Let's develop an ASR inter-sample test procedure for DACs!

[NTTY]

Hi everyone,

In my previous example, it was a 5512.50Hz at 67.5° phase shift. It creates an harmonic at 16537.5Hz if clipped. That’s why I like this test tone, also because it creates a peak level up to +0.69 dBFS “only” and in audio band. So I kind of expect all DACs to handle well at least this one.

And back to my example with 5512.50Hz on the Teac VRDS-25X, it obviously massively overloads its ASRC and generates non-harmonic distorsion components at -60dB from 1kHz to 3kHz. We can only hope for the rest of the music to hide that.

I agree the 11025kHz is an extreme case. But if not real, it could demonstrate resistance of a DAC when fed with hot records that have suffered from loudness war. In the end, the only intention here is to show the difficulty of a DAC to deal with 0dBFS+ levels.

I know my case is different because I like to use CD players, and after 40+ years of having bought so many CDs - a lot being too hot - I’m eager to know which player is likely to best handle them.

From my reviews of CD players here, I discovered a lot of members still use them as transports feeding an external DAC, which might not offer digital volume control from S/PDIF inputs prior to feed their ASRC/SRC/OS filters. I think it’s interesting to know.

In terms of audibility, I’ll play with the Teac and see how I can share some test files with the community. That requires time though and is a different beast to cope with. In the meantime, I’ll continue to test IS over resistance

 

[tccalvin]

The signal that is usually shown to illustrate intersample-overs is a "double unicorn". To show a sine wave that has no sample >1 and yet have peaks of +3 dBFS, you have to satisfy 2 conditions exactly:

1. Signal frequency is exactly fs/4 (i.e. 1/4 of the sampling frequency)
2. Timings of when the samples are taken at phase angles: π/4, 3π/4, 5π/4, 7π/4, ...

View attachment 405134

That means the probability of this signal happening is similar to winning two lotteries in a row. If the signal is just a teeny tiny bit off, you'll find yourself with clipped samples, and that means the signal is irreversibly corrupted and cannot be reconstructed to resemble its original analog form.

Below shows a sine wave that is 0.24 fs and has peaks of 1 dB over full scale. The animation shows what happens when the timing of the sampling changes. The plot shows a little less than 4 full periods of the sine signal (each horizontal division is 2 sampling periods = 1 period at Nyquist frequency). The blue curve is the original signal, and the dashed red curve is the mathematically correct reconstructed signal. With less than 4 wave periods, in no case do we have all unclipped samples. Therefore the original and reconstructed signals cannot be the same.

View attachment 405136

So therefore, if you have more than a few intersample-over instances, it is almost guaranteed that you'd have clipped samples. While it is nice to be able to reconstructed the clipped signals the mathematically correct way, they are not going to resemble the original. The information to accurately reconstruct is forever lost due to clipping.

The real problem is that we have signal peaks over full scale in the source (hello loudness war). Having headroom to "reproduce intersample-overs" is just putting lipstick on pigs.

I've been reading your post over and over in order to make sense of your point.

I'm sorry but I failed.

I'm not sure what you are trying to say and to me your explanation seems like it's contradicting itself at points.

You have posted very similar graphs and animations earlier in this discussion. I'm sorry but to me it looks like these illustrations don't depict the issue at hand.

Are you perhaps implying that the original analog waveform in a recording is forever lost because the dynamic range is compromised when the digital volume is lowered? If that's the case, I see your point. However since we're talking about a -3dB to -6dB level reduction in DACs that can reach 120dB SINAD it would be hard (dangerous, even) for your ears to detect such little loss of information. That is assuming the original wave even had 120dB of dynamic range to begin with.

Am I misunderstanding? I'm trying my best here.

EDIT: I also don't get why you're trying to say that the issue is as rare as winning the lottery twice or that it's a "double unicorn". We have an abundance of evidence in this thread that recordings of all kinds can contain hundreds of ISPs. Why limit ourselves to theory when we can look at the empirical data?

 

[popej]

We have an abundance of evidence in this thread that recordings of all kinds can contain hundreds of ISPs.

The idea is simple. If we have hundreds of ISP, then we probably have thousands of clipped samples as well.

 

[tccalvin]

The idea is simple. If we have hundreds of ISP, then we probably have thousands of clipped samples as well.

What exactly do you mean by clipped samples? I'm genuinely trying to understand.

