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

[tccalvin]

In that case, I would probably chalk this up as a curious aliasing effect. Sampling at only peak, trough and null values can lead to weird outcomes. Nyquist's theorem doesn't guarantee that every assortment of samples will lead to a correct reconstruction of the original waveform. Consider for example a set of samples that all fall on the null crossings of a sine wave, You're left with nothing, i.e. catastrophic, uncorrectable aliasing.

This is a violation of the Nyquist theorem, as it states that all signals must have frequency componentes below half the sampling frequency. It doesn' say how much below though, as far as I know.

The frequency of that test signal is (slightly) below fs/2 so it is a valid signal.

 

[danadam]

The frequency of that test signal is (slightly) below fs/2 so it is a valid signal.

How so? Any discontinuity requires infinite bandwidth and that signal looks to me like it has a discontinuity (i.e. the abrupt start/end).

Also doing longer and longer FFT:

x = repmat( [1 -1], 1, 8 );

x1 = [ zeros(1, 8),   x, zeros(1, 8)   ];
x2 = [ zeros(1, 64),  x, zeros(1, 64)  ];
x3 = [ zeros(1, 512), x, zeros(1, 512) ];

y1 = abs( fftshift( fft(x1) ) );
y2 = abs( fftshift( fft(x2) ) );
y3 = abs( fftshift( fft(x3) ) );

y1( [1:4 end-3:end] )
y2( [1:4 end-3:end] )
y3( [1:4 end-3:end] )

shows that that the outward bins contain energy:

ans =
   16.00000   10.20230    0.00000    3.44489    0.00000    3.44489    0.00000   10.20230

ans =
   16.000   15.678   14.736   13.241   11.299   13.241   14.736   15.678

ans =
   16.000   15.994   15.975   15.944   15.901   15.944   15.975   15.994

I guess it may be that in the limit it will turn out that fs/2 has no energy, but I don't think it was shown/proved anywhere.

And plot for y3:

freqs = linspace(0, 1, length(x3)) - 0.5;
plot(freqs, y3);
xlim([-.5 .5]);
xlabel("freq");
ylabel("mag");
title(["FFT " num2str(length(x3))]);

 

[tccalvin]

How so?

It's just a simple observation. You can clearly see the reconstructed wave slowing down from fs/2 (it lags behind the samples for a while) at the point where the samples switch from the value of 0 to the value of +1/-1. And you can also see it speeding back up and slowing down when the sample values go from +1/-1 to 0 again. That's what happens when band-limited signals have to go through an abrupt change in amplitude, like in the case of square waves.

I'm not going to pretend I understand more than this, so I'll leave the simulations to you guys lol.

 

[LTig]

The frequency of that test signal is (slightly) below fs/2 so it is a valid signal.

No. If all samples fall on the null crossings of a sine wave its frequncy is exactly fs/2. This is not valid.

 

[tccalvin]

No. If all samples fall on the null crossings of a sine wave its frequncy is exactly fs/2. This is not valid.

Yes, this would be true of a series of "zero" samples, or even of a series of +1/-1 samples. But a band-limited signal containing +1/-1 samples preceded and followed by silence ("zero" samples) will describe a slightly different wave that has energy below Nyquist, and that energy is responsible for creating ISPs. At least, that is my limited understanding of the phenomenon.

 

[danadam]

But a band-limited signal containing +1/-1 samples preceded and followed by silence ("zero" samples) will describe a slightly different wave that has energy below Nyquist,

I don't think such signal is band-limited.

Here's 0.1ms-long signal at 16x48 kHz sampling rate:

The second half is 12 kHz and it has 16-samples-long fade-in. Spectrum shows that the signal is properly band-limited for its sampling rate:

If we just pick every 16th sample then the result is a repeating 0, +n, 0, -n sequence. Such sampling is obviously not correct because the input signal wasn't limited to 24 kHz bandwidth:

You also get a repeating 0, +n, 0, -n sequence when you directly generate 12 kHz at 48 kHz sampling rate with an abrupt start. So I think it's easy to see that signals with abrupt start are not band-limited.

Properly band-limited start of the signal looks in this case like this:

And here are three 10s-long signal. They start and end with 2.5s of silence. In the middle they have 5s of 6 kHz signal with varying duration of fade-in and fade-out (0.01s, 0.1s, 1s):

You can see that changing the signal level adds frequency components both below and above the base frequency. I think this shows that Fs/2 signal with varying level cannot be limited to (0:Fs/2) bandwidth.

