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TIME-DOMAIN TRANSIENT RESPONSE TESTS OF ADI-2 DAC FS & BIFROST MB DAC’s

[Edit/]
So I've learned a ton since I first posted this, less than a week ago, so I am adding edits to this original post (but preserving all the text, not removing anything) so that my errors don't mislead anyone or cause people to draw false conclusions. The main thing this first post does is capture the DSP filter response of the RME ADI-2 DAC FS, with the filter set to "SD Sharp", and the Schiit Bifrost Multibit. Later in this thread I capture the other filters.[/Edit]

Recently, I decided to take my work headphone listening setup to the next level, and get better headphones and a DAC and an amp (or a DAC / Amp combo unit) to go with them, so I started digging into head-fi and online reviews and websites again, wondering excitedly what new stuff from my favorite (or exciting new) companies had come along while I had been listening contentedly to my Sonos PORT +TIDAL lossless --> Bifrost Multibit (Gen 1) --> Asgard 2 --> Audeze LCD-2 set up.

Of course, one of the first things I did was go to Schiit’s website to see what was on offer, and was thrilled to see a Bifrost 2 with an ever better multibit implementation!

Because, I have to say, of all my hi-fi audio purchases, the Bifrost Multibit was one of the best and most important. Finally, finally, I was experiencing the kind of audio bliss I had been seeking, and even from just my Senn 595’s. To my ears, there was such a lovely detail and air and cleanness to the music, without any of the edge and digital glare I had been experiencing, to one extent or another, for years. I had sometimes heard that the DAC really didn’t make much difference and that if you thought you were hearing significant differences that you were fooling yourself (and the same for amps, provided they had enough power to avoid clipping), but after years of improving my headphones, and my sound-file source quality, and trying higher powered amplifiers, and not really feeling like there was much of a difference, I was ready to take advantage of Schiit’s 15 day return policy and give a high(er) end DAC a try to see if that was the missing piece of the puzzle in my quest.

And, well, it was. Was it ever! My Bifrost 1 Multibit was a revelation to me. I was so happy with it!

So, I was pretty excited about Bifrost 2! And I figured I’d go balanced and get the Jotunheim 2 (all to go with the Audeze LCD-XC 2021 carbon’s I had on order). Woo hoo! Yea!

While I was waiting for my Schiit order to get fulfilled, I got the LCD-XC’s, and while I did love their sound on the whole, I personally found it a bit too hot in parts of the treble to be as non-fatiguing as I would like. So then I was also thinking about how to get some parametric EQ’ing into my setup as well, as I do love the LCD-XC’s and felt they just needed a couple tweaks.

And in the process of researching all this, I ran across the Audio Science Reviews of the Schiit Multibit DAC’s, and they gave me more than a little bit of pause! How could the Bifrost Multibit measure so badly! What was going on? Had I just not ever heard a truly great DAC? Or, I don't know, something?

So I dug deeper, and ran across the RME ADI-2 DAC FS, which did measure very, very well, and, it had not only a very highly regarded DAC section, but also, a very powerful, low distortion headphone amplifier, and a built in 5 band parametric EQ to boot! All for the same price as Bifrost 2 + Jotunheim 2. Plus, I could get it in just a couple days, instead of 6-8 weeks. So I cancelled my Schiit order, and pulled the trigger on the RME ADI-2 DAC FS.

I excitedly read the quick start section of the truly awesome manual, hooked it up, and started listening and playing with the EQ. Immediately I felt it was pretty good, at the very least, and I actually didn’t mind the interface, and I loved all the customizability. I spent a number of hours each day listening to music through it, into the LCD-XC’s, as well as some of my other headphones (but mostly the LCD-XC’s).

And . . .

For me--to my ears--it just wasn’t as good as the Bifrost. It was good, no doubt. Just not as good. For me.

Even with EQ helping things out I still preferred the listening experience through my Schiit stack. (And no, it wasn’t due to volume differences, I don't think.)

To my ears, the ADI-2 just didn’t sound as good. It was more fatiguing, and less enjoyable, less realistic on acoustic music, flatter, and astonishingly, somehow also less detailed?!? How could that be?!? It measured so much better than the Bifost! What was going on?

I started with the assumption that the ASR measurements just weren’t telling the whole story and that my ears were picking up on the rest of the story, so to speak. And quickly from there, I realized, that, indeed it was possible that there was more to the story. Those reviews were frequency domain measurements almost entirely. I mean, yes, OK, jitter, but what about transients? What about, say, a square wave? I felt that there was maybe something to this—or rather that it was a good place to start to investigate things at least. It was significant to me that I found the differences between these two DAC’s most apparent on acoustic music.

So, start simple. Use a tone generator program to make digitally perfect square, saw, pulse, and triangle waves and feed them into both DAC’s to see if there would be differences, and to look not on a spectrum analyzer, where you see frequency vs dB, but on an oscilloscope where you see voltage vs time. Maybe then I could start to see the differences that I thought I was hearing? I felt it was probably a long shot, but I still wanted to do the work to find out.

But honestly, I really didn’t expect to see a lot of difference. Not anything close to the differences I did find. And I didn’t expect the ADI-2 to deviate as much as it does from the ideal of the input wave. [Edit] The ADI-2's Short-Delay Sharp filter is what is called a minimum-phase filter, which can be thought of as a minimum-delay filter. It does distort wave-shapes that go into it, but, it's main advantages are two-fold: it has no pre-ringing ahead of an impulse or step, and it decays faster than a linear-phase filter (which does a better job of preserving wave-shape, but does have pre-ringing). The ADI-2 has many other filters, however, and if you want, you can change them--see follow up posts for more information[/Edit]. I couldn’t believe it when I first saw the ADI-2’s output, of a square wave input, on my oscilloscope! I thought for sure there was something wrong! That I was over-driving it or that the 1Mega-Ohm impedance of the scope was the problem. I had fed it a -6dbFS (6 decibels down from digital full-scale) square wave, at 96kHz sample rate, which I had thought was enough headroom, but I immediately changed that to -12dbFS. No change. Then I consulted with one of the other engineers here at Sonos, who is one of the people who designs the amplifier sections of our players, and had been involved with the line-out section of PORT. He suggested a 10kOhm load instead of going directly into the scope.

