Consequences of insufficient reconstruction filter in a DAC

[LTig]

This is a followup of OT postings in thread Focal Clear Review (headphone) covering the consequences of insufficent filtering at the output of a DAC chip.

Maybe you’ve missed the theory.

Any f between 0 and fs/2 at the output of a converter can be a mirror of n x fs ± f at the input. “Converter” here means ADC or DAC.

So, in the case of a DAC @ 44.1kHz for example, 20kHz in analog can indeed be 24.1kHz in digital if that has not been properly filtered in the digital domain — but you don’t retrieve 24.1kHz in the analog domain.

Nope. You do retrieve the 24.1 kHz if the reconstruction filter is poor or missing. See Ken. C. Pohlmann Principles of Digital Audio, in the 4th Edition from 2000 in chapter 4 Output Lowpass Filter on page 94. If you do not use a proper lowpass filter those mirror signal are contained in the analog signal.

You can see this in practice at stereophile. @John Atkinson measures the behaviour of DACs using both broadband noise and a single 19.1 kHz sinus. A good example is the Holoaudio May, see figure 3:

Fig.3 HoloAudio May, NOS mode, wideband spectrum of white noise at –4dBFS (left channel red, right magenta) and 19.1kHz tone at 0dBFS (left blue, right cyan) into 100k ohms with data sampled at 44.1kHz (20dB/vertical div.).

You can see that with the NOS filter the analog output signal in fact contains all mirror tones of 19.1 kHz.
The same DAC has a much better filter where the mirror signals are very well suppressed:

Fig.5 HoloAudio May, OS mode, wideband spectrum of white noise at –4dBFS (left channel red, right magenta) and 19.1kHz tone at 0dBFS (left blue, right cyan) into 100k ohms with data sampled at 44.1kHz (20dB/vertical div.).​

But that 20kHz in the analog domain could also be 64.1kHz (44.1 + 20), 68,2kHz (2x44.1 - 20), 108,2kHz, etc. etc. in the digital domain.

I don't understand this. If an analog 20 kHz signal is sampled the sampled sequence contains these signals:

• 20 kHz (0*fs + 20) and 24.1 kHz (0*fs + fs/2 + (fs/2 - 20))
• 64.1 kHz (1*fs + 20) and 68.2 kHz (1*fs + fs/2 + (fs/2 - 20))
• 108.2 kHz (2*fs + 20) and 112.3 kHz (2*fs + fs/2 + (fs/2 - 20))
• ...
• N*fs + 20 and N*fs + fs/2 + (fs/2 - 20)

See Pohlmann Figure 2.4 on page 30.

Coming back to the RME DAC, not only did you only feed the DAC with a 20kHz pure wave (so no 24.1kHz was present at the input, thus no aliasing could theoretically happen), but also you cannot retrieve any 24.1kHz at the output (which means the analog oscilloscope graph cannot be that of 20kHz + 24.1kHz).

But I did retrieve it. If I find some time on the weekend I'll repeat this experiment with a second ADC (I cannot run the ADC and the DAC of the RME at different samplerates). The spectrum display in REW will show what's in the signal better than the time domain display of the DSO.

Your initial second screenshot btw shows f=17.57kHz, as opposed to the first showing f≃20kHz — not sure what that particularly means for your particular DSO.

Since the input signal is not a single frequency but the sum of two (or more) you can't rely on what the DSO says.

 

[melowman]

OK, in my reasoning I forgot the fact that you were supposing that no reconstruction filter was applied, while I was supposing there was, that's why I said that you could not have 24.1kHz output (at least that high) by the DAC.

Now, here's from RME ADI-2 DAC FS manual; as you'll see, the ADI-2 DAC's "NOS" is filtering:

 

[LTig]

I measured the output of my RME ADI-2 PRO fs with a 20 kHz sinus signal at -20 dBFS at +24 dBU output into my DSO (Siglent SDS 1202X-E), using its FFt algorithm to see what's in the output. Center frequency is 40.2 kHz, span is 90.2 kHz, linear amplitude (the DSO is only 8 bits).

