Which is more accurate: digital or vinyl?

Hello Almarg.

Reciprocating your respect, truly, I wouldn't expect you to have encountered it before.

I bought a UNIX box in 1999 to do simulation research with Maple (the pro math package). Then I found that, sadly, the journals don't like results which don't parrot the mainstream "wisdom". So I did recreational things like investigating this. In any case, it's unpublished, so you'll have to do it yourself.

The algorithm is quite simple: set the number N of samples per waveform, calculate the step functions appropriately, and calculate the difference squared between that and a sine wave. Divide by the area under the sine. That gives you RMS distortion.

Let N increase. At about N=250 you will see the distortion falling towards 5%.

Oversampling does not help much. Unless the original signal is also processed this way, you merely end up with a curve that more closely approximates a distorted sine.

Regards,
Terry

Hi Terry,

It seems to me that the flaw in that analysis, as my previous post intimated might be the case, is that it does not take into account low pass filtering that is applied in the d/a process to smooth out the stepped character of the sampled waveform.

Essentially, your distortion percentage is incorporating ultrasonic spectral components that represent sampling artifacts (as opposed to distorted musical information), which ultimately get filtered out.

Another way to look at it is that were your claim true, then for redbook cd an audio frequency of 44100/250 = 176 Hz would be distorted by 5% when it is played back, and higher frequencies would be distorted by a far greater percentage than that. Clearly the cd medium, while far from perfect, does better than that!

Regards,
-- Al

Hello Al.

Thanks for the note, but I find the arguments unconvincing. While it is easy to speak of step functions being "smoothed out", it is imprecise. To make the statement precise, the smoothed function must be measured from real devices rather than theoretical, if for no other reason that every RC filter introduces its own distortion. Once an empirical function is obtained with adequate precision, it may be possible to fit the curve analytically, or, at worst, as an approximation using some technique such as cubic splines. Then, when an expression for the smoothed function is obtained, the analysis can be re-run, and an amended error figure derived. In the absence of such a Herculean effort, which should, of course, be borne by those who market the technology, I think that we are entitled to simplify the problem as I have done (see below).

Furthermore, I hold little hope that this effort will much reduce the distortion figure. Perhaps this is why we have not seen it reported. I alluded to the problem in my previous post - the smoothed curve will lag the sine except at the peak and trough. Hence the smoothed curve will closely approximate another smooth function, albeit one with two higher frequency distortion components, both of which will be some function of frequency. That other smooth function will not be a sine, having a (relative) hollow on the left edge and a bulge on the right. The RMS error, being referenced to a true sine function, will remain high.

As for your riposte, that a 176 Hz tone would be 5% distorted, that is not implausible to me. I find even the mid-range on CD's to be unclear compared to analogue (Linn Unidisk source into electrostatics). You are absolutely right to make the calculation and challenge me on it, but I have already made that calculation and found it plausible, so I suppose we must agree to disagree on that point.

If you would like to proceed as I suggest in the first paragraph, and achieve a better approximation, I applaud your devotion to science. And I will modify my opinions with a dose of humble pie if you prove me wrong.

Thanks for engaging.

Terry

all digital recordings are made using analog mikes - so unless there is A/D converter that can do it 100% identical as mikes picks it up - then all analag recordings will be better (as long as there is no digital involved in the process) - which was true in vinyl days....
kind of same as photography - kodachrome was always better than digital....

Hi Terry,

Rather than getting into a lot of esoteric mathematics that would be necessary to provide a quantitative perspective on all of this, I’ll just make a couple of additional qualitative points. I suspect that following your rebuttal we'll then, as you say, have to agree to disagree.

I agree that the low pass filtering/analog reconstruction process cannot be done to absolute perfection. However, consider the spectral components that distinguish an audio frequency sine wave from that sine wave as sampled at 44.1 kHz. The spectral components that distinguish those two waveforms are all at ultrasonic and RF frequencies, and as such are essentially inaudible to us. (The reason I say “essentially” is that, as you may be aware, some seemingly credible studies have suggested that we may be somehow able to sense the presence of frequencies up to perhaps as high as 100 kHz if they are accompanied by frequencies that are within the nominal 20 kHz range of our hearing). Consider especially the spectral components corresponding to the transition times between steps. Those are at radio frequencies!

Yet in referring to them as “distortion,” and citing that “distortion” as the basis for defining the threshold of sample rate acceptability, your analysis implicitly assigns audible significance to ALL of these ultrasonic and RF spectral components, little or no differently than if they were some low order distortion components lying well below 20 kHz. It also implicitly assigns audible significance to these ultrasonic and RF spectral components that is no different than if during the analog reconstruction process no filtering were applied to them at all.

Second, consider the hypothetical situation where an infinitely long sample record is available, with each sample having infinite resolution (i.e., zero quantization noise). The rationale behind your contention that 250 samples per cycle are necessary to achieve 5% distortion would seem to be no less applicable to that situation than it is to real world digital scenarios, despite the fact that (as I think you would agree) only a little more than 2 samples per cycle are necessary in that hypothetical situation.

The bottom line, IMO and with respect , is that I doubt your contention that a sample rate of more than 100x the Nyquist rate is necessary to achieve reasonable (although still high!) levels of distortion would be likely to receive widespread support even among the most ardent vinyl advocates, or at least those among them who have sufficient technical background to comprehend the issues.

Regards,
-- Al

Hello Al.

Thank you for your expert and thoughtful response. I find myself agreeing with your premises while disagreeing with your conclusions.

I agree with your aside concerning filtering, but, would you not agree that every capacitor introduces distortion? And that therefore we should be concerned with physical measurements rather than idealizations? I hope that this does not misrepresent your point.

I also agree that the spectral components are all above 20KHz. Would you not agree that this creates a very rich ultrasonic environment? And further, that this is mainly generated from harmonies in a fairly narrow 4 octave range, suggesting that the ultrasonics are also clustered? I note that different frequencies "beat" against each other; e.g. 33KHz and 34KHz signals beat to form their difference, or 1 KHz. Further, these beats will be related to the fundamentals in no simple respect, producing distortions which have not been characterized. If they were especially irritating, only a small audio component would be required to render digitally processed signals unpleasant. Which is what some of us observe.

Were it true that ultrasonic distortion was inaudible, SACD would be no improvement on CD, which is not observed. Therefore, I stand by the assertion that total distortion is what is important, until it is proved otherwise.

Having said that, I agree with your (implicit) point that another useful simulation would use linear interpolation between subsequent sample points. Then it would be an empirical question of which method better approximated the physical effects, and whether the ear responded as the approximation would lead us to expect. A Ph.D. dissertation there.

Your point about a periodic waveform of infinite duration is absolutely correct. I was restricting myself to waveforms which are physically possible. Since physical possibility precludes the use of the Shannon Sampling Theorem to justify reasoning, I stand by my assertion.

I also suspect that many will disagree with me, for whatever reason. I respect your reasons, but nevertheless must disagree.

Thank you for an enjoyable and enlightening discussion. Respectfully,

Terry

Hi Terry,

I agree with your aside concerning filtering, but, would you not agree that every capacitor introduces distortion? And that therefore we should be concerned with physical measurements rather than idealizations?

Absolutely. The various non-idealities of low pass filters, in both the recording and playback parts of the chain (anti-aliasing and reconstruction filters, respectively) are a major issue in digital audio.

I also agree that the spectral components are all above 20KHz. Would you not agree that this creates a very rich ultrasonic environment? And further, that this is mainly generated from harmonies in a fairly narrow 4 octave range, suggesting that the ultrasonics are also clustered? I note that different frequencies "beat" against each other; e.g. 33KHz and 34KHz signals beat to form their difference, or 1 KHz. Further, these beats will be related to the fundamentals in no simple respect, producing distortions which have not been characterized.

Agreed. In fact, arguably the most important reason for low pass filtering the d/a output is to eliminate (or at least greatly attenuate) beat frequencies that would otherwise arise as a result of non-linearities downstream in the system (and perhaps to some extent in our hearing mechanisms as well).

Were it true that ultrasonic distortion was inaudible, SACD would be no improvement on CD, which is not observed. Therefore, I stand by the assertion that total distortion is what is important, until it is proved otherwise.

As indicated in this Wikipedia writeup:

Because of the nature of sigma-delta converters, one cannot make a direct technical comparison between DSD and PCM. DSD's frequency response can be as high as 100 kHz, but frequencies that high compete with high levels of ultrasonic quantization noise.[36] With appropriate low-pass filtering, a frequency response of 50 kHz can be achieved along with a dynamic range of 120 dB.[2] This is about the same resolution as PCM audio with a bit depth of 20 bits and a sampling frequency of 96 kHz.

