Understanding the Role of DACs in a Simple Audio Setup

[FunkyBassMan]

does a DA converter perfectly
reproduce the analog voltage recorded by an AD converter?

It’s a Yes or No question.

Yes, to a degree far beyond the range of human hearing.

And again, analog refers to the storage format, not the electrical signal. You keep using the word analog wrong.

bigshot is literally totally backwards wrong on this. In the system @eq1849 describes, the input electrical signal is analog and the storage medium is digital.

Just boggles the mind how after 20 YEARS here he could not even understand the most basic things.

 

[bigshot]

Digital audio is capable of audible transparency. You’re arguing a blend of semantics and misconceptions.

 

[Lohil]

No, you can’t have a straight line and the amplitude is always smooth, even with a huge spike in amplitude!
For the first thing to happen (a straight line) you would NOT need some “pretty high frequency components”, you’d need to break the laws of physics and so obviously “nevertheless they were there” is false! The second thing (a 10000% increase in amplitude) is well within the laws of physics, is not extremely uncommon and is well within the capability of 16/44.1, by nearly 3 orders of magnitude!

Starting to realize you guys take things very literally / in rigid context - which I guess is fair given the context is audio, but, this is just a parenthetical to demonstrate what I was talking about when I said there was no information between sampling points. Realistically yes to get that triangle wave I'd need an inf sum of inf. high frequency components which the air would not support, but I could theoretically get something approximating a triangle wave in air though, and I could also detonate a hand-grenade in the recording studio to get my amplitude spike

What higher order component, why would you invent an ADC that aliased an amplitude spike and why consider a question that doesn’t exist?
So you think that sound somehow magically avoids the laws of physics? The “sound as it was emitted originally” was constrained by whatever emitted the sound (what freqs it actually produced in the first place) and by wave propagation in air (EG. Air absorption of high freqs as well as roughly the inverse square law). Then, when we capture the sound, we’re constrained by the mechanical limits of a microphone plus the limits of an amplified analogue signal.

Yeah so I have been contextually neglecting the effect the ADC has on the color of sound as well... for simplicity of argument on just what a DAC would do to sound I'm imaging a digital file taken using an idealized ADC with inf. sampling rate.... but I can understand why that would not be the first place people's minds would go to.

No, there isn’t. What frequencies are detectable by the human ear was settled many decades ago and detectable differences in phase was settled several decades ago.
The human ear is not a high speed control system and the “jury” is NOT “still out on what the human ear can hear”, the jury returned the verdict in the 1930’s!

1. It’s not pointless, there are various specific applications for sample rates above 44kHz. It is pointless for audio distribution however.
2. What “specific to the DAC” audibly colours the sound is a faulty DAC design (such as a filterless NOS design) or a different output voltage but of course the latter can be neutralised by accurate volume matching. If a DAC is not audibly neutral (after volume matching), it is broken!

As BS by a scientist in a completely different field who doesn’t understand how audio works and is a disgrace! His papers (related to audio) are based on audiophile myths/misunderstandings, have been throughly debunked and discredited and he is treated as a joke (albeit a pernicious one). Many questioned the utter failure of the peer review process to weed out such BS papers before they reached publication, have heavily criticised the AES (and others) and demanded the papers be withdrawn. So severe was the criticism that the AES actually responded, along the lines (if I remember correctly) that their peer review process did not fail, they are well aware that the papers are incorrect but publishing them still serves the scientific and audio engineering community because they sparked so much debate. A BS response to cover their own asses, if they know the papers are wrong they should not have been published in a scientific journal in the first place and should have been withdrawn if published in error!

Well so this does answer a lot in where you guys are coming from, which is ult. a totally different direction than my own. If a DAC is neutral then the og question is essentially a pointless question. I have to say though ult. as I've never heard any audio equipment reproduce sound as though I'd heard it live (what I consider the ult. aim of HiFi) to me the jury is out on how to do that - the DAC (and ADC) apart of that question

As for the paper there is also this one posted http://boson.physics.sc.edu/~kunchu...isalignment-of-acoustic-signals---kunchur.pdf, cited as a sister paper, I don't know if it falls under simular critisism...

But I totally understand not believing papers (but part of that is being able to peg down what specifically was the inaccuracy/oversight/neglection [i.e. I would be interested in the specific refutation for that paper]), ult. one needs to confirm something for themselves.

I'd be surprised if no-one's already done this but you can back of the napkin this yourself, we know (in so far as it is testable claim for yourself, and is relatively non controversial) that the auditory spacial accuracy of a human is about 1 degree (I think) and so you can work out for a given frequency, the distance between the ears and a given spacial target - what the phase accuracy must be of the human ear...
Which I suppose I should work out when I have the time to find a napkin.

