorry, I'm so lost on what is being said here that I don't know how to contribute.

Does this have to do with waveforms that can be constructed in a digital environment that are meant to represent waveforms that exceed full scale?  It sounds as though this may be the case?

To Bob Katz - yes, the definition of the word "legal" in this context can get difficult, but we often use that term to describe a waveform that fits within the bounds of the Nyquist requirements and thus will be accurately reconstructed.  A waveform that contains content above <.5sample rate has "illegal content," and a waveform that exceeds full scale, despite no individual samples exceeding full scale, also has "illegal content."  I assume this is how the term was being used?

Nika.