So, I changed my setup and soldered 10kOhm 1/4 watt resistors across the ends of the left and right RCA cables, and used a 1GHz, 1MegaOhm, 1pF N2795A Keysight active differential probe (so as to avoid any potential for ground loops), to measure the voltage across the resistor into the Keysight DSO404A 4GHz 20GSa/s oscilloscope.

But the results didn't change.

Apparently what I was seeing from the ADI-2 wasn’t due to overdriving or impedance mismatching or clipping. I now suspect that it isn't a bug. I suspect it is part of a feature. I suspect that the AKM DAC chip is limiting the impulse response due to some kind of Finite Impulse Response filter (like the Parks-MacClellan filter, perhaps). But I’m getting ahead of myself. Backing up . . .

Here is what I saw, here is what I was getting from it:

To me, this looks like fairly bad amplifier ringing! (Here’s an example of an amplifier ringing like that, for reference: PS Audio Transients 2

I increased the sample rate to 192kHz, and things got a little bit better, but not very much better:

Now I was really curious to see how the Bifrost Multibit would fare! Would it be just as bad? Marginally better? Worse?

Turns out, it was definitely better! [Edit/] Not actually better or worse, necessarily, just different than ADI-2's SD Sharp. But if you change the ADI-2's filter to Sharp, or SD LD you get something pretty close to the Bifrost[/Edit]

And let’s just compare that against the ADI-2 with the same voltage / divisions scale on the scope to make things fair:

The ringing on the ADI is so large it goes off scale. The ringing is about 40 percent of the entire amplitude of the square wave. And note how it is not symmetrical. It is not reversible in time, like the original signal that went in.

Not so with the Bifrost. It maintains very good time-symmetry. [Edit/]This is just a consequence of the linear-phase nature of the filter used in the Bifrost, and the ADI-2 can use a similar filter.[/Edit] The signal could be reversed in time and be pretty much the same. There are slight differences, but this is to be expected because we are asking the output stage to have such a large skew (voltage / time) rate and then stop on a dime.

The Bifrost also maintains better frequency domain fidelity to the input signal than the ADI-2. How do I know that without showing a spectrum analyzer output (or FFT analysis—which I plan on doing, btw)?

Well, what we are seeing with the ADI-2 DAC, is definitely not the Fourier components that fall within the 1/2 sample-rate bandwith (or even just the audio bandwith), leaving out all of the higher-order ones. A square wave has only odd harmonics of the sine-wave function. So we would have 1kHz, 3kHz, 5, kHz, 7kHz, 9kHz, 11kHz, 13kHz, 15kHz, 17kHz, and 19kHz, at least. That is 10 partials, which should make a wave that looks very much like the Bifrost’s output, and not very much like the ADI-2’s. If you check out this Wolfram Mathworld link, you can see a square wave get approximated by more and more partials, shown in different colors on the graph. There are only five partials shown, so 10 would get you a lot closer to an ideal square wave than what is show in the last sum of partials here, but you can already see where it is going, and it’s not going towards the ADI-2’s output. It’s going towards the Bifrost’s.

So, if the Bifrost Multibit is this good at 96kHz, what about at 192kHz? See for yourself:

Look at that thing. Other than a little bit of overshoot at the leading edge and a finite slope on the rising and falling traces, it’s nearly a perfect square wave!

What about going down in sample rate? Well, here are images of ADI-2 and Bifrost at 48kHz and 44.1kHz:

Again we see the same differences. With the Bifrost, there is a lot less flatness on top and bottom, but it’s still doing a pretty good job of approximating a square wave. The ADI-2, on the other hand, still looks like a badly ringing amplifier stage that was fed a square wave, and the ringing lasts longer, and is at a lower frequency.

So, let’s up the ante here and push things even more. Let’s do a 12kHz square wave at 96kHz sample rate into both and see what happens. That’s only 8 samples per entire waveform. Not much to go on! How well will the reconstruction filters work on both DAC’s? Let’s see:

What is going on with the ADI-2 now? That’s not even symmetrical about ground! It’s not even symmetrical flipped around it’s midline! It’s off-scale on the bottom and not on top, and looks very different bottom vs top.

The Bifrost, on the other hand, seems to me to be doing a very good job of intelligently filling in the gaps between the 8 points it was given. It comes up quickly, goes through the first one at the top (and keeps going a bit beyond), then turns around and heads down through the 2nd one at the top, up through the 3rd, then down through the fourth, all the way to the first point (fifth total) on the bottom, and similarly up and down through the others, finishing off by going up through the final fourth bottom (eighth total) point, and starting the waveform again.

This is what Schiit means, I think, when they say that the original samples are “retained”. The reconstruction filter works around and through those points to do the best interpolation it can do, optimizing not just for the frequency domain but also for the time domain.

And certainly the ADI-2 is not preserving the original samples here. If it were, it wouldn’t be so asymmetrical. Here it is again with the whole waveform on the screen:

I honestly have no idea what it’s doing here or why. Perhaps someone who has studied all the various filters out there can tell us? But whatever it’s doing, it’s not being faithful to the original 8 samples per waveform it was fed.

Let’s relax things just a little bit and see what happens with a 1kHz pulse waveform at 10 percent duty cycle. So, basically a 10kHz-width pulse up, baseline, 10kHz width pulse down, back to baseline, repeating 1,000 times per second:

So, thankfully, the ADI-2 is doing something sane at least, even if there is the same ringing we saw before, but again, the Bifrost is being more faithful to the signal that went in. There's not much ringing, there is more evenness on top of the pulses, and tighter control.