 

[tccalvin]

I don't think such signal is band-limited.

Here's 0.1ms-long signal at 16x48 kHz sampling rate:

View attachment 478451

The second half is 12 kHz and it has 16-samples-long fade-in. Spectrum shows that the signal is properly band-limited for its sampling rate:

View attachment 478452

If we just pick every 16th sample then the result is a repeating 0, +n, 0, -n sequence. Such sampling is obviously not correct because the input signal wasn't limited to 24 kHz bandwidth:

View attachment 478453

You also get a repeating 0, +n, 0, -n sequence when you directly generate 12 kHz at 48 kHz sampling rate with an abrupt start. So I think it's easy to see that signals with abrupt start are not band-limited.

Properly band-limited start of the signal looks in this case like this:

View attachment 478454

And here are three 10s-long signal. They start and end with 2.5s of silence. In the middle they have 5s of 6 kHz signal with varying duration of fade-in and fade-out (0.01s, 0.1s, 1s):

View attachment 478455

You can see that changing the signal level adds frequency components both below and above the base frequency. I think this shows that Fs/2 signal with varying level cannot be limited to (0:Fs/2) bandwidth.

Fair enough.

 

[John_Siau]

If the solution is to reduce dynamic range, it means that you disadvantage huge amount of music that doesn't have this problem in order to deal with small amount of content. In other words, if the headroom is permanently built into the DAC, then you lose that dynamic range for all uses, not just in the case of intersample overs. This is one of the reason that the DACs that have this feature are not at the top of our chart.

The right solution is to have an option in the music player to perform the dynamic range reduction on a per track basis. An online database could be built to instruct the player to do this automatically.

I completely disagree!

This is a problem the affects nearly half of all CD-format recordings.
Archimago recently analyzed 31,400 tracks in his personal music library. 44% contained peaks exceeding 0 dBFS.

Please see:
Archimago's Musings - August 9, 2025

He found that he needed the following amounts of DSP headroom the play 99% of the tracks in each of the following genres:

Classical +0.79dB
Soundtracks +1.70dB
Vocals +1.82dB
Country +1.89dB
Hard Rock/Metal +2.03dB
Classic & Progressive Rock +2.35dB
Jazz & Blues +2.42dB
Pop +2.87dB
Rap / Hip-Hop +3.08dB
Electronica +4.22dB

The dynamic range of most DACs now exceeds what is usable in most listening situations. If the peak SPL at the listening position is 115 dB, then any DAC with a 115 dB or better dynamic range will not produce any audible noise at the listening position (assuming the DAC is properly gain staged to the power amplifier). If we allocate 3 dB to headroom, then we would need a DAC with a 117 dB or better dynamic range. A large portion of the DACs tested by Amir exceed this dynamic range requirement.

Trading a few dB of dynamic range to eliminate hard DSP overload clipping is a good tradeoff.

As things stand now, most DACs cannot properly play 44% of the CD tracks that are in Archimago's library. One reader scanned 11,588 tracks and found similar results.

The sad truth is that most DACs cannot properly play nearly half of all CD-format recordings. Many DACs have far more dynamic range than needed, and some of this should be traded off to provide headroom above 0 dBFS.

The biggest problem is that Archimago is about the only person testing DACs for digital headroom.

Amir needs to get on board with this test if this site is going to continue to be a go-to site for DAC reviews.

 

[tmtomh]

I completely disagree!

This is a problem the affects nearly half of all CD-format recordings.
Archimago recently analyzed 31,400 tracks in his personal music library. 44% contained peaks exceeding 0 dBFS.

Please see:
Archimago's Musings - August 9, 2025

He found that he needed the following amounts of DSP headroom the play 99% of the tracks in each of the following genres:

Classical +0.79dB
Soundtracks +1.70dB
Vocals +1.82dB
Country +1.89dB
Hard Rock/Metal +2.03dB
Classic & Progressive Rock +2.35dB
Jazz & Blues +2.42dB
Pop +2.87dB
Rap / Hip-Hop +3.08dB
Electronica +4.22dB

The dynamic range of most DACs now exceeds what is usable in most listening situations. If the peak SPL at the listening position is 115 dB, then any DAC with a 115 dB or better dynamic range will not produce any audible noise at the listening position (assuming the DAC is properly gain staged to the power amplifier). If we allocate 3 dB to headroom, then we would need a DAC with a 117 dB or better dynamic range. A large portion of the DACs tested by Amir exceed this dynamic range requirement.