 

[popej]

If you increase volume of digital signal over 0dB then you should notice both: ISP above 0dB and samples above 0dB. The best way to handle saples is to reduce them to 0dB and this is clipping.
Now we discuss what DAC is doing with ISP and we don't like the idea of clipping ISP when upsampling. But whatever it is doing to ISP, it won't restore already clipped samples.

 

[tccalvin]

If you increase volume of digital signal over 0dB then you should notice both: ISP above 0dB and samples above 0dB. The best way to handle saples is to reduce them to 0dB and this is clipping.
Now we discuss what DAC is doing with ISP and we don't like the idea of clipping ISP when upsampling. But whatever it is doing to ISP, it won't restore already clipped samples.

Okay... You're talking about normal digital clipping.

Sure, we could check how many recordings have actual peaks (the non-inter-sample kind) over 0dBFS and it would be interesting. I'm willing to believe that the percentage of clipped samples found in professionally made masters is close to 0, but it would still be cool to measure.

But I just don't see how this is relevant to the conversation. Sure, a signal that's digitally clipped can't be recovered while a signal with ISOs can. And...? Now what...?

 

[popej]

Now what...?

The problem remains
I think clipping introduce ISP too. Test for ISP can be an indication, how well DAC handle clipping.

 

[NTK]

But I just don't see how this is relevant to the conversation. Sure, a signal that's digitally clipped can't be recovered while a signal with ISOs can. And...? Now what...?

The origin of ISO is that the original analog signal or synthesized signal in floating point format) have peaks above full scale. Below is how it is often illustrated.

This picture shows an extremely rare event (a measure zero in measurement theory). There is a sine wave with peaks at 3 dB (1.414) above full scale, but the digitized samples are all within full scale. This case can only happens when the samples are digitized at the exact right moments, and the signal frequency is exactly fs/4.

Let see what happens if the samples are digitized just a little bit later than the above picture. We've got clipped samples! The signal was above 1.0 when the clipped samples were digitized.

If they were digitized just a little earlier, same thing happens.

How about if the frequency is not exactly fs/4 (in this case, it is 0.24 fs).

Therefore, you'll need an almost infinite amount of luck to get what is usually shown -- you've got ISO but without clipped samples. Needless to say, that extremely rarely happens in real life. So, if your signals have ISO, it is almost certain that you've got clipped samples.

 

[melowman]

@NTK what you demonstrate does not happen in reality. You describe a situation where someone would record an analog signal very hot at the point of clipping. Nobody (mainly recording engineers) do that. This is Recording 101. Even the so called ‘bedroom producers’ don’t do that

 

[popej]

This is Recording 101

This is the loudness war.

 

[melowman]

Nope. The loudness war does not happen when recording analog signals (vocals, instruments, etc.). It is foolish to think otherwise
No audio engineer on Earth records at the point of clipping. None.

 

[NTK]

Nope. The loudness war does not happen when recording analog signals (vocals, instruments, etc.). It is foolish to think otherwise
No audio engineer on Earth records at the point of clipping. None.

The problem doesn't need to be originated at the recording stage of the process. It can (and most often) happen during mastering too. Same effects. If people actual follow the whatever 101's, there should never be any ISO's.

 

[melowman]

The few mastering engineers who clip their converters, do it purposefully with critical listening. Only a few select mastering engineers still do that today; the immense majority of masters does not go through that process — 100% digital clipping is used instead (i.e. not going through DA/AD).

You just can’t state: “the presence of ISOs most certainly implies that clipping occurred during A to D conversion”, as a general rule.

Also, it’s been discussed earlier: in the digital realm, the unfortunate thing is that there has been no “101” hard rules regarding digital headroom. No enforced norm, no standard, no nothing. So naturally a race for loudness occurred - just because we can and noone forbids one to do so. The rest is history.

 

[KSTR]

The reality is what it is.

IMHO, a DAC shall not make strong assumptions about its input signal and thus it should handle IS-overs gracefully, within reasonable practical limits.

No one is expecting that IS-overs beyond 2..3dB or so are faithfully reproduced so the only way to keep demands on additional headroom practical is stable soft clipping beyond that point in order to never exceed 3..4dB final output (of the DAC chip voltage or current).

On the input/digital side of a DAC chip, in upsampling and filter stages (or re-sampling, at times), 12dB headroom would be nice to have, in order to give the soft-clipper a signal to work upon.

4dB headroom on top of on a 2Vrms nominal output means +-4.5Vpeaks which can be handled even with a measly +-5V supply when rail-to-rail opamps are used.