OK, enough of things that are square. Let’s move on to something a lot easier, we hope, for a DAC to handle. A triangle wave:

Both DAC’s are doing a nice job here, but you can see that the ADI-2 looks cleaner. And well, it is. This DAC has less noise than the instrumentation setup I was using! It’s a stellar piece of engineering, and a lot of thought went into its design and build. Here is the inherent noise of the ADI-2 as seen when connected directly to the oscilloscope:

It’s like a mV or so, and that is probably just due to noise pickup on the RCA cables. Awesome performance! How does the Bifrost fare on this? Well, not great. You can already see from the width of the line on the triangle that it has more noise, but this really shows you how much:

About 5-10 times more noise. And this is into the 1Meg load of the oscilloscope. Things are worse against 10kOhm, and when trying to reproduce an actual signal. Here is both DAC’s fed a -48dbFS 1kHz sine wave:

Clean and clear showing by the ADI-2, but look at all that noise in the Bifrost! You can still clearly see (and hear) a 1kHz sine wave, but there’s a lot of noise around it. Not great. But clearly not the whole story!

So, again, this is another reason why I suspect that the performance of the ADI-2 against square waves and pulses is due to the design of the whole digital-to-analog conversion system and not due to some failing of the ability of the components or circuits. This is a fabulous piece of kit! So I suspect, honestly, that it is baked into the sigma-delta AKM chip, and couldn’t be taken out even if RME tried. [Edit/] THIS IS TOTALLY WRONG! Not only could RME take this out, they did--you can take it out with the turn of a knob, even to the point of almost entirely taking out the output reconstruction filter, if you want (called "NOS"). Apologies for my ignorance of basic DSP![/Edit]. I doubt that Schiit would go to all the trouble to take a DAC chip that is not meant for audio at all and design all the support circuits and stages around it to make it fulfil that role if they could have just used an off-the-shelf AKM chip!

In any case, let’s get back to transient response testing. How about a sawtooth wave? Let’s see how the two DAC’s will fare!

Ouch! Again, I have to ask, what is going on with the ADI-2?

The midpoint is offset by almost four tenths of a volt, and it’s definitely not symmetrical and has got significant ringing going on. Bifrost, by contrast, has significantly less ringing, is symmetrical, and is centered on 0 volts across the RCA outputs. Pretty darn good showing! Even better than with the square wave, I would say.

Finally, let’s make sure that both DAC’s give us a sine wave output when fed a square wave at 1/4 the sample rate frequency. So both here are at 48kHz sample rate, and are being fed a 12kHz “square” wave.

Ignore the voltage scale, I took one capture at -6dbFS and the other at -12dbFS and I had the volume turned down on the ADI-2—this was early on, and was a sanity check—but what you can see is that both are giving us sine waves despite being fed a square wave.

One way to explain that is to go back to the Fourier analysis and look at the partials, and see that 12kHz is the fundamental so the first overtone is 36kHz, which is greater than 1/2 the sample rate (thus would violate the Nyquist criteria and be folded back into the spectrum at a lower frequency than the fundmental), and so it is truncated as are all higher order harmonics.

But, this is kind of a misguided way to look at this, honestly. The DAC does not know what kind of wave was behind the samples that it is getting! It only sees the samples.

And when you have only four samples per waveform, what kind of information do you have, really? With that little information, you can’t differentiate between a square, a sine, or a triangle wave! So the best thing for the DAC to do is to reconstruct a sine wave, so as not to introduce any nasty higher order harmonics that weren’t there in the original music. Better to leave out something, than to create something that was never there.

This is the whole reason for the reconstruction / interpolation filter of a DAC (well, that and quantization noise). It’s because, honestly, our sample rates are probably too low! It’s easy to claim that our hearing kind of sucks up that high and there’s no loss of information, but I do not believe that that is a proven fact, for a number of reasons.

But either way you fall on that topic, right now, for better or worse, we’re stuck with most of our music being at 44.1 or 48 or, if we’re lucky, 96kHz, so we need our DAC’s to be absolutely as faithful to the samples that we do have as possible, while at the same time intelligently interpolating between them so as not to introduce terrible sounding and unmusical harmonics.

And from what I've seen so far, it is my opinion that the Schiit combined time-and-frequency domain filter seems to be doing a really great job at this. And that, I suspect, is the reason why the Bifrost Multibit sounds so good to my ears. Yes, the THD is worse than the ADI-2. Yes, the jitter is worse. Yes, the noise floor is worse. But all that is fairly picayune compared to what is better, to what it is getting right, which is huge.

[Edit/]The Schiit proprietary filter seems to be doing pretty much what a linear phase filter does, and what the ADI-2 "sharp" filter does, so at this point I can't say that it is special nor that it is doing a better job than the ADI-2 with the sharp filter in place. I'm in the process of listening to the ADI-2 with the other filters, and will update this first post, but at the moment, I think I do like it better with "sharp" instead of "SD Sharp". Not sure how it will stack up, for me personally, against the Bifrost Multibit, but I will continue to listen[/Edit]

OK, well I have a lot more to do around this whole subject, and I plan on measuring some more DAC’s, and on learning more about DAC’s and giving all this a lot more thought, but I was excited to share what I have so far.

And, excited to learn. If this has already been done; if anyone can shed more light on this; if anyone can suggest next steps to take; please do chime in! Constructive feedback is welcome! And I haven’t spent much time (or really any time) here over the past five years or so, and I didn’t even do a lot of searching (sorry) before posting this thread. So if I’m missing stuff, please pardon my ignorance.

OK, I will leave it here for now. I hope some readers find this interesting! Cheers!

 

[cgb3]

TIME-DOMAIN TRANSIENT RESPONSE TESTS OF ADI-2 DAC FS & BIFROST MB DAC’s

Recently, I decided to take my work headphone listening setup to the next level, and get better headphones and a DAC and an amp (or a DAC / Amp combo unit) to go with them, so I started digging into head-fi and online reviews and websites again, wondering excitedly what new stuff from my favorite (or exciting new) companies had come along while I had been listening contentedly to my Sonos PORT +TIDAL lossless --> Bifrost Multibit (Gen 1) --> Asgard 2 --> Audeze LCD-2 set up.

Of course, one of the first things I did was go to Schiit’s website to see what was on offer, and was thrilled to see a Bifrost 2 with an ever better multibit implementation!