First the SD Sharp filter:

OK, just the sinus at 20 kHz as expected.

Now the NOS filter:

Not only do we see the 20 kHz and the 24.1 kHz signal, we also see the next two mirror signals around 66 +/- 2 kHz.

I increased the frequency span to 200 kHz to see if we find more mirror signals, and in fact we see three more mirror groups:

So the NOS filter does not seem to filter very well as I suspected. Just looking at the rise time of the signal made this clear to me.

Regarding the FR response of the different filters in the manual: it covers just the range from +2 .. -18 dB, so we cannot
safely expect that the curves continue to go down like this into the noise floor. Maybe @MC_RME can chime in and explain it.

The measurements ot the other filters are behind the spoiler.

Spoiler

SD Slow filter:

We see the 20 kHz and the 24.1 kHz signal but no other mirror signals.

Sharp filter:

Just the sinus at 20 kHz, no mirrors at all.

Slow filter:

We see the 20 kHz and the 24.1 kHz signal but no other mirror signals.

 

[melowman]

Thank you very much for these measurements.
It is very confusing, to say the least.

According to your plot, with the "NOS" filter, the 24.1kHz signal is roughly 3dB softer than the 20kHz signal; while the manual states that it should be at least 14.5dB softer.

Maybe Matthias could chime in and explain yes...

 

[LTig]

According to your plot, with the "NOS" filter, the 24.1kHz signal is roughly 3dB softer than the 20kHz signal; while the manual states that it should be at least 14.5dB softer.

Yep, that's true. But I'm actually very happy that the NOS filter is so very slow because the rise time of a square signal is quite a bit shorter than with the other filters. Good for testing electronics.

 

[MC_RME]

According to your plot, with the "NOS" filter, the 24.1kHz signal is roughly 3dB softer than the 20kHz signal; while the manual states that it should be at least 14.5dB softer.

Sorry, but the manual does not state that. I went to great lengths to explain how critical, for many applications even useless or dangerous NOS is.

The measurement that you refer to is mainly there to point out the early treble loss with Slow and NOS. But I understand (and confess to not have realized that before) that the shown stopband behaviour in this measurement might cause confusion, as it indeed shows a wrong, not existing stopband behaviour of Slow and NOS.

This is a complicated topic, and we had this here before a long time ago when Amir measured some french high-end juwel. As soon as the DA filters are more open, trying to measure the output level to get a frequency response graph is full of issues. Namely mirrored signals that are included, plus phase dependency to the used ADC. The latter happens typically if you use a software like HpW that uses ASIO, and your DA and AD have to run at the same sample rate.

HpW uses a clever FFT-based multitone signal that allows you to see the frequency response in real-time, as FFT result, updated several times per second and with no sweep time because not sweeping at all. But as most other methods it will be disturbed by mirroring. HpW therefore added some code to prevent such ill effects. These cause the steep stopband for slower filters that you see in the measurement. Without these the result would look even more crazy, and it's not HpW's fault. Check this measurement of the AP software using ASIO with an ADI-2 Pro analog out to in, using a stepped sine sweep.

The level rises near sf/2? Impossible - and indeed that is not the case. The total level rises due to the mirrors that are included, and the graph no longer describes the frequency response of the filter. SD Slow has a different stopband as Slow? Not at all, they are spot on. The measurement result changes with phase relation, when changing the AD from Sharp (phase linear) to SD Sharp (minimum phase). Oops!

Here is an edited graph that shows the real filter behaviour. I will use this in the manuals to not confuse you and others.

 

[KSTR]

This whole reconstruction filter issue is a can of worms, notably at low fs (44.1kHz).
Let's look at the two extremes to see.

1) No reconstruction filter at all, that is, filterless NOS output at fs (but with the correction of the high-frequency droop). This invokes a plethora of imaging product above fs/2 with no attenuation, periodically repeating. As those frequencies are beyond the perceptional range, they are of no consequence though, unless we have subsequent distortion in the chain leading to intermodulation products folded back to below 20kHz. Now with analog lowpass filter, we can reduce the level but it is almost impossible to get deep attenuation at 22050Hz and still only be 0.x dB off at 20kHz.

2) Full sinc reconstruction with massive upscaling (4x...16x), something similar to what the Chord M-Scaler does but with even higher precision in a pure software solution. This results in the textbook-perfect linear-phase true brickwall filter. Again this also produces a lot of "artificial" high frequency content, this time as severe ringing at one single frequency, fs/2. This is of no conseqeunces either as the frequency is above our perception limits (again, unless we have severe distortion issues downstream this is irrelevant) and more importantly, with real recorded music the massive pre- and post-ringing is hardly ever exited. It is most excited when the signal is illegal, not band-limited, to begin with (a single sample pulse or a step change). Assuming the ringing were actually audible (not fully proven), then it all comes down if the music was recorded with a proper ADC process where the anti-aliasing filter is absolutely paramount for the essential band-limiting of the audio.

So, there obviously isn't a straightforward way to define what is correct (least compromised) in an actual engineering solution.

And the bottom line is this HF content is actually irrelevant, and hence the details of reconstruction filters don't matter too much. The only place where the filter is truly relevant is during analog to digital conversion! And likewise, in the generation of artificial sounds (synths) where proper bandlimiting also should take place.

I've now tested both ways to some extend with my ADI-2 Pro. With my hearing stopping at 15kHz or so, I'm having a really having a hard time to tell the two versions apart, and zero success in blind testing so far.

 

[KSTR]

Below some responses of DAC and ADC using one ADI-2 Pro to measure another, at a higher sample rate so it captures the > fs/2 stuff:

 

[KSTR]

For the full sinc upscaling, see here for details, and of course the article by Keith Howard.

 

[melowman]

The latter happens typically if you use a software like HpW that uses ASIO, and your DA and AD have to run at the same sample rate.

So basically, in order to get a proper FR of the NOS filter in the fs/2 region — or any filter anyways —, just sampling the output with a higher fs would be suffissent?
(That’s almost a rhetorical question ^^)

 

[DonH56]

DAC images touched on here:
https://www.audiosciencereview.com/...ital-audio-converters-dacs-fundamentals.1927/

ADC aliasing touched on here:
https://www.audiosciencereview.com/forum/index.php?threads/digital-audio-aliasing.1920/

Two different consequences of the sampling theorem.

 

[melowman]

And the bottom line is this HF content is actually irrelevant, and hence the details of reconstruction filters don't matter too much. The only place where the filter is truly relevant is during analog to digital conversion!

That’s not my experience with reconstruction filters — you cannot say reconstruction filters are irrelevant solely based on the very subtle HF content differences, and ringing being barely there with real music. Those differences between recon. filters and others that I absolutely don’t know about, are a big deal for me and the way I perceive music, the way music is hitting me.

I’m not trolling or BSing; ok I only did AB tests but that only tells me that I absolutely don’t like the Sharp filter (the linear-phase one) nor the NOS. I did those AB tests several times several weeks appart, it ended up with the same dislikes and likes — it’s not ABX tests, I know that, but I’m confident in what I’m hearing. The main difference is how I perceive low-end and how transients are reproduced. The most obvious filter to recognise is the linear-phase Sharp, it has very distinctive sound characteristics.

Anyway, I don’t want to open another can of worms here. The day I’ll do proper ABX tests I will report them. As for now I’m pretty confident, and maybe it’s because I can hear up to 19.5kHz (I said maybe) but most importantly I am an audio engineer and thus pay attention to details most people don’t pay attention to and don’t care about. Hence the debate. But we need ABX tests I agree.

JohnYang1997 did an interesting experiment (even though it has its limits); he also did a proper ABX test between 2 filters and he did quite well.

Anyways, yet another subjectivism vs scientifism post ...

 

[Tks]

@melowman

You said you're an audio engineer, so it's safe to assume you're not under the age of 22. You're saying you're aged 22+ and can heard (I know you said maybe) up to 19.5kHz? You realize you're possibly golden ears if this is remotely true. With training, you could literally be golden eared...

 

[melowman]

I do hear up to 19.5kHz (the “maybe” was meaning “I’m hearing DA filter differences maybe because I’m hearing up to almost 20kHz) and do am 22+ yes.

Being certified “golden ears” won’t help me pay my bills! That’s the least thing I care about : )

 

[abdo123]

I do hear up to 19.5kHz (the “maybe” was meaning “I’m hearing DA filter differences maybe because I’m hearing up to almost 20kHz) and do am 22+ yes.

Being certified “golden ears” won’t help me pay my bills! That’s the least thing I care about : )

if you're an audio engineer you would definitely care about how good your hearing is. What do you mean?

 

[melowman]

If having golden ears was a condition to become an audio engineer, there wouldn’t be a lot of them
Fortunately it’s not a condition to be a talented engineer and praised for one’s work.
That are even engineers that don’t hear 6kHz, just 6kHz... ‍ He actually never noticed that until performing a hearing test, and it didn’t prevent him to be very talented!

 

[KSTR]

That’s not my experience with reconstruction filters — you cannot say reconstruction filters are irrelevant solely based on the very subtle HF content differences, and ringing being barely there with real music. Those differences between recon. filters and others that I absolutely don’t know about, are a big deal for me and the way I perceive music, the way music is hitting me.[...]

Thanks for your input, and no objections from my side.
When I wrote "irrelevant" I meant that in a statistical sense, with the assumption that a significant percentage of audiophiles (in the un-biased meaning of the word) won't be able to successfully ABX (or other proper blind test, for that matter), if only for the fact that many of us might be 50++ years old and have diminished high-frequency response.
Obviously, some individuals will be able to identify differences, be it for better hearing in general or be it for intensive training and experience (which plays a big role here, IMHO). I'm 100% certain I will identify differences once I get to lower Nyquist frequencies. 10 years ago, I could tell a 32kHz file from a 44.1kHz one in an instant because the top end air frequencies were missing. Today, not that easy anymore...

EDIT: As for your experience, do you feel that at 88.2kHz/96kHz (or even at 48kHz) the filter choice becomes irrelevant (other than for NOS when not droop-corrected), with native source material?

 

[melowman]

EDIT: As for your experience, do you feel that at 88.2kHz/96kHz (or even at 48kHz) the filter choice becomes irrelevant (other than for NOS when not droop-corrected), with native source material?

I don't have much of these native higher SR music material, I have to say that my concern regarding DA filter was mainly about 44.1kHz SR so far. I'd have to make some testing in that direction and see what happens.

 

[MC_RME]

So basically, in order to get a proper FR of the NOS filter in the fs/2 region — or any filter anyways —, just sampling the output with a higher fs would be suffissent?
(That’s almost a rhetorical question ^^)

It's not, and no, it doesn't solve the problem. It improves, though. The main issue is the analyzer side, which should only read the level of the test signal. This is impossible with a standard stepped sine measurement - the analyser can not measure the 20 kHz but ignore the 24 kHz mirror. Etc.

AP has a method that should work, but I can't check this right now. Discussion on that was around here:

https://www.audiosciencereview.com/...-totaldac-d1-six-dac.8192/page-18#post-204664

I tried the Continous Sweep but it failed as software solution (AP software plus ADI via ASIO, no AP hardware) in the same way as the Stepped Sine Sweep did.

People are used to measure out of band with white noise, see tons of such pics floating around and also Amir's stopband ones. KSTR always amazes me, I have never seen so clear and clean measurements of that before (obviously not using noise).

 

[melowman]

KSTR always amazes me, I have never seen so clear and clean measurements of that before (obviously not using noise).

Maybe he (@KSTR) could explain his magic? : )