Understanding the Role of DACs in a Simple Audio Setup

[old tech]

There's been quite a bit of back and forth on this thread already and I've only just skimmed it, so hopefully I'm not going over what's already been said. To the question directly from my perspective I'd agree, a DAC ideally faithfully recreates an analogue of what was once analog but is now digital for the time being. Any coloration therefore should later come from an amp or the kinetics of the equipment itself being used to create the sound.

The issue from a technical standpoint is that such a thing is never really possible / a very difficult problem.
You have of course this classic image of a digital representation of a sin wave and the noise that it generates as a result over time, Source

Now this above would be very noisy and is more just to be illustrative as ultimately these transitions would be better sampled, smoothed out by filtering and ultimately even smoothed partly by the kinetics of the the w/e you're using to reproduce the sound.

But the overall problem remains I'm trying to take a continuous waveform, discretize it, and then take that discretized waveform and make something continuous out of it again.
So in the end all we have are these points in time, but no information about the smooth curve on which they connect to one another which will always impart a change to the sound. So the DAC designer has to figureout how to approch this problem and that decision will make an effect on the final sound. As for approximations themselves how close of an approximation to a continuations waveform do you need to get before it no longer effects the sound perceptually, I don't know, but is of interest to me.
And this is just the issues a perfect DAC might have, which can produce a specific voltage at a specific point in time - there is of course a host of electrical challenges then to the degree of accuracy you can accurately reproduce the individuated samples.

So tl;dr and to get back to the og question every DAC could be said to effect the sound in some way, you can scientifically measure what it is that the DAC is doing to that sound, but imo what exactly makes "good sound" or in this context "a good approximation" is not totally understood.

It is not an approximation as there is only one solution between the samples, and that is the original band limited analogue signal. It is a bit trickier with bit depth and quantisation which errors will create noise, but at 16 bits the noise is well below audibility at normal listening levels and that is even before differing.

 

[old tech]

Even two points is enough to define a circle, you just have to agree that one coordinate is the center and the other one is a point of the perimeter.

A circle can be drawn on a 2D plane (X and Y coordinates) just like how an electrical signal can be drawn on a 2D plane where the X-axis could represent time and the Y-axis could represent Voltage, so the curve is perfectly capable of representing a voltage changing over time, signals aren't any different or more complex than a 2D shape in that sense.

Yes you are right, only two samples are needed, just as only two samples are needed to define a sine wave (at 1hz).

 

[gregorio]

But the overall problem remains I'm trying to take a continuous waveform, discretize it, and then take that discretized waveform and make something continuous out of it again.

What do you mean the overall problem of “trying to take a continuous waveform and discretise it …” remains? It maybe remains in false audiophile marketing but it certainly does not remain in the real world. That “problem” was actually solved in 1948 (by Claude Shannon), about 35 years before digital audio was even released to consumers!

So in the end all we have are these points in time, but no information about the smooth curve on which they connect to one another which will always impart a change to the sound.

NO! Again, you’re regurgitating false audiophile marketing as fact. Shannon proved in 1948 that 100% of “information about the smooth curve on which they connect to one another” can be captured and therefore your assertion is false, it will NOT impart a change to the sound!

So the DAC designer has to figureout how to approch this problem and that decision will make an effect on the final sound.

Why would a DAC designer have to “figure out how to approach to this problem” that was already figured out and proven 75 years ago? Are you referring to an 8 year old DAC designer in their bedroom who doesn’t know what digital audio is? This is typical audiophile marketing BS, state a problem that doesn’t exist or was solved decades ago and then sell a fake/snake oil solution to it!

As for approximations themselves how close of an approximation to a continuations waveform do you need to get before it no longer effects the sound perceptually, I don't know, but is of interest to me.

There is no approximation, the result (analogue signal) is ideal but with some dither noise. How that “affects the sound” is easy to know/calculate, providing you know the basics of what sound is, and it’s physical limits. “Sound” can only exist within a range, it’s maximum is about 191dB SPL (due to the wave rarefaction pressure) and it’s minimum is about -23dB SPL (due to Brownian motion of air molecules). So, if you have dither (or jitter or any other noise) at say -120 dB and your peak listening level is at say 85dB SPL then that noise would be at -35dB SPL but as -35dB SPL cannot exist, it therefore CANNOT “effects the sound”, even if you had hypothetically perfect speakers/HPs! However, anything, including absolutely no difference or effect on the sound whatsoever can affect perception, for example, false marketing.