 

[2leftears]

I have to say though ult. as I've never heard any audio equipment reproduce sound as though I'd heard it live (what I consider the ult. aim of HiFi) to me the jury is out on how to do that - the DAC (and ADC) apart of that question

I've had this debate a few times in the past with a few sound engineers on this forum, and I had to conclude that my understanding of "heard it live" was a misconception. It is not as straightforward as it seems if you take the time to consider all factors involved. E.g. placing a stereo microphone at your listening position is not a good place to start, even if that would feel like an intuitive thing to do. There are a number of very good sounding 'single' stereo microphone recordings I have heard, but when I saw how awkwardly the band needed to be arranged around the mic I realised this would not work as a good 'live' performance at all even though the final mix sounded great. It is complicated, that much I know...

 

[bigshot]

Digital audio is capable of audible transparency at the ADC and the DAC.

 

[chesebert]

OP, digital has been perfected in theory for decades. However practical implementation improvements are still ongoing and many of the techniques are not cheap to implement. For example, military grade ceramic multi layer custom PCB with heavy copper bus is great for reducing noise, jitter etc and can improve all aspects of dac but they are expensive and you won’t find them in less than $20k dacs

For regular folks here is my practical guide on how to tell between the 2 DACs which one is the higher quality. The higher quality dac has the following characteristics:

1. Deeper and greater quality and quantity of sub bass
2. Greater bass weight and slam
3. Greater tonal weight across the frequencies but doesn’t mean warm sounding
4. Deeper and wider soundstage
5. Lesser “hi-fi” sounding re initial attack compared to the other dac
6. Sounds more laid back compared to the other dac
7. May appear to sound less detailed or lower resolution through mid and upper mid compared to the other dac (you are hearing noise not detail)

Have fun with your dac shopping.

 

[bigshot]

That sounds like a recipe for expectation bias.

Number 8 is a dowsing rod.

 

[sander99]

OP, digital has been perfected in theory for decades. However practical implementation improvements are still ongoing and many of the techniques are not cheap to implement. For example, military grade ceramic multi layer custom PCB with heavy copper bus is great for reducing noise, jitter etc and can improve all aspects of dac but they are expensive and you won’t find them in less than $20k dacs

For regular folks here is my practical guide on how to tell between the 2 DACs which one is the higher quality. The higher quality dac has the following characteristics:

1. Deeper and greater quality and quantity of sub bass
2. Greater bass weight and slam
3. Greater tonal weight across the frequencies but doesn’t mean warm sounding
4. Deeper and wider soundstage
5. Lesser “hi-fi” sounding re initial attack compared to the other dac
6. Sounds more laid back compared to the other dac
7. May appear to sound less detailed or lower resolution through mid and upper mid compared to the other dac (you are hearing noise not detail)

Have fun with your dac shopping.

Complete nonsense. A $10,- Apple dongle is already audibly transparent (audibly perfect) under certain conditions (proper load impedance, no clipping).

 

[old tech]

does a DA converter perfectly
reproduce the analog voltage recorded by an AD converter?

It’s a Yes or No question.

It is the wrong question. A better question is does a digital recording, storage/distribution and playback chain preserve the original signal better than an all analogue chain? The answer should be bleeding obvious.

 

[sander99]

I'd be surprised if no-one's already done this but you can back of the napkin this yourself, we know (in so far as it is testable claim for yourself, and is relatively non controversial) that the auditory spacial accuracy of a human is about 1 degree (I think) and so you can work out for a given frequency, the distance between the ears and a given spacial target - what the phase accuracy must be of the human ear...
Which I suppose I should work out when I have the time to find a napkin.

Here a quote about temporal resolution that you may find enlightening. Some people think the temporal resolution of 44.1 kHz 16 bit PCM is 1/44100 but that is not the case, it is much better:

IIRC, you are some kind of engineer. You may have had some training in sampled-data systems (aka discrete-time systems). The ability to resolve temporal differences between 2 sets of sampled data depends on the nature of the signal (the highest slope therein) and the number of possible values (resolution or bit depth). The steeper the max slope and the larger the number of possible values (states), the better the temporal resolution. For sine waves the calculation is rather straightforward:

​

where ∆t_res is the temporal resolution, f_sig is the frequency of the sine wave (the signal) and N_st is the number of states of the values.
The best case sine wave for 44.1/16 is: f_sig=22050Hz and N_st=65536, then ∆t_res=110ps. I imagine @gregorio mistakenly used the sampling frequency rather than the Nyquist frequency.
Perhaps more "typical" would be f_sig=2205Hz at -20dBFS (N_st=6554), with ∆t_res=11ns

FYI, I've seen a handful of papers giving human auditory temporal discrimination of about 5µs, easily handled by 44.1/16, unless the signal is small and exclusively low frequency.