The purpose of this thread was and is to find a simple and practical test that weeds out the crap which does not gracefully handle even tiny IS-overs.

 

[tccalvin]

The origin of ISO is that the original analog signal or synthesized signal in floating point format) have peaks above full scale. Below is how it is often illustrated.

This picture shows an extremely rare event (a measure zero in measurement theory). There is a sine wave with peaks at 3 dB (1.414) above full scale, but the digitized samples are all within full scale. This case can only happens when the samples are digitized at the exact right moments, and the signal frequency is exactly fs/4.

Let see what happens if the samples are digitized just a little bit later than the above picture. We've got clipped samples! The signal was above 1.0 when the clipped samples were digitized.

View attachment 405174

If they were digitized just a little earlier, same thing happens.

View attachment 405175

How about if the frequency is not exactly fs/4 (in this case, it is 0.24 fs).

View attachment 405176

Therefore, you'll need an almost infinite amount of luck to get what is usually shown -- you've got ISO but without clipped samples. Needless to say, that extremely rarely happens in real life. So, if your signals have ISO, it is almost certain that you've got clipped samples.

I see what you mean now. Unfortunately, that’s not how it works.

Every wave for which the sample points don’t line up exactly with the peak of the wave will have higher amplitude than what the samples would suggest.

I spent way too much time doing this graph. Math is not my forte.

These waves all have the same frequency but different amplitude and phase.

As you can see, the samples don’t even have to hit 0dBFS (or 1 in this case) for the reconstructed wave to go over the threshold. This is the issue we’re trying to solve.

EDIT: Typos.

 

[restorer-john]

IMHO, a DAC shall not make strong assumptions about its input signal and thus it should handle IS-overs gracefully, within reasonable practical limits.

That's back to front thinking and really doesn't help the issue.

If every DAC maker decides overnight to handle 3dB overs "gracefully", what do you think will happen? Recording will increase in level yet again and we'll be needing another adjustment, this time requiring sophisticated signal waveform prediction and reconstruction in real time to account for bad recordings.

It's too hot recordings and unnecessary oversampling after the fact causing the "problem".

 

[VientoB]

That's back to front thinking and really doesn't help the issue.

If every DAC maker decides overnight to handle 3dB overs "gracefully", what do you think will happen? Recording will increase in level yet again and we'll be needing another adjustment, this time requiring sophisticated signal waveform prediction and reconstruction in real time to account for bad recordings.

It's too hot recordings and unnecessary oversampling after the fact causing the "problem".

No, recordings cannot increase in level. You're missing the point. The samples are presently at the max and the peaks in between go over the max.

 

[NTK]

As you can see, the samples don’t even have to hit 0dBFS (or 1 in this case) for the reconstructed wave to go over the threshold. This is the issue we’re trying to solve.

Yes. The reconstructed waveform can peak above the samples, and my figures showed that.

I'd suggest a simple numerical experiment. To make the math a little simpler I'll use a sampling rate of 1 (i.e. t = 0, 1, 2, 3 ,4 5, ...).

• You can use a spreadsheet to calculate: w = A sin( 2 π f (t + δt) ) for a number of t's.
• The usual illustrations use A = sqrt(2), f = 0.25 and δt = 0.5.
• Try a smaller A and a slightly different f, and see how many periods of the waveform it takes before you hit w > +/-1. There you have clipped samples.
• Think what the probability of not having clipped samples will be with real life signals.

Remember that most of the frequency contents in whatever we listen to are mostly of frequencies << fs/4 (for redbook CD fs/4 = 11 025 Hz).

 

[TNT]

As someone said - it happens at 11 kHz and the first harmonic is a 22kHz... so:

a) is this really a SQ problem? Probably not at all...
b) no, its not technically "nice"! Beauty contest prizes for grabs...

Q: Could anyone detect a 3dB compression at 11kHz - what music contains such levels at such frequencies?

//

 

[Sokel]

Going more on my atypical hunt for IS-overs we scanned my nephews library (21 yo now) but not the classical/study section.
We scanned what goes around these days with popular stuff along with some stuff like Evanescence,Wolfsheim but pop too and the shorts.

To cut the long story short,it's a horror story,specially the metal-ish stuff,something like a 10% of these specially some (unknown to me) smaller ensembles.
And to listen to them is just that,the glare that pure,old clipping brings,it does not shout "IS-Overs",it shouts bad recording intended to play low and stick out as loud.
It makes 50 yo stuff of Deep Purple for example to look SOTA,despite the age.