Because, I have to say, of all my hi-fi audio purchases, the Bifrost Multibit was one of the best and most important. Finally, finally, I was experiencing the kind of audio bliss I had been seeking, and even from just my Senn 595’s. To my ears, there was such a lovely detail and air and cleanness to the music, without any of the edge and digital glare I had been experiencing, to one extent or another, for years. I had sometimes heard that the DAC really didn’t make much difference and that if you thought you were hearing significant differences that you were fooling yourself (and the same for amps, provided they had enough power to avoid clipping), but after years of improving my headphones, and my sound-file source quality, and trying higher powered amplifiers, and not really feeling like there was much of a difference, I was ready to take advantage of Schiit’s 15 day return policy and give a high(er) end DAC a try to see if that was the missing piece of the puzzle in my quest.

And, well, it was. Was it ever! My Bifrost 1 Multibit was a revelation to me. I was so happy with it!

So, I was pretty excited about Bifrost 2! And I figured I’d go balanced and get the Jotunheim 2 (all to go with the Audeze LCD-XC 2021 carbon’s I had on order). Woo hoo! Yea!

While I was waiting for my Schiit order to get fulfilled, I got the LCD-XC’s, and while I did love their sound on the whole, I personally found it a bit too hot in parts of the treble to be as non-fatiguing as I would like. So then I was also thinking about how to get some parametric EQ’ing into my setup as well, as I do love the LCD-XC’s and felt they just needed a couple tweaks.

And in the process of researching all this, I ran across the Audio Science Reviews of the Schiit Multibit DAC’s, and they gave me more than a little bit of pause! How could the Bifrost Multibit measure so badly! What was going on? Had I just not ever heard a truly great DAC? Or, I don't know, something?

So I dug deeper, and ran across the RME ADI-2 DAC FS, which did measure very, very well, and, it had not only a very highly regarded DAC section, but also, a very powerful, low distortion headphone amplifier, and a built in 5 band parametric EQ to boot! All for the same price as Bifrost 2 + Jotunheim 2. Plus, I could get it in just a couple days, instead of 6-8 weeks. So I cancelled my Schiit order, and pulled the trigger on the RME ADI-2 DAC FS.

I excitedly read the quick start section of the truly awesome manual, hooked it up, and started listening and playing with the EQ. Immediately I felt it was pretty good, at the very least, and I actually didn’t mind the interface, and I loved all the customizability. I spent a number of hours each day listening to music through it, into the LCD-XC’s, as well as some of my other headphones (but mostly the LCD-XC’s).

And . . .

For me--to my ears--it just wasn’t as good as the Bifrost. It was good, no doubt. Just not as good. For me.

Even with EQ helping things out I still preferred the listening experience through my Schiit stack. (And no, it wasn’t due to volume differences, I don't think.)

To my ears, the ADI-2 just didn’t sound as good. It was more fatiguing, and less enjoyable, less realistic on acoustic music, flatter, and astonishingly, somehow also less detailed?!? How could that be?!? It measured so much better than the Bifost! What was going on?

I started with the assumption that the ASR measurements just weren’t telling the whole story and that my ears were picking up on the rest of the story, so to speak. And quickly from there, I realized, that, indeed it was possible that there was more to the story. Those reviews were frequency domain measurements almost entirely. I mean, yes, OK, jitter, but what about transients? What about, say, a square wave? I felt that there was maybe something to this—or rather that it was a good place to start to investigate things at least. It was significant to me that I found the differences between these two DAC’s most apparent on acoustic music.

So, start simple. Use a tone generator program to make digitally perfect square, saw, pulse, and triangle waves and feed them into both DAC’s to see if there would be differences, and to look not on a spectrum analyzer, where you see frequency vs dB, but on an oscilloscope where you see voltage vs time. Maybe then I could start to see the differences that I thought I was hearing? I felt it was probably a long shot, but I still wanted to do the work to find out.

But honestly, I really didn’t expect to see a lot of difference. Not anything close to the differences I did find. And I didn’t expect the ADI-2 to deviate as much as it does from the ideal of the input wave. I couldn’t believe it when I first saw the ADI-2’s output, of a square wave input, on my oscilloscope! I thought for sure there was something wrong! That I was over-driving it or that the 1Mega-Ohm impedance of the scope was the problem. I had fed it a -6dbFS (6 decibels down from digital full-scale) square wave, at 96kHz sample rate, which I had thought was enough headroom, but I immediately changed that to -12dbFS. No change. Then I consulted with one of the other engineers here at Sonos, who is one of the people who designs the amplifier sections of our players, and had been involved with the line-out section of PORT. He suggested a 10kOhm load instead of going directly into the scope.

So, I changed my setup and soldered 10kOhm 1/4 watt resistors across the ends of the left and right RCA cables, and used a 1GHz, 1MegaOhm, 1pF N2795A Keysight active differential probe (so as to avoid any potential for ground loops), to measure the voltage across the resistor into the Keysight DSO404A 4GHz 20GSa/s oscilloscope.

But the results didn't change.

Apparently what I was seeing from the ADI-2 wasn’t due to overdriving or impedance mismatching or clipping. I now suspect that it isn't a bug. I suspect it is part of a feature. I suspect that the AKM DAC chip is limiting the impulse response due to some kind of Finite Impulse Response filter (like the Parks-MacClellan filter, perhaps). But I’m getting ahead of myself. Backing up . . .

Here is what I saw, here is what I was getting from it:



To me, this looks like fairly bad amplifier ringing! (Here’s an example of an amplifier ringing like that, for reference: PS Audio Transients 2

I increased the sample rate to 192kHz, and things got a little bit better, but not very much better:



Now I was really curious to see how the Bifrost Multibit would fare! Would it be just as bad? Marginally better? Worse?

Turns out, it was definitely better!



And let’s just compare that against the ADI-2 with the same voltage / divisions scale on the scope to make things fair:



The ringing on the ADI is so large it goes off scale. The ringing is about 40 percent of the entire amplitude of the square wave. And note how it is not symmetrical. It is not reversible in time, like the original signal that went in.