Trading a few dB of dynamic range to eliminate hard DSP overload clipping is a good tradeoff.

As things stand now, most DACs cannot properly play 44% of the CD tracks that are in Archimago's library. One reader scanned 11,588 tracks and found similar results.

The sad truth is that most DACs cannot properly play nearly half of all CD-format recordings. Many DACs have far more dynamic range than needed, and some of this should be traded off to provide headroom above 0 dBFS.

The biggest problem is that Archimago is about the only person testing DACs for digital headroom.

Amir needs to get on board with this test if this site is going to continue to be a go-to site for DAC reviews.

I think your final sentence is a bit over the top, but otherwise I take the point of your post. It seems to me that your recommended solution and @amirm's recommended solutions are both theoretically equally valid, but on a practical level I'd agree with you that an industry standard of built-in headroom of 3-5dB for DACs - or at the very least the promotion of a culture of disclosure that would increase broad market demand for this feature in DACs - is the more workable solution. I think it would be fairly simply for music players to incorporate the dynamic system Amir describes - but I am less optimistic about the feasibility of creating, maintaining, and keeping up to date an online database of which CDs need to have this feature enabled and how much headroom each one needs.

 

[John_Siau]

I think your final sentence is a bit over the top, but otherwise I take the point of your post. It seems to me that your recommended solution and @amirm's recommended solutions are both theoretically equally valid, but on a practical level I'd agree with you that an industry standard of built-in headroom of 3-5dB for DACs - or at the very least the promotion of a culture of disclosure that would increase broad market demand for this feature in DACs - is the more workable solution. I think it would be fairly simply for music players to incorporate the dynamic system Amir describes - but I am less optimistic about the feasibility of creating, maintaining, and keeping up to date an online database of which CDs need to have this feature enabled and how much headroom each one needs.

I don't mean to be "over the top", but I don't understand the resistance to testing for a known problem that can create high-level distortion products when playing a large percentage of the available CD-format material.

This is a DAC hardware problem. It is easy to solve in hardware, and it is easy to test the hardware. It is very hard to solve this problem with other methods.

 

[JIW]

[...]
As things stand now, most DACs cannot properly play 44% of the CD tracks that are in Archimago's library. One reader scanned 11,588 tracks and found similar results.
[...]

The volume control on the latest ESS chips is before the interpolator so headroom for ISOs can be introduced this way. AKM seems to do it the same way in the latest designs assuming DATT is the digital attenuator since the attenuator is referred to as ATT later in the data sheet (see e.g. AK4191). In the cheaper stand alone devices with volume control, this is likely the typical implementation. How many other DACs are there besides them to make them a minority? Also, is this about DACs in use, recently released or something else and by total number produced or the total number of products?

 

[tccalvin]

this is likely the typical implementation

This is exactly the problem.

Why can't we know for sure how a DAC handles ISPs? Why do we have to be in the dark and rely on guessing or on chip specifications?

I'm not just asking reviewers but also the people who strongly resist acknowledging ISPs as a significant issue.

We don't have that kind of approach with SINAD numbers, for example. We don't just assume that "it's likely fine" even though virtually all DACs use the same chips that we already know.

 

[danadam]

I completely disagree!

You already replied to the same message almost a year ago

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

Oct 1, 2024

If the solution is to reduce dynamic range, it means that you disadvantage huge amount of music that doesn't have this problem in order to deal with small amount of content. In other words, if the headroom is permanently built into the DAC, then you lose that dynamic range for all uses, not just in the case of intersample overs. This is one of the reason that the DACs that have this feature are not at the top of our chart.

The right solution is to have an option in the music player to perform the dynamic range reduction on a per track basis. An online database could be built to...

• John_Siau

• 

 

[JIW]

This is exactly the problem.

Why can't we know for sure how a DAC handles ISPs? Why do we have to be in the dark and rely on guessing or on chip specifications?

I'm not just asking reviewers but also the people who strongly resist acknowledging ISPs as a significant issue.

We don't have that kind of approach with SINAD numbers, for example. We don't just assume that "it's likely fine" even though virtually all DACs use the same chips that we already know.

SINAD depends on several factors besides the DAC chips used. Manufacturers could also reveal the relevant part of the digital signal flow and let the consumers decide what to do with it.

 

[IPunchCholla]

This is a DAC hardware problem. It is easy to solve in hardware, and it is easy to test the hardware. It is very hard to solve this problem with other methods.

