[Roam]

Quote:

Originally Posted by hciman77 /img/forum/go_quote.gif The Nyquist-Shannon theorem dictates that it must do this perfectly with a sampling frequency of 2f i.e for 22.05khz you need 441khz sampling. After the analog wave is reconstructed then it can be fouled up any way you choose

Claude Shannon's theorem is as follows:
If a function s(x) has a Fourier transform F[s(x)] = S(f) = 0 for |f| > W, then it is completely determined by giving the value of the function at a series of points spaced 1/(2W) apart. The values sn = s(n/(2W)) are called the samples of s(x)

Meaning a signal which consists of sine waves with a maximum frequency of W is completely described by recording its values twice as fast as W. So far, so good.

However, there's a slight problem, that being the interpolation required to get back to the original sine wave or signal. Shannon provides a formula for that as well:

What's the problem you ask? Notice that it's an infinite sum. What does this mean? Unless one has an infinite number of samples, it will be impossible to exactly reconstruct the original signal. Whoops.

 

[Fitz]

Quote:

Originally Posted by bordins /img/forum/go_quote.gif EDIT: Fitz. I didn't see your post below. I am not aware of the exact study you asked but will try to find out later. However, what I meant was people may think waveforms out of two DAC chips are the same but they actually are not at the level of human's "waveforms".

Ok, so if you didn't mean that the waveforms measure identically, then what differed in the measurements?

 

[courierdriver]

Um...this is all very interesting, but I've noticed that all these posts (and graphs/formulas) talk about the DACs, and their interpretation of the digital bits into an audible form (ie. music). Perhaps I've missed it, somewhere in these posts; but I've seen no mention about the importance of how that signal is delivered to the the outputs. The power supply is the most overlooked part of cheap CD/DVD players, IMO. You can use the most expensive dacs on the market in constructing a player, but they could still sound like garbage, without a decent power supply.

The better CD or DVD players have more money invested in their power supplies, to make sure the signal you're getting at the outputs is clean. The power supplies found in cheap $100 CD or DVD players aren't up to the task of removing and filtering electronic noise or AC-related grunge, from your electrical AC wall outlet. Upgraded transformers, resistors and capacitors add to the weight and size of a CD or DVD player (especially if the machine's designers uses separate output stages for digital and analogue). Such added weight may require a more sturdy enclosure also. The overall results (with proper implementation), are a stronger, cleaner signal; and therefore better sound quality.

 

[bigshot]

Quote:

Originally Posted by bordins /img/forum/go_quote.gif But psychoacoustic studies have shown that human hearing system is so complex, and it is *very* sensitive.

What studies are you referring to? The ones I've seen all say that we're only able to detect minor differences between sounds when there is direct A/B switching between the two. If you listened to one for a while, then waited thirty seconds and listened to something a little different, you wouldn't be able to tell any difference. It's hardly worth spending thousands of dollars to make things sound better in a situation like that.

See ya
Steve

 

[hciman77]

Quote:

Originally Posted by Roam /img/forum/go_quote.gif However, there's a slight problem, that being the interpolation required to get back to the original sine wave or signal. Shannon provides a formula for that as well: What's the problem you ask? Notice that it's an infinite sum. What does this mean? Unless one has an infinite number of samples, it will be impossible to exactly reconstruct the original signal. Whoops.

Interesting, so perfect is a slight overstatement, as the vinyl folks have always said - but two identically specced DAC chips would be equally "not quite perfect" - there should be nothing non-deterministic about their behavior ?

I will settle for as near as damn it

 

[hciman77]

Quote:

Originally Posted by courierdriver /img/forum/go_quote.gif Um...this is all very interesting, but I've noticed that all these posts (and graphs/formulas) talk about the DACs, and their interpretation of the digital bits into an audible form (ie. music). Perhaps I've missed it, somewhere in these posts; but I've seen no mention about the importance of how that signal is delivered to the the outputs. The power supply is the most overlooked part of cheap CD/DVD players, IMO. You can use the most expensive dacs on the market in constructing a player, but they could still sound like garbage, without a decent power supply. The better CD or DVD players have more money invested in their power supplies, to make sure the signal you're getting at the outputs is clean. The power supplies found in cheap $100 CD or DVD players aren't up to the task of removing and filtering electronic noise or AC-related grunge, from your electrical AC wall outlet. Upgraded transformers, resistors and capacitors add to the weight and size of a CD or DVD player (especially if the machine's designers uses separate output stages for digital and analogue). Such added weight may require a more sturdy enclosure also. The overall results (with proper implementation), are a stronger, cleaner signal; and therefore better sound quality.