Not so with the Bifrost. It maintains very good time-symmetry. The signal could be reversed in time and be pretty much the same. There are slight differences, but this is to be expected because we are asking the output stage to have such a large skew (voltage / time) rate and then stop on a dime.

The Bifrost also maintains better frequency domain fidelity to the input signal than the ADI-2. How do I know that without showing a spectrum analyzer output (or FFT analysis—which I plan on doing, btw)?

Well, what we are seeing with the ADI-2 DAC, is definitely not the Fourier components that fall within the 1/2 sample-rate bandwith (or even just the audio bandwith), leaving out all of the higher-order ones. A square wave has only odd harmonics of the sine-wave function. So we would have 1kHz, 3kHz, 5, kHz, 7kHz, 9kHz, 11kHz, 13kHz, 15kHz, 17kHz, and 19kHz, at least. That is 10 partials, which should make a wave that looks very much like the Bifrost’s output, and not very much like the ADI-2’s. If you check out this Wolfram Mathworld link, you can see a square wave get approximated by more and more partials, shown in different colors on the graph. There are only five partials shown, so 10 would get you a lot closer to an ideal square wave than what is show in the last sum of partials here, but you can already see where it is going, and it’s not going towards the ADI-2’s output. It’s going towards the Bifrost’s.

So, if the Bifrost Multibit is this good at 96kHz, what about at 192kHz? See for yourself:



Look at that thing. Other than a little bit of overshoot at the leading edge and a finite slope on the rising and falling traces, it’s nearly a perfect square wave!

What about going down in sample rate? Well, here are images of ADI-2 and Bifrost at 48kHz and 44.1kHz:









Again we see the same differences. With the Bifrost, there is a lot less flatness on top and bottom, but it’s still doing a pretty good job of approximating a square wave. The ADI-2, on the other hand, still looks like a badly ringing amplifier stage that was fed a square wave, and the ringing lasts longer, and is at a lower frequency.

So, let’s up the ante here and push things even more. Let’s do a 12kHz square wave at 96kHz sample rate into both and see what happens. That’s only 8 samples per entire waveform. Not much to go on! How well will the reconstruction filters work on both DAC’s? Let’s see:





What is going on with the ADI-2 now? That’s not even symmetrical about ground! It’s not even symmetrical flipped around it’s midline! It’s off-scale on the bottom and not on top, and looks very different bottom vs top.

The Bifrost, on the other hand, seems to me to be doing a very good job of intelligently filling in the gaps between the 8 points it was given. It comes up quickly, goes through the first one at the top (and keeps going a bit beyond), then turns around and heads down through the 2nd one at the top, up through the 3rd, then down through the fourth, all the way to the first point (fifth total) on the bottom, and similarly up and down through the others, finishing off by going up through the final fourth bottom (eighth total) point, and starting the waveform again.

This is what Schiit means, I think, when they say that the original samples are “retained”. The reconstruction filter works around and through those points to do the best interpolation it can do, optimizing not just for the frequency domain but also for the time domain.

And certainly the ADI-2 is not preserving the original samples here. If it were, it wouldn’t be so asymmetrical. Here it is again with the whole waveform on the screen:



I honestly have no idea what it’s doing here or why. Perhaps someone who has studied all the various filters out there can tell us? But whatever it’s doing, it’s not being faithful to the original 8 samples per waveform it was fed.

Let’s relax things just a little bit and see what happens with a 1kHz pulse waveform at 10 percent duty cycle. So, basically a 10kHz-width pulse up, baseline, 10kHz width pulse down, back to baseline, repeating 1,000 times per second:





So, thankfully, the ADI-2 is doing something sane at least, even if there is the same ringing we saw before, but again, the Bifrost is being more faithful to the signal that went in. There's not much ringing, there is more evenness on top of the pulses, and tighter control.

OK, enough of things that are square. Let’s move on to something a lot easier, we hope, for a DAC to handle. A triangle wave:





Both DAC’s are doing a nice job here, but you can see that the ADI-2 looks cleaner. And well, it is. This DAC has less noise than the instrumentation setup I was using! It’s a stellar piece of engineering, and a lot of thought went into its design and build. Here is the inherent noise of the ADI-2 as seen when connected directly to the oscilloscope:



It’s like a mV or so, and that is probably just due to noise pickup on the RCA cables. Awesome performance! How does the Bifrost fare on this? Well, not great. You can already see from the width of the line on the triangle that it has more noise, but this really shows you how much:



About 5-10 times more noise. And this is into the 1Meg load of the oscilloscope. Things are worse against 10kOhm, and when trying to reproduce an actual signal. Here is both DAC’s fed a -48dbFS 1kHz sine wave:





Clean and clear showing by the ADI-2, but look at all that noise in the Bifrost! You can still clearly see (and hear) a 1kHz sine wave, but there’s a lot of noise around it. Not great. But clearly not the whole story!

So, again, this is another reason why I suspect that the performance of the ADI-2 against square waves and pulses is due to the design of the whole digital-to-analog conversion system and not due to some failing of the ability of the components or circuits. This is a fabulous piece of kit! So I suspect, honestly, that it is baked into the sigma-delta AKM chip, and couldn’t be taken out if AKM tried. I doubt that Schiit would go to all the trouble to take a DAC chip that is not meant for audio at all and design all the support circuits and stages around it to make it fulfil that role if they could have just used an off-the-shelf AKM chip!

In any case, let’s get back to transient response testing. How about a sawtooth wave? Let’s see how the two DAC’s will fare!





Ouch! Again, I have to ask, what is going on with the ADI-2?

The midpoint is offset by almost four tenths of a volt, and it’s definitely not symmetrical and has got significant ringing going on. Bifrost, by contrast, has significantly less ringing, is symmetrical, and is centered on 0 volts across the RCA outputs. Pretty darn good showing! Even better than with the square wave, I would say.