I put a link to the part in one of the xiph videos where timing is covered, just watch 2 minutes from this point:

 

[old tech]

OP, digital has been perfected in theory for decades. However practical implementation improvements are still ongoing and many of the techniques are not cheap to implement. For example, military grade ceramic multi layer custom PCB with heavy copper bus is great for reducing noise, jitter etc and can improve all aspects of dac but they are expensive and you won’t find them in less than $20k dacs

For regular folks here is my practical guide on how to tell between the 2 DACs which one is the higher quality. The higher quality dac has the following characteristics:

1. Deeper and greater quality and quantity of sub bass
2. Greater bass weight and slam
3. Greater tonal weight across the frequencies but doesn’t mean warm sounding
4. Deeper and wider soundstage
5. Lesser “hi-fi” sounding re initial attack compared to the other dac
6. Sounds more laid back compared to the other dac
7. May appear to sound less detailed or lower resolution through mid and upper mid compared to the other dac (you are hearing noise not detail)

Have fun with your dac shopping.

Marketing departments love people like you.

 

[chesebert]

Actually, marketing people love “science focused” audiophiles because they can simply order an evaluation board, pop a monolithic dac chip in there, add power supply and case and voila they have a cheap dac that will test great on APx555 and can charge you $500 for it while spending next to nothing on engineering.

 

[danadam]

As for the paper there is also this one posted http://boson.physics.sc.edu/~kunchu...isalignment-of-acoustic-signals---kunchur.pdf, cited as a sister paper, I don't know if it falls under simular critisism...

This and and the previous paper assume that 0.5 dB level difference is way below the discrimination threshold. Here are some test files and my ABX log for 0.4 dB difference: https://mega.nz/folder/x4Jg1QxA#wXJiwGJAswIsBht6TRLTVg

Spoiler: ABX log

foo_abx 2.2.1 report
foobar2000 v2.1.6
2024-12-02 01:38:08

File A: sin7k_-3.00_dBFS.flac
SHA1: 578bbacdaeb89012acde3d17bde6e5ed008e72b2
File B: sin7k_-3.40_dBFS.flac
SHA1: 7686c67eba1cd129153ae74c784b790a4854e6ca

Output:
Default : Headphones (Samsung Type-C to 3.5pi gender adapter)
Crossfading: NO

01:38:08 : Test started.
01:38:49 : Test restarted.
01:38:49 : 01/01
01:38:59 : Test restarted.
01:38:59 : 02/02
01:39:18 : Test restarted.
01:39:18 : 03/03
01:39:45 : Test restarted.
01:39:45 : 04/04
01:40:01 : Test restarted.
01:40:01 : 05/05
01:40:15 : Test restarted.
01:40:15 : 06/06
01:40:27 : Test restarted.
01:40:27 : 07/07
01:40:42 : Test restarted.
01:40:42 : 08/08
01:40:56 : Test restarted.
01:40:56 : 09/09
01:41:18 : Test restarted.
01:41:18 : 10/10
01:41:46 : Test restarted.
01:41:46 : 11/11
01:42:02 : Test restarted.
01:42:02 : 12/12
01:42:02 : Test finished.

----------
Total: 12/12
p-value: 0.0002 (0.02%)

-- signature --
679076026a99a5c952058e96af0b446db2b11a34

foobar2000 ABX Log Signature Tool

It's for a good reason that blind test protocols require volume matching to 0.1 dB.

 

[bigshot]

The JDD (just detectable difference) for level varies according to frequency. In some ranges, it’s below .5dB. In others, it’s significantly higher.

 

[danadam]

The JDD (just detectable difference) for level varies according to frequency. In some ranges, it’s below .5dB. In others, it’s significantly higher.

The papers apply it to 7 kHz frequency, the test files in my link are also 7 kHz frequency.

Here a quote about temporal resolution that you may find enlightening. Some people think the temporal resolution of 44.1 kHz 16 bit PCM is 1/44100 but that is not the case, it is much better:

Here's an animation nicely showing how it is rather bit-depth and not sampling frequency that determines time resolution:
https://audiophilestyle.com/forums/...-of-digital-sampling/page/13/#comment-1087853