So although comparison between the parameters of the two formats is not straightforward or precise, it would seem clear that the performance of DSD is, at least potentially, superior to that of redbook cd in terms of dynamic range, and also in terms of providing greater margin relative to the Nyquist rate. That increased margin can be expected, at least potentially, to lessen the side-effects of anti-aliasing and reconstruction filters that may occur at audible frequencies, just as it can for hi rez PCM, relative to redbook PCM.

In summary, I think that our positions are similar in a lot of respects, but we agree to disagree on the need for a sample rate that approaches the one you have advocated. My thanks to you, also, for a stimulating and mutually respectful discussion.

Regards,
-- Al

Almarg and Terry9, thank you for a fabulous exchange; extremely informative and a model of civility. Very impressive.

This is a technical question, and it can be answered with an accurate oscilloscope. Simply compare the two wave forms on a double trace scope. I would wager "digital" because of the consistency of reproduction.

Orpheous10, brings up a good point.
In practice rather than in theroy, how much distortion is produced in typical vinyl rigs?

Unsound and Orpheus - one can measure "distortion" all one wants. The problem is, some types of "distortion" are much more musically harmful than others. There is admittedly more "distortion" in analog, however the distortions of digital are much more musically objectionable because of the frequencies at which they occur, and for other reasons. So the measured amount is beside the point, really. IMO, too many audiophiles get hung up on measuring instead of training and using their ears to tell them what sounds more like the real thing.

Learsfool, I find the ticks and pops much more objectionable.

Sorry, clicked too soon. I think Orpheus10's remark was in response to Terry9's post.

Yes, Unsound, I realize that Orpheus 10 was responding to Terry9. That in no way invalidates what I said, however. In this particular context, I mainly wanted to make the point that far too many audiophiles rely on measurements instead of their ears, especially when "distortions" are in question.

I was responding to the fact that I'm a technician, and the question is not "audiophillic" if there is such a word; but technical.

As a technician, I rely on my ears as opposed to measurements when we are in the "audiophile domain", and as an "audiophile" I'm sure you know what I mean. Nothing can measure subtle nuances.

Orpheus10, I don't think that a 'scope is the best way to investigate this.

I can clearly hear differences between waveforms that look identical on a scope, such as small differences in IM distortion. The resolution is simply not there. That may be because a scope's display is painted on a phosphor-coated screen, and it cannot react very fast. Only specialized phosphors are likely to react faster than 1KHz, much less 20 KHz. Knowing this, the scope's manufacturer is likely to have embedded averaging routines, so that one does not observe an event, but an average of events. Therefore, the question reduces to the temporal resolution of the instrument's display, as distinct from it's electronic frequency response to periodic waveforms repeated over thousands or millions of cycles. Alternately, specialized electronics "freezing" the action would work - but not a garden variety scope. Not being an expert, I may have got this part wrong - if so, please correct me.

I also note that consistency is a poor substitute for accuracy.

Second, digital representations of waveforms near the Nyquist criterion (half the sampling frequency) are aperiodic, except over several waves. To see this, consider a 20KHz sine wave being sampled at 44KHz. It is sampled, on average, at a rate of 44,000/20,000 = 2.2 times per wave. Since the wave evolves over a period of 2pi, the distance between two samples is 2pi/2.2 ~ 2.856. Without loss of generality, assume that the first sample is taken at point 0, the second at 2.856, the third at 5.712, etc. Then

Point Sin
0 0
2.8 .28
5.7 -.54
8.6 .76
11.4 -.99
14.3 .99
17.1 -.99
20 .91
22.8 -.76
25.7 .54
28.6 -.28
31.4 0

Which then repeats.

A linear interpolation of these points is the best a digital algorithm can do, unless it makes assumptions about the character and frequency of the waves. That linear interpolation results in asymmetrical triangular waveforms with peaks ranging from an absolute minimum of .28 to an absolute maximum of .99. The result is a waveform periodic over 5 of the original 20KHz waves, or 4KHz. Thus a 20KHz signal is rendered into a highly complex waveform which waxes and wanes over a 4KHz period. Furthermore, the waveform must be triangular and asymmetric, with attendant beats, unless heroic processing is invoked. And even if it is, that 20KHz tone must wax and wane over a 12dB range.

Clearly the effect worsens as one approaches the Nyquist frequency. The brick wall filters which prevent signals higher than Nyquist also impose their own distortions and phase shifts at lower frequencies, but that is another matter.

Finally, thank you Learsfool, for supporting my point about different types of distortion, especially those which have yet to be characterized. I think you may have said it better.

Terry9, vinyl doesn't deliver the degree of consistancy needed for the measurements you're talking about, and you must have consistency for any scientific comparison. Unfortunately, digital and vinyl are apples and oranges; consequently the only comparison that can be made is subjective.

The human hearing system, meaning the ear combined with the brain's perceptions, is still not fully understood. It is definitely more sophisticated than any machine yet made. To name just one example that affects the audio world, it has been proven by research that the brain does indeed perceive frequencies above 20,000Hz, even though supposedly the ear cannot hear them. This phenomena has not been explained. However, it is my understanding that the vast majority of designers of digital audio equipment still routinely process out all frequencies above that, on the theory that we can't hear them.

I'm well aware of this phenomena. In a test I could not hear over 17,000Hz, but I can perceive at least to 20 KHz; which is why I have a tweeter that goes that high.

I can tell the difference when someone has a tweeter that only goes to 18 KHz, but I can't quite explain it.

Learsfool, it has to be "harmonics". People only think of harmonics going up the ladder, but I reason that if they go up the ladder, they have to come down the ladder as well.

Orpheus10, are you suggesting that the brain can somehow fill in the mathematical missing rungs (gaps) of the harmonic ladder? If so, it does seem somewhat plausible. If not, then what? Please accept my apologies if I'm going too off topic here.

No, you're absolutely correct.

When I got my FCC license, I thought I knew everything; working with scopes, frequency meters, etc. There was nothing I couldn't measure; and then I got into high end audio. That was when I discovered those dumb "audiophiles" who didn't even know ohm's law, could hear things that I couldn't measure.

First of all, an audiophile has very good hearing. Once upon a time I said if two amps measure the same, they sound the same; of course you know I was wrong, and so it is with harmonics, we can hear in between the rungs.

In addition, harmonics are always presented as a lower frequency affecting a higher frequency, but never how higher frequencies affect lower frequencies. I'm saying these higher, inaudible frequencies affect lower frequencies. Can anyone shed light on that.

Please pardon me while I abuse the analogy to extrapolate enough to put the ladder on shaky ground; one might presume that the more rungs that are actually there, the less the brain has to work at filling in the missing rungs, even if one is scaling the ladder blind folded.

Oops, I think I may have fallen off the high end, and into the deep fertilizer. :-)

While "harmonics" are unrelated to the subject, they are very much related to what we hear as audiophiles.

My new stance on this subject is totally unscientific, because "high end" audiophiles hear things that go beyond any instruments ability to measure. When CD's came out, I bought them to hear the same music I had on LP, only better. One CD in particular was inferior to the LP, it lacked "nuance"; and as jazz lovers know "nuance" is everything.

I down loaded this LP to my computer, and on playback all the "nuance" was there; complete with record noise. What do you make of that?

Which is more accurate, digital or vinyl; was the question. Although the question implied CD, it was not implicitly stated. Computers operate in the digital realm.

While the CD was inferior to the LP, when the LP was transferred to the "digital" realm of the computer; the analog playback came back completely intact including "nuance" and record noise; therefore, one has to ask "Which digital are you referring to?"

FWIW, I didn't read it as though digital was limited to CD.

01-31-12: Orpheus10
In addition, harmonics are always presented as a lower frequency affecting a higher frequency, but never how higher frequencies affect lower frequencies. I'm saying these higher, inaudible frequencies affect lower frequencies. Can anyone shed light on that.

I'm not sure I understand the question. The character of what we hear is a function of the combination of fundamental frequencies, harmonics, and broadband spectral components that are present at any given time.

As Learsfool and I stated, seemingly credible studies have indicated that frequencies that are significantly above 20 kHz can be sensed under some circumstances, particularly if lower frequencies are simultaneously present.

02-01-12: Orpheus10
When CD's came out, I bought them to hear the same music I had on LP, only better. One CD in particular was inferior to the LP, it lacked "nuance"; and as jazz lovers know "nuance" is everything.

I down loaded this LP to my computer, and on playback all the "nuance" was there; complete with record noise. What do you make of that?

Orpheus, an obvious question: What makes you assume that the CD and the LP were mastered identically?

Frogman, thanks very much the kind comment in your post of 1-26.

Regards,
-- Al

My point was, that the computer, which is digital; reproduced the LP as good as any TT I've ever heard, as a matter of fact it was identical. When comparing the CD to the LP, there are many possibilities and variables. This was an early CD, and I hear they've gotten better.

In regard to the harmonics, we are all in agreement. When we listen to music, high frequencies affect low frequencies, and the question of harmonics is really "moot".

I also agree on frequencies above the "audible" range. We hear, or sense with our entire body.

Let me settle this once and for all. Since there is no such thing as a "nuance meter", and a computer and a vinyl LP can both reproduce something that is beyond any meter's ability to measure; lets call it a draw.

Terry9 says:

"Were it true that ultrasonic distortion was inaudible, SACD would be no improvement on CD, which is not observed. Therefore, I stand by the assertion that total distortion is what is important, until it is proved otherwise."

Actually, on various hybrid CD/SACDs from Telarc and Mobile Fidelity, so the recording is the same, this is exactly what I have observed. I still have very good hearing, and on a moderately high-end system (Revel Salon 2s) I can't hear any improvement with the SACD layer over the CD layer. Not a bit.

I suppose there will be those that say my SACD player isn't good enough (Sony 5400ES), or that I'm not a good listener, or whatever, but if there is a difference it is very subtle.

I think a lot of CDs don't sound very good because they weren't mastered very well. I think a lot of SACDs sound better than CDs because they were mastered well. But I've never heard an SACD that sounds better than the best CDs I own.

I have downloaded a few high-res files, but I can't directly compare them to CD, because I don't have CD versions. But the high-res stuff are all purist recordings, so naturally they sound good.

Is analog better than any digital format? Better for recording than 24/192? 30ips 1/2 inch tape is pretty good, but can it compete with a noise floor at least 20db lower? Or no wow and flutter at all. If I were trying to make the world's best recording I'd start with digital.

When asked about the LP, Rudy Van Gelder, who gained fame for recording: Miles Davis, Thelonious Monk, Sonny Rollins, Joe Henderson, Grant Green, Wayne Shorter, John Coltrane, and many others on Blue Note, replied, "Good riddance". That tells me something.

Once the original signal goes to the mic, accuracy is lost, engineer twiddling on the eq also departs from accuracy. So the question should be..... what screws up the signal less, digital or analog. The high rez digital I have heard recently equalled the best analog I have heard and exceed lesser analog by a good margin. The best is the one which uses the best mic and has the least recording engineer editoralizing. Both digital and analog can be great, but will the engineer allow it?....jallen

Great post by Jallen. Kudos on that one.

Vinyl has presence, you are there, something digital needs to improve on.

To me, "more accurate" and "better sounding" are the same thing.

In both cases, the best analogue I've heard still beats the best digital I've heard - although the gap is narrowing year by year.

.

***Which is more accurate: digital or vinyl?****

Good question.
Fun question.
Misplaced question?

My vinyl front end sounds more musical and is more satisfying than my digital set up. The answer to this question is a personal one each of us has to make. My advice is to be an artist as you set up your front end. Digital or vinyl. That is...set it up with passion and follow what pleases you. Most of don't have unlimited financial resources and their are extremely musical systems to be created at all prices levels irregardless of format. This will sound weird but instinctively it comes to me as being true. The sound of plastic, ie vinyl, imparts a beautiful tone to the music recorded onto it. Because materials have to do with resonances and real instruments are materials vibrating, i believe it to have a inherent sonic advantage because of this and possible downfall if pops and ticks drive you crazy. For the most part and i know they're are always exceptions, vinyl sounds just a little bit more "human" to me than does digital. Therefore in a democratic audiophile world i would vote that vinyl is "more accurate". I might be wrong about this but this is where my journey has led me thus far.

Cheers...

This is a no brainer. Vinyl is more accurate! It picks up and lets you hear all the noise, distortion, clicks, pops, and rumble that CDs never let you hear. Vinyl also gets rid of that ear shattering dynamic range.

Wow Rok - what a funny response...in an ignorant kind of way...

Hfisher3380, I love your stereo rack. I wanted one but went with the Sanus Euro instead. I admit to being tight with the dollar. :) I am glad you found my response funny. These days we need all the cheer we can get.
Cheers.

Interesting.

Full analog, it seems, should capture harmonic structure much better than digital with ZERO interpolation, where digital can capture dynamic range and low background noise (can't toss a needle out of the record groove!).

But, it's hard to find true 24 bit digital from stem to stern on true digital equipment...and the end CD. Most 16-bit stuff is tape remastered to digital so the tape is obviously better than the CD...by far (listen to a record using the same master tape!). 24-bit not so bad to my ears but rare to find.