But it is also a cultural problem. It is a technically easy solution that you will need to get manufacturers to agree to, simultaneously. Or a regulatory authority to enforce. Since DACs are marketed in SINAD or THD

I'm not just asking reviewers but also the people who strongly resist acknowledging ISPs as a significant issue.

is it a significant issue? I haven’t seen any data on audibility of ISOs. I might have missed it even though I’ve been following this thread for a while.

I agree it is an engineering issue. But right now, until someone demonstrates audibility thresholds, it’s sorta like worrying about SINADs > 80. I would prefer higher, but it’s not like I can actually hear a difference.

 

[morillon]

But it is also a cultural problem. It is a technically easy solution that you will need to get manufacturers to agree to, simultaneously. Or a regulatory authority to enforce. Since DACs are marketed in SINAD or THD

is it a significant issue? I haven’t seen any data on audibility of ISOs. I might have missed it even though I’ve been following this thread for a while.

I agree it is an engineering issue. But right now, until someone demonstrates audibility thresholds, it’s sorta like worrying about SINADs > 80. I would prefer higher, but it’s not like I can actually hear a difference.

if it is not present in "classical" or very acoustic...it is because it would be audible in these circumstances...more demanding...

 

[tccalvin]

is it a significant issue? I haven’t seen any data on audibility of ISOs. I might have missed it even though I’ve been following this thread for a while.

I agree it is an engineering issue. But right now, until someone demonstrates audibility thresholds, it’s sorta like worrying about SINADs > 80. I would prefer higher, but it’s not like I can actually hear a difference.

I personally haven't found a study that proves that ISPs are audible yet.

On paper, depending on how the DAC reacts to the overloads, the added distortion can be much more audible than sub-optimal SINAD.

Still, we take great care not to overload ADCs when we are recording. We make sure to avoid clipping during audio processing. We rightfully complain about masters being too loud and compressed and we try pushing the industry to lower mastering levels. We test DACs thoroughly to confirm they are degrading the signal as little as possible with unwanted distortion/noise.

You could argue that none of these precautions are necessary because "people wouldn't notice anyway" (I'm sure I would have a lot of trouble spotting clipping anywhere without a meter), but these practices are necessary to preserve the information that we want to record/reproduce.

Yet, when it comes to taking measures to prevent clipping in DACs we're like "lol, whatever".

If we can avoid degradation of digital signals, why wouldn't we do it?

 

[IPunchCholla]

I personally haven't found a study that proves that ISPs are audible yet.

On paper, depending on how the DAC reacts to the overloads, the added distortion can be much more audible than sub-optimal SINAD.

Still, we take great care not to overload ADCs when we are recording. We make sure to avoid clipping during audio processing. We rightfully complain about masters being too loud and compressed and we try pushing the industry to lower mastering levels. We test DACs thoroughly to confirm they are degrading the signal as little as possible with unwanted distortion/noise.

You could argue that none of these precautions are necessary because "people wouldn't notice anyway" (I'm sure I would have a lot of trouble spotting clipping anywhere without a meter), but these practices are necessary to preserve the information that we want to record/reproduce.

Yet, when it comes to taking measures to prevent clipping in DACs we're like "lol, whatever".

If we can avoid degradation of digital signals, why wouldn't we do it?

All true, and I can’t think of a reason (other than time) to not test all DACs going forward.

 

[Geert]

if it is not present in "classical" or very acoustic...it is because it would be audible in these circumstances...more demanding...

It’s because most classical music has an higher dynamic range (the music itself as well as how it is mastered), is less repetitive (not beat driven) and has no synthesized audio signals. There’s no clear evidence that ISP’s are audible yet, so we certainly can’’t make a breakdown of audibility per genre.

 

[morillon]

It’s because most classical music has an higher dynamic range (the music itself as well as how it is mastered), is less repetitive (not beat driven) and has no synthesized audio signals. There’s no clear evidence that ISP’s are audible yet, so we certainly can’’t make a breakdown of audibility per genre.

If the dynamic range, even in classical music, is often a bit reduced despite everything... this is precisely the area where one might have been tempted to push the upper limits... The fact is that in the "variety" domain, isp don't seem to be a problem, even at a significant proportion... This is in line with the fact that it will also support digital compression (MP3, AAC, etc.) at fairly high levels (which won't be the case in very acoustic music...)
But.... chhhuuuuuutttt...
;-)