And this is just the issues a perfect DAC might have, which can produce a specific voltage at a specific point in time -

Again, NO! That is an issue which a NOS/filterless DAC might have but that is the exact opposite of a “perfect DAC”, it’s the most imperfect DAC topology anyone has has ever come up with, so much so that it’s effectively faulty/broken!

there is of course a host of electrical challenges then to the degree of accuracy you can accurately reproduce the individuated samples.

That doesn’t make any sense because (except with a filterless NOS DAC) no one is trying to “reproduce the individual samples”, what is being reproduced in the electrical domain is a continuous (analogue) waveform. At that point, then yes there are a host of electrical problems, including the insoluble one of Johnson/Nyquist (thermal) noise, however we still have to compare that with the ultimate limit of sound itself and of course consider the problem further downstream of converting (transducing) that electrical analogue signal into a mechanical sound wave.

So tl;dr and to get back to the og question every DAC could be said to effect the sound in some way, you can scientifically measure what it is that the DAC is doing to that sound, but imo what exactly makes "good sound" or in this context "a good approximation" is not totally understood.

Again, that’s a falsehood, it has been “totally understood” for more than 75 years and if it wasn’t, the digital age would not exist! The other problem is that contrary to another false assertion, you CANNOT “scientifically measure what it is that the DAC is doing to that sound” or rather it might be possible but it would be extremely difficult and no one to my knowledge does. You can certainly measure what a DAC is doing to the analogue output and of course many do, but you cannot measure what it is doing to the sound because that analogue signal has to be amplified and transduced in order to become sound and that process adds far more distortion/noise than the DAC process. So how could we measure the sound and determine what distortion/noise the DAC process is causing rather than the amps, speakers and microphone, even if it would be enough to exist as sound in the first place?

In any case the point of the image and my statement on not having any information is to illustrate how (given an implied non infinite sample rate) given two sample points you will be making an approximation of the original waveform which will always lead to an inherent non neutrality of the DAC.

Just repeating the same falsehood assertions (false marketing) will not eventually somehow make them true! My explanation above, which you can fact check (A Mathematical Theory of Communication - Claude Shannon - 1948) or on Wikipedia, explains why it false.

You really should be sure of the facts before posting them in this forum, posting marketing BS/audiophile myths as fact is of course rather rude in a science discussion forum. If you’re not sure if you understand the audiophile claims or the actual facts/science, then please phrase your points as questions rather than assertions of fact!

G

 

[bigshot]

You are absolutely right, when your aim is a reference sound. Then you should keep it simple and stick to defined parameters.
That is no longer my aim.

Balanced, or as close as you can get, is a good goal for a starting point. Then you adjust to taste.

 

[bigshot]

It’s always amazing how the people who don’t know what the hell they're talking about can be so supremely confident in what they say.

 

[2leftears]

So in the end all we have are these points in time, but no information about the smooth curve on which they connect to one another which will always impart a change to the sound.

As others already have pointed out, this is a common misunderstanding. We do have information re. the highest frequency components contained in the original signal because that is a requirement of the Nyquist-Shannon theorem; the source needs to be low-pass filtered prior to sampling.

If a suitably chosen reconstruction method then also limits the (re)generated signal bandwidth accordingly, then this places constraints on the smooth curve that 'connects the points' such that when using an ideal method only the smooth original signal will fit. It is in essence a complex parameterised curve-fitting problem; the proof of its efficacy happens in the frequency domain rather than in the time domain. The often-shown pencil-and-paper-style time-domain sample-and-hold reconstruction stair-step graphs are just about the worst reconstruction method imaginable and no DAC these days works this way (and for 16/44.1 never have AFAIK) unless people have been modding them stripping out the digital filters and doing NOS conversions. (And even then the results can't be all that horrible seeing so many NOS DAC conversion advocates claim it sounds so great...)

 

[Secco]

I would love to see some abx to debunk or confirm the so called subjectivity of "analog" vs "hi fi digital" sound or timbre or whatever. As headphones.com tested the dacs but with a subject that can hear over 20khz it makes the test not valid but the method of abx is right. Objectively speaking size and lenght of cables and output impedence matters in the equation for damping factor (wich is responsible for slow puffy bass or "analog" smooth decay if you will). That's the most I can say objectively so I would love some scientific abx demonstration and if the output would be that 100 and 10000$ dacs/amps are sounding the same it would be a big hit for the industry...