Finally, let’s make sure that both DAC’s give us a sine wave output when fed a square wave at 1/4 the sample rate frequency. So both here are at 48kHz sample rate, and are being fed a 12kHz “square” wave.





Ignore the voltage scale, I took one capture at -6dbFS and the other at -12dbFS and I had the volume turned down on the ADI-2—this was early on, and was a sanity check—but what you can see is that both are giving us sine waves despite being fed a square wave.

One way to explain that is to go back to the Fourier analysis and look at the partials, and see that 12kHz is the fundamental so the first overtone is 36kHz, which is greater than 1/2 the sample rate (thus would violate the Nyquist criteria and be folded back into the spectrum at a lower frequency than the fundmental), and so it is truncated as are all higher order harmonics.

But, this is kind of a misguided way to look at this, honestly. The DAC does not know what kind of wave was behind the samples that it is getting! It only sees the samples.

And when you have only four samples per waveform, what kind of information do you have, really? With that little information, you can’t differentiate between a square, a sine, or a triangle wave! So the best thing for the DAC to do is to reconstruct a sine wave, so as not to introduce any nasty higher order harmonics that weren’t there in the original music. Better to leave out something, than to create something that was never there.

This is the whole reason for the reconstruction / interpolation filter of a DAC (well, that and quantization noise). It’s because, honestly, our sample rates are probably too low! It’s easy to claim that our hearing kind of sucks up that high and there’s no loss of information, but I do not believe that that is a proven fact, for a number of reasons.

But either way you fall on that topic, right now, for better or worse, we’re stuck with most of our music being at 44.1 or 48 or, if we’re lucky, 96kHz, so we need our DAC’s to be absolutely as faithful to the samples that we do have as possible, while at the same time intelligently interpolating between them so as not to introduce terrible sounding and unmusical harmonics.

And from what I've seen so far, it is my opinion that the Schiit combined time-and-frequency domain filter seems to be doing a really great job at this. And that, I suspect, is the reason why the Bifrost Multibit sounds so good to my ears. Yes, the THD is worse than the ADI-2. Yes, the jitter is worse. Yes, the noise floor is worse. But all that is fairly picayune compared to what is better, to what it is getting right, which is huge.

OK, well I have a lot more to do around this whole subject, and I plan on measuring some more DAC’s, and on learning more about DAC’s and giving all this a lot more thought, but I was excited to share what I have so far.

And, excited to learn. If this has already been done; if anyone can shed more light on this; if anyone can suggest next steps to take; please do chime in! Constructive feedback is welcome! And I haven’t spent much time (or really any time) here over the past five years or so, and I didn’t even do a lot of searching (sorry) before posting this thread. So if I’m missing stuff, please pardon my ignorance.

OK, I will leave it here for now. I hope some readers find this interesting! Cheers!

After one year of training, I spent 3 years in the USAF (305X afsc) scoping (with very nice Honeywell scopes) various waves. This was on individual components and daughter boards of the big mainframe computers of the time (early '80's). Waves show faults (anomalies), not good sound (in my opinion).

Personally, I'll trust my ears to determine the gear that suits me. I've never looked at waves to make a purchase in the 40 years I've been without a scope.

 

[_js_]

After one year of training, I spent 3 years in the USAF (305X afsc) scoping (with very nice Honeywell scopes) various waves. This was on individual components and daughter boards of the big mainframe computers of the time (early '80's). Waves show faults (anomalies), not good sound (in my opinion).

Personally, I'll trust my ears to determine the gear that suits me. I've never looked at waves to make a purchase in the 40 years I've been without a scope.

It was much more about seeing if I could find measurements to corroborate what I was hearing, and not really so much about distrusting my ears.

And about seeing what was going on with Schiit’s time and frequency domain optimized filter / interpolation.

 

[b0bb]

It was much more about seeing if I could find measurements to corroborate what I was hearing, and not really so much about distrusting my ears.

And about seeing what was going on with Schiit’s time and frequency domain optimized filter / interpolation.nice

Nice to see the behavior on the various filter types.
RME uses minimum phase for their DAC.
Schitt uses linear phase.

I can reproduce your observations with Roon's DSP module.
Roon provides various DSP options when upsampling 44.1k-->705.6k

Minimum phase, precise setting, similar to RME

Linear phase precise, similar to Schiit.

 

[b0bb]

Increasing the sampling rates produces outputs closer to the ideal.

Below is the same 1kHz square wave at 768k sampling.

I use this to fine tune the transient response of my DAC's output stage for 768k output.

The capture is taken of the work in progress.
There is work left to be done to handle the spur on the falling edge.

Below is the trace of of the output before applying transient compensation.
The is measurable overshoot on both the rising and falling edges of the wave. (Orange marker legend)

 

[_js_]

Increasing the sampling rates produces outputs closer to the ideal.

Below is the same 1kHz square wave at 768k sampling.

I use this to fine tune the transient response of my DAC's output stage for 768k output.

The capture is taken of the work in progress.
There is work left to be done to handle the spur on the falling edge.


Below is the trace of of the output before applying transient compensation.
The is measurable overshoot on both the rising and falling edges of the wave. (Orange marker legend)

Great info! Thanks so much for the post and scope shots!

So RME offers SD sharp (short delay, sharp), sharp, SD soft, soft, and NOS.

Would any of those have linear phase?

And what DAC created the output shown above? (That you used Roon’s DSP upsampling on)

And what other DAC’s besides Schiit’s use linear phase?

And can you define those two terms more exactly? Phase of what relative to what?

I noticed when looking at the FFT’s of some of the 12khz waveforms that the RME was clearly closer to the ideal frequency domain response. Does that have something to do with it?

And is Schiit’s filter just a flavor of a linear phase filter and nothing special or is it something more?

And where can I learn more about all this?

I am just starting to read this text book. But would welcome any other resources!

Thanks again!

​

 

[whitefang]

Great info! Thanks so much for the post and scope shots!

So RME offers SD sharp (short delay, sharp), sharp, SD soft, soft, and NOS.

Would any of those have linear phase?