I think you need to back this (importance of power supply) assertion up with measurements, graphs, and charts

 

[audiofil]

Let's take voltage regulators for example. Here's a graph:

The graph represents the noise generated by 2 very common and cheap voltage regulators - LM317 and LM337. They are cheap and do cheap (work that is) .... Noisy as hell.... Yakk

Implementing Jung configurations, shunt regulators, Zenner + emitter-follower, etc in power supplies is not quite cheap and rare to be found in mainstream electronics.

Want to see the difference? Here is a graph of a Jung configuration:

 

[hciman77]

Quote:

Originally Posted by audiofil /img/forum/go_quote.gif Let's take voltage regulators for example. Here's a graph: The graph represents the noise generated by 2 very common and cheap voltage regulators - LM317 and LM337. They are cheap and do cheap (work that is) .... Noisy as hell.... Yakk Implementing Jung configurations, shunt regulators, Zenner + emitter-follower, etc in power supplies is not quite cheap and rare to be found in mainstream electronics. Want to see the difference? Here is a graph of a Jung configuration:

The two graphs refer to the exact same circuit apart from the reguators ?

So the DAC chip itself may be almost silent but a Voltage regulator can add a load of noise - interesting - what is the signal strength for these measurements is it 0db ? So for a full amplitude digital signal the noise is 60db down - yes ?

This noise would show itself up as hiss on the analog output ?

Does this affect the shape of the reconstituted waveform ?

Presumably as it is a DAC the noise is only there when there is a signal i.e unlike TTs where you get noise from a silent groove you only get noise when there is a signal, such noise levels ought to be highly audible. But if it is -60db on a 0db signal then I wonder how much masking effect you get - I can certainly hear hiss on my old Nikko amp (1975 ?) but only at really high volumes and without a signal. From that period it is unlikely that the SNR would be better than say 70db.

 

[Roam]

Quote:

Originally Posted by hciman77 /img/forum/go_quote.gif Interesting, so perfect is a slight overstatement, as the vinyl folks have always said - but two identically specced DAC chips would be equally "not quite perfect" - there should be nothing non-deterministic about their behavior ?

The answer to this is a lot more involved than one would suspect. Firstly, there are three basic families of DAC chips, the R2R ladder DAC, single bit converters, and multi-bit delta-sigma DACs. If one were to look at the raw output from each of these chips they'd be distinctly different. Using a sine wave as an example, the R2R DAC will output something which looks like a sine wave, but with many discrete steps; a single bit DAC will basically put out what looks like a wall of random noise while multi-bit delta-sigma chips are somewhere in between.

Next, there are several types of R2R chips, ranging from 16 bit to 24 bit with a whole range of sampling frequencies, and each manufacturer is going to have a slightly different way of implementing the design. Assuming one has the same model chip from the same manufacturer, then the raw output will be identical, but that's just stating the obvious.

A similar story applies with multi-bit convertors, assuming the same number of bits from the same maker, the outputs should once again be identical. However, expecting a 3-bit delta-sigma DAC from Crystal Semiconductors to have the same output as one from Burr-Brown is not entirely realistic. They will have differing algorithms and thresholds for switching the signals between the 8 possible levels on the 3-bit DAC.

This is looking at the raw outputs from the conversion alone. Except for R2R DACs, the raw output is not useable in any way, it must be extensively filtered, interpolated, and noise-shaped, and again, everyone's going to have a different idea on how to do that. There's literally a million different algorithms dealing with the above, each will have its own advantages & disadvantages.

So to make a long story short, pulling the bits off a CD and converting them into an analogue waveform is still as much of an artform as reading squiggles off a vinyl record with a needle.

 

[hciman77]

Quote:

Originally Posted by Roam /img/forum/go_quote.gif This is looking at the raw outputs from the conversion alone. Except for R2R DACs, the raw output is not useable in any way, it must be extensively filtered, interpolated, and noise-shaped, and again, everyone's going to have a different idea on how to do that. There's literally a million different algorithms dealing with the above, each will have its own advantages & disadvantages.

Thanks for the added info.

Do you have any examples for the fully reconstructed filtered, interpolated, and noise-shapedwaveforms from different DAC types ?

Edit: So fundamentally 2 DACs could give rise to slightly different waveforms. Then the issues include how much difference. Can the difference include differences in amplitude ?, surely not in frequency as that would be terrible. The specs I have seen for pretty much all modern CD players show an effectively straight-line from 20 - 20k varying no more than +/- 0.5db (conservatively) but probably +/- 0.2db realistically for anything half decent, those measurements for the analog out - for the digital out +/- 0.01 is more common. So if not amplitude and not frequency then what ?

 

[bordins]

Quote:

Originally Posted by Fitz /img/forum/go_quote.gif Ok, so if you didn't mean that the waveforms measure identically, then what differed in the measurements?

Maybe you may get confused a bit. Given we feed the same track on a CD, I don't think two DAC chips willl produce the same waveform because they make different sonics heard by listeners.

 

[Fitz]

Quote:

Originally Posted by bordins /img/forum/go_quote.gif Maybe you may get confused a bit. Given we feed the same track on a CD, I don't think two DAC chips willl produce the same waveform because they make different sonics heard by listeners.

Oh come now, don't avoid the question so you don't have to back up what you originally said.

 

[hciman77]

Quote:

Originally Posted by Fitz /img/forum/go_quote.gif Oh come now, don't avoid the question so you don't have to back up what you originally said.

Yes, we need graphs, big graphs - and lots of them and we need them now - and real graphs too not just manufacturer promos

I am personally intrigued by the idea that two DACs could render a wave form that was fundamentally different in shape and would really like to see some examples.

 

[bordins]

Quote:

Originally Posted by bigshot /img/forum/go_quote.gif What studies are you referring to? The ones I've seen all say that we're only able to detect minor differences between sounds when there is direct A/B switching between the two. If you listened to one for a while, then waited thirty seconds and listened to something a little different, you wouldn't be able to tell any difference. It's hardly worth spending thousands of dollars to make things sound better in a situation like that.

The studies I referred to are mainly in the areas of cogitive psychology and physiology, not the ones related to the hi-fi community such as the subjectivist and objectivist debates.

If you look under the signal detection theory for decision making, you will see a lot of studies in both visual and auditory perception systems that humans can perform detection tasks very very well, on certain conditions.

http://www.audiology.org/publications/reviews/r0024.htm

This is unlike listening to a piece of music then getting asked what power cord or cables being used. IMHO, this kind of randomized ABX testing is too hard for human ability.

In constrast, if you are tested against one of your favorite music tracks that you listen regularly on your system (over a hundred or perhap a thousand times), it will be very easy for you to detect any subtle difference in the song being played. I believe many of us play a familiar song when testing a system. This is a signal detection task, the song is noise and any change is a signal.

This is my proposition that explains two different DAC chips produce different sounds. You can detect sonic changes in your favorite songs. The way cognitive scientists look at sounds is not through the physical waveform but human perception instead.

However, whether it is worth to spend thousands of dollars for an upgrade is very subjective. Good CD players for you may be bad for others.

 

[hciman77]

Quote:

Originally Posted by bordins /img/forum/go_quote.gif In constrast, if you are tested against one of your favorite music tracks that you listen regularly on your system (over a hundred or perhap a thousand times), it will be very easy for you to detect any subtle difference in the song being played. I believe many of us play a familiar song when testing a system. This is a signal detection task, the song is noise and any change is a signal. This is my proposition that explains two different DAC chips produce different sounds. You can detect sonic changes in your favorite songs. The way cognitive scientists look at sounds is not through the physical waveform but human perception instead.

Human perceptual abilities are well documented, discrimination thresholds are well known, psychophysics is a pretty mature field. Blind tests can show if a difference between stimuli can be reliably detected. The point being that it is a real difference i.e a measurable difference. Sighted tests are notoriously unreliable for this kind of discrimination task, humans are prone to all kinds of biases, persuasions and tricks. When sighted tests are followed by blind tests, the obvious differences found sighted often disappear. Where the differences still exist the you can generally find real measurable differences to explain the perceptual differences.

Whilst two DACs may have differences in THD, SNR, FR, DR and so on - they generally start from a position of technical competence that is very high i.e 93-96db dynamic range, 100+db SNR, FR flat +/- 0.2db and THD so low as to academic.

That we can detect differences at such high levels of performance is my point of query...