 

[castleofargh]

I would love to see some abx to debunk or confirm the so called subjectivity of "analog" vs "hi fi digital" sound or timbre or whatever. As headphones.com tested the dacs but with a subject that can hear over 20khz it makes the test not valid but the method of abx is right. Objectively speaking size and lenght of cables and output impedence matters in the equation for damping factor (wich is responsible for slow puffy bass or "analog" smooth decay if you will). That's the most I can say objectively so I would love some scientific abx demonstration and if the output would be that 100 and 10000$ dacs/amps are sounding the same it would be a big hit for the industry...

This might need some serious extra details and explanations because as is, the most I get is a surprised Pikachu face. Each sentence is saying something strange or very much lacks information to make what you mean clear. And it doesn't help that I don't see the link between one sentence and the next.
Maybe it's me?

 

[Secco]

This might need some serious extra details and explanations because as is, the most I get is a surprised Pikachu face. Each sentence is saying something strange or very much lacks information to make what you mean clear. And it doesn't help that I don't see the link between one sentence and the next.
Maybe it's me?

I'm sorry my english is not perfect I was trying to say that the problem stated in the beginning it's also valid to me. To be certain about we would need a lot of people abx testing different dac/amps with above 95% accuracy. If I try to justify the differences a lot of reviewer find in a so called analog/organic/smooth device vs a sharp/hifi/digital sounding one (quoting them) I suppose that is due to synergy behind the dac/amp and headphone/iem/speaker regarding 2 aspects that have proven to alter the sound: damping factor and load impedence, the first one indicates a fast or slow driver decay (mostly in bass) the second one can affect the frequency response so practically alter what you hear when you gave the same dac/amp a different load(speakers or headphones for ex.) And it reacts altering the frequency response mostly on the upper frequencies, but in most cases is a really small deviation.A combo of low damping factor and rolling off in the upper frequencies could be responsible for a more smooth, loose sound. Since all modern devices for ex. Dongles have very good specs but people continue to percieve them differently, I'm also interested in this subjective component ("measurements aren't the full story") and if in a succesful abx test the reason for the result can be addressed to some form of scientifical evidence. This is only my pov and idea from what I know so excuse me for imprecisions

 

[WoodyLuvr]

It’s always amazing how the people who don’t know what the hell they're talking about can be so supremely confident in what they say.

Arrogance, we are all guilty of it especially when typing out our thoughts & ideas.

 

[Secco]

Arrogance, we are all guilty of it especially when typing out our thoughts & ideas

I hope you re not referring to me I didn't want to come off as arrogant and I want to know more about the subject , sorry

 

[WoodyLuvr]

I hope you re not referring to me I didn't want to come off as arrogant and I want to know more about the subject , sorry

No, that was simply a general statement aimed at no one specific but rather to us all collectively Cheers!

 

[bigshot]

As headphones.com tested the dacs but with a subject that can hear over 20khz it makes the test not valid but the method of abx is right.

I’m not sure what you’re referring to here, but there aren’t many people that can hear over 20kHz, and the ones that can are teenagers, and can only hear a note or two beyond 20kHz. And there isn’t much content beyond 20kHz in commercially recorded music, and the frequencies that do exist are masked by lower frequencies in loud cymbal crashes.

This isn’t something that would affect a well conducted test.

 

[Secco]

I’m not sure what you’re referring to here, but there aren’t many people that can hear over 20kHz, and the ones that can are teenagers, and can only hear a note or two beyond 20kHz. And there isn’t much content beyond 20kHz in commercially recorded music, and the frequencies that do exist are masked by lower frequencies in loud cymbal crashes.

This isn’t something that would affect a well conducted test.

Yea you re right, in the video a subject abx some dacs succesfully and later they discover that he is capable of hearing something over 20k, really rare stuff. Its a headphones.com video on yt.

 

[bigshot]

Yea you re right, in the video a subject abx some dacs succesfully and later they discover that he is capable of hearing something over 20k, really rare stuff. Its a headphones.com video on yt.

Skeptical of that. Sounds more like someone gaming the test, or some sort of weird filter being engaged.