And what DAC created the output shown above? (That you used Roon’s DSP upsampling on)

And what other DAC’s besides Schiit’s use linear phase?

And can you define those two terms more exactly? Phase of what relative to what?

I noticed when looking at the FFT’s of some of the 12khz waveforms that the RME was clearly closer to the ideal frequency domain response. Does that have something to do with it?

And is Schiit’s filter just a flavor of a linear phase filter and nothing special or is it something more?

And where can I learn more about all this?

I am just starting to read this text book. But would welcome any other resources!

Thanks again!

​

This is from ADI-2 Manual

Sharp and Slow has symmetrical impulse which should mean linear phase.

Maybe you could run some tests with other filter settings.

And this might be helpful to you.
https://forum.rme-audio.de/viewtopic.php?pid=142226#p142226

 

[Sonic Defender]

Do some really well controlled, level matched, blind listening tests. Do twenty trials, but absolutely level matched, completely blind trials. If after the 20 trials you can tell the DACs apart with at least 90% accuracy you would have proof of audibility. Measurable does not mean audible.

 

[b0bb]

Great info! Thanks so much for the post and scope shots!

So RME offers SD sharp (short delay, sharp), sharp, SD soft, soft, and NOS.

Would any of those have linear phase?

And what DAC created the output shown above? (That you used Roon’s DSP upsampling on)

And what other DAC’s besides Schiit’s use linear phase?

And can you define those two terms more exactly? Phase of what relative to what?

I noticed when looking at the FFT’s of some of the 12khz waveforms that the RME was clearly closer to the ideal frequency domain response. Does that have something to do with it?

And is Schiit’s filter just a flavor of a linear phase filter and nothing special or is it something more?

And where can I learn more about all this?

I am just starting to read this text book. But would welcome any other resources!

Thanks again!

​

Put your RME thru the various filter option settings and see how the scope traces change.

Linear and minimum phase are the actual names of the class of filters.
This is part of DSP basics. The link below has a further description.
https://www.dsprelated.com/freebooks/filters/Minimum_Phase_Filters.html

The DAC used to generate my traces is a ES9038Pro operating in mono mode.
Roon is doing all the DSP work so the DAC is just a basic D/A converter.

 

[_js_]

Excellent, excellent information! Thank you all!

Yes, I will do listening tests at some point!

And yes, I will get some scope captures of the RME with the various filters!

I should obviously have read the whole manual before now—then I would have seen the discussion about filters and impulse response. I’m super excited to try the other filters now.

Many thanks!

I’m also still quite interested to know more about the proprietary Schiit filter and how it differs from the RME “slow”.

 

[b0bb]

I’m also still quite interested to know more about the proprietary Schiit filter and how it differs from the RME “slow”.

Schiit's impulse response looks to me like a linear phase filter.

The squiggly section at the flat part of the squarewave is a consequence of reconstructing the square wave from a limited number of harmonics.
What your seeing here is not a limitation of the DAC but how signal reconstruction works.

This is explained by the Gibbs phenomenon
https://en.wikipedia.org/wiki/Gibbs_phenomenon

 

[_js_]

Schiit's impulse response looks to me like a textbook linear phase filter.

The squiggly section at the flat part of the squarewave is a consequence of reconstructing the square wave from a limited number of harmonics.
What your seeing here is not a limitation of the DAC but how signal reconstruction work

Yeah, I get that.

I was thinking about it some more and it dawned on me that the only signal that would get through the filtering on the A/D side up near 20khz is a pure sine wave. Even if it were actually a triangle wave, the filters would remove all the higher order harmonics, leaving you with a sine wave. So reconstruction on the other end can (and must) take that into account.

and yes, I studied all this mathematics in college. I took differential equations for two semesters, and partial differential equations after that, and then a class that was a combination of PDE II, real analysis, and set theory (Georg Cantor stuff), as well as Differential Topology (mathematics of General Relativity—is how I thought of it).

So I’m excited to learn more about DSP and filters as I do have the mathematical foundation needed to understand it.

Plus I work for Sonos, so it’s more or less job related, but it’s not what I do here.

I actually had just found out who here is the main DSP person and was planning to ask them tomorrow about what I was seeing.

Thanks again!

 

[Sonic Defender]

I applaud your curiosity and open-mindedness. I look forward to following the thread as you discuss what you discover and learn. But please, really, really care about science, setup the properly designed multiple-trial, level matched, blind listening tests with 20 trials. As mentioned if you can detect a difference under level matched, blind listening at 90% and above you will have some evidence of an audible difference. So few people bother and this is actually disturbing really. People will spend hours upon hours measuring, swapping cables, filters, changing components, measuring room modes (with speaker based systems) and yet never bother doing very easy to construct actual valid listening trials.

Congratulations to Sonos by the way on the work done with the Ikea lifestyle speaker. Pretty impressive stuff as demonstrated by Amir over at audiosciencereview. Sonos have always impressed me and I like seeing their marketplace category move forward.

 

[_js_]

I applaud your curiosity and open-mindedness. I look forward to following the thread as you discuss what you discover and learn. But please, really, really care about science, setup the properly designed multiple-trial, level matched, blind listening tests with 20 trials. As mentioned if you can detect a difference under level matched, blind listening at 90% and above you will have some evidence of an audible difference. So few people bother and this is actually disturbing really. People will spend hours upon hours measuring, swapping cables, filters, changing components, measuring room modes (with speaker based systems) and yet never bother doing very easy to construct actual valid listening trials.

Congratulations to Sonos by the way on the work done with the Ikea lifestyle speaker. Pretty impressive stuff as demonstrated by Amir over at audiosciencereview. Sonos have always impressed me and I like seeing their marketplace category move forward.

I totally understand where you're coming from, and I definitely agree with and sympathize with it, and I promise, yes, I will do controlled, blind tests if / when I get to that point.

I'm pretty busy these days, so I don't know when I'll get to that, but I'm listening to the RME with the "Slow" filter, and I think I can tell the difference right away! I think I might prefer (and be able to hear) phase linear filter setting. But that's just a first impression, and I would agree that it's only that.

I will comment, though, that your threshold seems pretty high. Multiple-trial, blind testing, with 20 trials minimum, with a 90 percent success / confidence level is possibly a bit much to ask in this context, I feel, before we have "some evidence" of an audible difference.

But setting that aside, I've seen at least a few posts from people on ASR where they discount the notion that an A / B blind test could take more than a few seconds or a minute or so at most. And that if it does, it's somehow not valid. I have experienced first hand where I could not tell a difference switching back and forth in a fast A / B test, but then, could definitely tell when I listened to a whole album or more. I see no reason why the A / B test is somehow less valid if it takes the listener 20 minutes or more between switches. There's a lot going on below the conscious level in humans, in general, and specifically when it comes to hearing and that can take a while to register. This notion that "if you hear it you hear it"--meaning you can tell in seconds--is not correct, in my opinion.

In any case to start, I'm going to take some more captures of the ADI-2 to show the effects of the various filters--super curious about that!--and if the results are what I expect, I will edit my first post above (saving the original bits for historical record), to correct all the things I got wrong (and they are adding up at this point, so I feel some urgency to set the record straight).

Then I'm going to spend some quality time doing some extended listening on just the RME to the various filters. And more importantly, a lot of time learning about DSP and what phase-linear and minimum-phase means, what's happening, etc. And learning about DAC's and ADC's in general. (I'm as much an engineer / scientist as I am an audiophile)

And after all that, then and only then, I might set up some blind listening tests on just the ADI-2, to see if I can really hear the difference between the filters. That will be a lot simpler to set up, as everything will be volume / voltage matched, and it will be easy to do the switching blindly.

Then I'll move on to the ADI-2 / Bifrost comparison, informed by the previous tests.

In the meantime, though, I think all of this is super interesting. Thanks again everyone for your awesome contributions! Much appreciated!

 

[_js_]

OK, so here are the various RME ADI-2 DAC FS filters applied against a 1kHz -6dbFS square wave at a 96kHz sample rate. "SD" in the filter name stands for "short delay", meaning low latency, meaning it doesn't gather a bunch of samples first before acting, thus having low latency. It also means it can't see ahead at what's coming next, which explains a lot. Here they are. First the one I took earliest, which is SD sharp (filter not labeled on the image), then all the others (filter IS labeled on the image):

So, I expected "Slow" to look the most like the Bifrost, but it seems sort of like some combination of SD LD and Sharp. I am actually pretty glad it isn't the same as any of them, as Schiit makes some pretty strong claims about their filter. Here is what they say on their site:

What’s this bullschiit about a unique time- and frequency-domain optimized digital filter, and why does it matter?
Most digital filters destroy the original samples in the process of upsampling. They’re just like sample rate converters or delta-sigma DACs. We’re all about the original samples, so we created a unique digital filter that performs a true interpolation, which means it retains all the original samples. This is a major difference between Schiit True Multibit DACs like Yggdrasil and every other DAC in the world.

I don't believe you!
Then ask Mike Moffat, the father of audiophile digital playback, about his 5-year quest to perfect this digital filter, involving 1917 Western Electric papers on pulse-code modulation, a professor emeritus of mathematics who devised a way to get around the divide-by-zero problem, a RAND corp mathematician to implement it, and a master programmer to get it to run on our SHARC processor engine. In his words:

"The below are the claims of the digital filter/interpolator/sample rate converter in Yggy:

1. The filter is absolutely proprietary.
2. The development tools and coefficient calculator to derive the above filters are also proprietary.
3. The math involved in developing the filter and calculating has a closed form solution. It is not an approximation, as all other filters I have studied (most, if not all of them). Therefore, all of the original samples are output. This could be referred to fairly as bit perfect; what comes in goes out.
4. Oversimplified, however essentially correct: The filter is also time domain optimized which means the phase info in the original samples are averaged in the time domain with the filter generated interpolated samples to for corrected minimum phase shift as a function of frequency from DC to the percentage of nyquist - in our case .968. Time domain is well defined at DC - the playback device behaves as a window fan at DC - it either blows (in phase) or sucks (out). It is our time domain optimization that gives the uncanny sonic hologram. (It also allows the filter to disappear. Has to be heard to understand.) Since lower frequency wavelengths are measured in tens of feet, placement in image gets increasingly wrong as a function of decreasing frequency in non time domain optimized recordings - these keep the listener's ability to hear the venue - not to mention the sum of all of the phase errors in the microphones, mixing boards, eq, etc on the record side. An absolute phase switch is of little to no value in a non time domain optimized, stochastic time domain replay system. It makes a huge difference with an Yggy.
5. This is combined with a frequency domain optimization which does not otherwise affect the phase optimization. The 0.968 of Nyquist also gives us a small advantage that none of the off-the shelf FIR filters (0.907) provide: frequency response out to 21.344KHz, 42.688KHz, 85.3776KHz, and 170.5772KHz bandwidth for native 1,2,4, and 8x 44.1KHz SR multiple recordings - the 48KHz table is 23.232, 46.464, 92.868, and 185.856KHz respectively for 1,2,4, and 8x. This was the portion of the filter that had the divide by zero problem which John Lediaev worked out, to combine with #4 above AND retain the original samples.

This is what other DACs typically offer: frequency domain optimization FIR filters with Parks-McClellan optimization. Any avoidance of the Parks-McClellan pablum requires a lot of original DSP work. Am I a prophet who received the tablets from God or some other high-end audio drivel. Hell, no. I was the producer and director of this project and worked with Dave Kerstetter (hardware-software), John Lediaev (Math), Tom Lippiat (DSP Code), Warren Goldman (Coefficient Generator and development tools) for a total of 15 or so man years. These folks either taught math at The University of Iowa, Computer Science at Carnegie-Mellon University, worked at think tanks like the Rand Corporation – you get the idea. We did this for no money - What we all had in common was that we loved audio. All other audio pros were interested in Parks-McClellan and pointed and laughed at us. That's the way it happened. It was worth it, every hour, day, and year."

Here is the Bifrost, for reference: