Frankly, I believe all you're hearing is your own confirmation bias.
Not sure how that was - I didn't know what the source was being switched for comparison. It was simply - ok, agree to these passages on this music at these time points - switching was done in another room by another party.
The routine included included many "switches" with no actual change of source. I reliably reported no difference on those. In the cases where I could I hear the differences - different samplings were indeed present. There were no cases of reported improvement with lower sampling.
And I did limit my earlier comment to only some program material.
Dude - I didn't want to hear a difference - I wanted to save storage. I took close to three hours on that, and made it as fair as I knew how.
Try it for yourself.
I don't say it requires expensive equipment - but I don't believe you'll hear a difference if all you run is junk and listen to Britany Spears at full volume. Otherwise, I invite you to try it out. With a variety of program sources.
On some source material - I could not tell a difference.
Your claims against me are too harsh by half. I already stated that I heard a difference on some material only.
Traveling Wilburys, Trip Wamsley, Stanley Clarke, various classical, various acoutic, various electric.
BTW - I tried several MP3 and AAC sampling rates for this. I found better range, tonal and dynamically, in the AACs - except when I couldn't tell a difference.
No prob on the 45 mill - I simply assumed that was what happened. Unlike some forums, this one doesn't give you an edit button, and people make a federal case out of the lamest things instead of cutting a little slack. I especially liked the idea that we needed help in the form of some 1200 HDTVs to graph a single second of CD audio. So we could _understand_ digital audio. Golly, that was helpful. Never mind that the same guy correcting your 45 mill got it as 41.1 k.
As for mods - didn't mean to sound too harsh on that. I've been following/. since a few months after its inception, and generally keep up. Lost my low-numbered acct when I forgot my password - and they no doubt mailed my password to the email account that was no more. Got a new id, and got flamed the first day for not waiting and lurking and then saying something intelligent.:P
What was it we used to say? Life is short and slashdot karma is cheap?
I meta-mod and mod when I get the chance, which is less often than when I'm offered points. I take modding seriously and that means it takes time and the efforts to not look at the id and to put away one's own opinions on a subject. I think people get fans - or memes do - and some mods operate in packs. I'd go thru a stretch where I'd get a +5, insightful for saying a ham sandwich is tasty and then a few days later get modded at troll or flamebait for posting a link to an article that _supported_ TFA.
Well before/. there was another saying - on the internet, no one can tell if you're a dog. But some of us can tell who belongs in an RL conversation and who needs to be 86'd.
Sound is simply a sense, and like vision, it can be a form of trainable observation. One day you're listening to Birdland by Weather Report and you become unhappy with the bridge to the cacophony - so you go looking for weak spots causing it - whether it's your speakers, a scuff on a CD or something else.
All I care about is the music. It's why I leave my electronics out of sight - I don't want to see or think about how I'm getting it. Takes longer speaker wire. So what. So you like MP3s in a car. What's wrong with that? My opinion, as long as it's better than radio, I'm winning. Stuff where I couldn't hear a difference - or one to speak of - I listen in the house to AACs, and save the storage for those recordings where it makes a difference.
Nice to exchange with someone who isn't all dogmatic about it.
Well, why not? The sideband frequencies will never appear at (lower than) 1/2fs because we band limited the signal before sampling it.
No problem. I've seen more than a few filter designers who've tried to get rid of the complex conjugate by not really understanding that were looking at invalid transform results. Better designers never had that problem - but in my generation there were few of those.
I'm taking a systemic approach, the DAC can only operate properly if the data it is fed obeys certain constraints. Not every possible combination of bits can be 'legally' reconstructed as a waveform!
Well, I'm pedantic, but I'm not a peasant about it.:) Throughout, I'm presuming real-world and reasonable constraints.
Do you mean amplitude quantisation error or timing errors (jitter)? There will *always* be amplitude errors, but they can (and indeed must) be removed with 1/2lsb dither.
I apologize. I had simply thought that all readers would be clear with my choice of terminology - completely my bad.
I'm unconcerned - for the sake of this discussion and the points I was putting forth - with quantization error. One chooses 8, 12, 16 or 24 bits largely by convention and the application and ya just live with it. I'm not overconcerned with 2^16 quantization levels being insufficient because I'd expect it to match or exceed the noise of the analog components (microphone, mixers) in the original analog recording. In other words, you have to start somewhere, and with dithering, filters and a certain uncertainty that the input signal is indeed perfect - as I express it - ya just live with it.
But timing jitter. I've not heard not that term in quite some time. If you'd caught my earlier reference, I did say that there's a reason that the PDF is related to LaPlace transforms (I _believe_ I remember mentioning it in this thread) - and I therefore, not without foundation, refer to that as sampling error.
It had simply never occurred to me that modern readers would read that quantization error, so I apologize.
Have you ever tried this experiment:
Have a friend give you some exponentially damped cosine waves at audio frequencies and then the same with a few raised cosine pulses summed in and have them give you that as the analytical function - as a blind experiment, let someone else choose that. Ensure that the function is piecewise continuous and give it a start point offsetting it from zero time by some irrational value multiplied by the sampling rate. Run the function, sample at 44.1 kHz, transform it, and compare to analytic results. Next - using the same functions - sample at 317 kHz and compare to 44.1 kHz and to analytic results.
You may be surprised.
This was illustrative of the crux of my sampling argument - and I thank you for not quoting wikipedia's sample theory pages to tell me about what I don't get and have instead responded kindly and intelligently.
People have built dacs with simple one pole R/C filters, or no filter at all, but they do sound a bit harsh. I suspect this is not due to the ultrasonic side bands being audible, but to the way they may cause IMD in amplifiers and tweeters.
That is all I needed in the way of correction on filter use for this application. Again, thanks.
In directly, it illustrates one part of my point - that sampling itself, played back - is wrong. After that, the argument reduces to ADC/DAC quality and the filters.
And I simply have chosen to ring the dinner bell that once the sampling - time jitter by your terms - is screwed up, then filters cannot correct that.
Is there any way the output from an ideal DAC can be analysed to tell that source is a DAC rather than a band limited analog signal+noise?
Crediting that all reasonable conditions exist for this experiment then under most signals - perhaps I'll go so far as to sa
If you are capable of improving the article and refuse to do so, then you're in no position to complain about the state of the article.
I've already pointed that finger at myself and have stated my regret more than once for the harshness of my criticism.
Does it occur to you that it's incredibly difficult to satisfy the tremendous amount of AC posts in this thread?
Also, there's no "voting process for knowledge" involved in Wikipedia. Editors don't vote on facts. It's meant to be based on research from reliable sources, and yes, sometimes there's voting on which details are worthy of inclusion - but you seem kind of resentful of how Wikipedia works, perhaps because you misunderstand its policies?
Yes, for continuous functions with unlimited time sampling, gee, that's completely true.
And for transients? Where you cannot control where the transient will actually be sampled?
Once again -
Have a friend give you some exponentially damped cosine waves at audio frequencies and then the same with a few raised cosine pulses summed in and have them give you that as the analytical function - as a blind experiment, let someone else choose that. Ensure that the function is piecewise continuous and give it a start point offsetting it from zero time by some irrational value multiplied by the sampling rate. Run the function, sample at 44.1 kHz, transform it, and compare to analytic results. Next - using the same functions - sample at 317 kHz and compare to 44.1 kHz and to analytic results.
I have to agree you really have some things confused or missing from your understanding of DSP.
Yes. In some areas, that is true. Not quite as many as I'm being accused of in this thread, but why quibble? Fundamentally, you're right.
The use of higher oversampling at the DAC spreads the DAC quantization error out across a wider frequency band, providing less in-band noise and allowing a simpler (lower order) reconstruction filter for the DAC. This is not equivalent to oversampling at the ADC.
I am more experienced at ADC - no practical field experience at DAC.
The audio domian is not the only place that digital signal processing and sampling are used.
The new digital workstations used for professional mastering are all either 24 or 32 bits and when i listen to tracks being played back on those systems that are sampled even at 24bit/96khz they sound nothing short of amazing.
Cool.
One of my DVD players I got specifically because of its SACD capability - and have yet to hear a single one of those recordings.:-(
How does what you're listening to compare with that? Any projections for when that will hit the consumer market?
Man, if you do lectures in this stuff, I'd hate to be one of your students.
OK.
The signal is band limited to 1/2 fs BEFORE it is quantised, and so the aliasing frequencies are not "at plus or minus a (hopefully small) margin about that frequency.", but instead ALWAYS above 1/2 fs. So these can be filtered off in the reconstruction filter. (And this is trivial nowadays with oversampling DACs).
I am completely familiar with this filtering fact - and some of its myth.
Are you aware that you're trying to justify that you can filter the complex conjugate of the sampled signal? I ask that in complete candor, and without sarcasm.
I'm also familiar that at many schools, aliasing is the term given specifically to the misunderstood components of the other half of the S plane. In such a case, you were likely taught to use the terms, "frequency estimation error" or "frequency component leakage" where I am identifying that as another form of an alias. Am I correct?
Now - I am not arguing against anti-aliasing filters, per se. Their value is well-established for many applications. I do argue that much of the math used to teach them is not sufficiently rigorous.
As for reconstruction filters, yes, I understand what you're trying to get to and how I ignored that completely. However - I honestly wonder to the extent that speaker diaphram momentum was taken into account - and if the reconstruction filter was needed as much as believed. Again - a bit of speculation, but given that few perform decent speaker measurements, and given that that momentum term is already contributing to smooth any hypothetical staircase, I thought that the whole reconstruction point wasn't that big a deal.
Except, you're of the school that sufficient oversampling applies. Me, too - but to a more limited point. It suggests you'll getter better confidence of your low-frequency estimates (relative to the sampling rate).
Remind me, if you will, as to how oversampling at the DAC weighs higher than oversampling at the ADC. (No sarcasm intended if that was a simple typo on your part - and if not, it's an honest question.)
The slew rate of amplifiers has NOTHING to do with this.
Then I stand corrected and thank you.
I agree that samples are not signals.
It's a good starting point for clarity.
The "waveform" you see when looking at a collection of samples in a wave editor has little to do with the analog waveform that leaves a DAC.
And with sampling error, I question how well that analog waveform that left the DAC resembles the analog waveform that went into the ADC.
And it is precisely upon this point that I am so unforgiving.
The Nyquist criteria is that *any* frequency *less* than 1/2 fs can be *completely* reconstructed. A frequency of exactly 1/2fs cannot have it's amplitude and phase components reconstructed.
Or, you could have said - with greater simplicity - that the real axis is crossed at DC and 1/2 dt. You say *less* - I said *within* - yes, you'd have hated to have had me - or not.
...brush up on sampling theory.
Yes. I agree. I recommend it as a daily activity, myself.
You are assuming that there is one AC, perhaps some of us are not just here to wind you up.
OK. Despite the fact that I earlier stated that I couldn't tell if there was more than one AC I was talking to... I'll just take that one lying down.
I believe that to plagarise I would have to be passing it off as my own work.
Agreed - I choose the wrong word. Kindly correct me - were you copying that from somewhere, or trying to phrase something that you believe that you know?
Reference please, AES?
No, you'd find it in the IEEE Journal of Radiation Effects, and then a related work published by the Applied Computational Electromagnetics Society.
Digital signal processing existed long before the AES got seriously into it.
At least one of my algorithms was implemented in one of the earlier HP digital oscilloscopes - and that model was used to get results in more than a few AES papers, AFAIR. As was the Nyquist criteria tech note that I'd re-written for HP. And I'm proud to say that I never got a nickel for that (and no, I never worked for HP) - that was just free and open before that was popularly known.
If you're a practitioner in the field, I will kindly and sincerely apologize - when you correct your post with discipline.
One filter to band-limit the analog input signal and try and avoid aliasing during sampling...
The idea that you can avoid aliasing during sampling is the most often quoted, and most completely wrong, statement by undergraduates. Some never get past that C and yet find work writing that stuff in later life.
Go to the graduate library, and begin by reading anything you can find by Cornelius Lanczos.
...one filter on the output of D/A to remove frequency images.
And do that lookup for Lanczos' work right after you've taken any elementary classes in physics, calculus and electrical engineering.
If these filters are *perfect* then everything works hunky-dory - at least in the sense that the filtered input signal can in theory be reconstructed.
You can't even plagiarize at all close to well.
That pokey feeling is the fork I just stuck in you - you're completely done now.
Under that condition, it will appear at (K*Nyquist_criteria) + actual_frequency - and in our case, the next occurrence won't happen until past 22.05 kHz.
It was late when I wrote that, so this correction is offered - the above equation holds true for even K. For odd, it's ((K+1)*Nyquist_criteria) - actual_frequency.
In short, cutting off information about 15k makes no difference in how we experience the audio, much like a camera not recording ultraviolet doesn't affect a photograph.
True, but only trivially so - very few sources have significant content above 16 kHz anyway. Except for triangles, some violins, some harpsichords and some synthesizers.
MP3 encoding is pointed at reduced sampling - and then betting on psychoacoustics. You can get close that way - that's why it was accepted by people in the first place. Add in that a great many people listen through low fidelity equipment, and the margin for MP3 improves.
But sampling in any form introduces error - and given the right program content and decent equipment in a decent environment - one can hear differences.
Close enough for rock and roll? Probably.
But why bother with MP3 in the first place? They're patented and out of date. If you're going to accept a lossy format, why not AAC, at the very least?
But in all of the arguments for or against audibility of lossy formats, such as MP3, one other factor is left out - using which encoder? More than one exists for MP3, so you can't really characterize MP3 by bit rate alone unless we can jointly agree on which encoder will be used in the first place.
I, for one, am in no position to do that.
And another point you raise about the ultraviolet - we all seem to agree that we don't see at that wavelength. But if you're calling for any double-blind tests, how about an ear check for all participants and sorting the hypothetical results further with that criteria.
People get their knickers in a bunch about physical criticisms - but how many people working next to jet engines, operating construction equipment, firing guns regularly, or lovers of loud head-banging music actually can hear anything above 8 kHz?
If 99% of your test subjects don't hear above 8 kHz - and 1% do - would that study prove that MP3 is inaudible compared to non-lossy digital - or would it prove it only for the hearing-imparied?
What are the ranges of hearing for the adult population? At one time, Bell Labs used to publish that - and it varied by age, gender and environment. I haven't seen such study results for many years.
So, until you qualify the MP3 encoders and until you specify music program content and specify the test subjects' hearing range - I'm not sure that you'll make solid points with your MP3 argument.
And you're going to need several double-blind tests to really prove anything - because there are more variables than you seem to be counting.
aliasing doesnt have anything to do with sampling (e.g. quantization errors) either in frequency or amplitude). aliasing is simply an unwanted side effect of not having enough sampling resolution
Correct that it has nothing to do with quantization errors - but absolutely incorrect that aliasing can be cured with higher sampling rates. It simply cannot - discretization error is unavoidable unless you get to Plank time.
It's a fantasy that increased sampling rates gets rid of aliasing. Only dumb luck in sampling does that - and that will self-limit to occasional frequencies in time.
Have a friend give you some exponentially damped cosine waves at audio frequencies and then the same with a few raised cosine pulses summed in and have them give you that as the analytical function - as a blind experiment, let someone else choose that. Run the function, sample at 44.1 kHz, transform it, and compare to analytic results. Next - using the same functions - sample at 317 kHz and compare to 44.1 kHz and to analytic results.
You may be surprised.
Finally the one thing that i never hear the analog audiophile types talk about (keep in mind i have nothing against it: if you prefer analog good for you) is that the same quantization errors that apply to digital audio also apply to analog...
Right on, and I'm glad you mentioned it. Only, to be canonically correct, I'd state it mo' more better as "...noise errors that apply to digital audio also apply to analog..." But FWIW, I think you covered the point admirably in your follow-on statements.
So. What is noise?
It's uncertainty in the signal. There's a reason in the maths that probability functions and LaPlacian equations have similarities. And uncertainty tends to increase as we go up in frequency.
Now, considering the playback medium - what are the choices? Hysteresis phenomena with tape playback or lateral acceleration problems with a stylus in a groove.
For all of its woes, I'm terribly happy with CD audio. It's good enough to really enjoy decent performances on an intimate performance - even with an inverted mike (or something in that feed) on the sax - (Dave Brubeck Quartet, Take the A Train).
And I'd be even happier at twice the sampling rate - not to eliminate aliasing - but to further reduce sampling error - because, no, I'm not happy with a 4 stairstep equivalent at 11 kHz.
But I am happier with that than the work of dealing with a head amp, moving coil cartridges and a multiple tonearm turntable mounted on a massive plinth, a ritual of pre-play cleaning - and no repeat playback on rare vinyl or at least a half-hour for cooling, because the stylus contact pressure does soften the vinyl - and before CDs came along, I did just that.
All I can say is - don't knock it 'til you've tried it. Then knock it.:)
I know a lot of people who insist that analog sounds better - and I've known them for decades - and many of them haven't heard live acoustic music in decades and I know for a fact have never in their lives heard a record played with even a clean stylus.
But some people do know what decent analog sounds like compared to live acoustic sources, and they prefer it to digital music. To each their own.
My intention was not to denigrate the fine work done by Red Book. I was just overly frustrated at having to once again explain this sort of thing, and I'm too lazy - or something - to contribute to wikipedia to improve things. (Or, I just don't believe in a voting process for knowledge - there's no democracy in physics, right?)
That's the first point at 0 volts for 1/44100 sec, the peak held for 1/44100 sec, 0 volts for 1/44100 of a second, and then the negative peak at 1/44100 second - it looks like a triangle if you connect the dots like in school - but that's a control function for electronics, so it ends up as 4 steps representing that particular frequency.
So, you see - it only gets worse, the better you understand what's going on.
As for 16 bits vertical, I've asked whether any electronics can accurately measure line voltage divided by 65535. That's like, serious millivolts. Lot of bits are being thrown away in both directions. Don't believe me? Stand back, and turn up the volume.
16 analog-to-digital converters are well within our tech. If we model amplitude vertically and time horizontally, it's cool that they've attempted to mitigate vertical error with such high sampling - and then counterpointing that with amplifier response time for each quantization level - pretty cool, actually. But the time sampling, well - as I keep repeating, it's a wonder than CDs work as well as they do.
The authors make no bones about it - the entire MP3 approach is to exploit psychoacoustics. The algorithms for this, and other codes, are quite fascinating - and all in all, they do a pretty good job.
But the bottom line for MP3 audio - 1) psychoacoustics, 2) not all MP3 encoder algorithms are equal, irrespective of bit rates, 3) the algorithms are adaptive to the input waveform because they know that it's lossy and they try to limit that.
Why do I call that delicious? Because that's what Vincent Price would call this insanely scary reality:
All you have to do in any of these articles to be modded as 5, funny, or 5, insightful, is to bray like a jackass that MP3 after a certain point is just so good that humans simply can't hear any better - and anyone who thinks differently is some kind of audiophile - you know - a psycho.
The irony can't get much thicker than that.
But psychoacoutics may be a perfect science - ask Bose. Those products are perfect too, aren't they?
Oh - and not any mods are paying attention - but just in case - Bose radios wired with Airport Express using AirTunes is one way to go for the guy that started this thread with his question. Now I can laugh some more if I'm modded off-topic - which I am.:-P
It's not 45 million, it's 41,100 for CD audio. And ALL samples are instantaneous...
No, the sampling is not instantaneous - by definition.
Anyway, I only suggested it as a way to visualize how straightforward PCM audio is on CDs. earlymon just wants to sound like he's smarter than the average Wikipedia editor.
Close, but no cigar. In this case, I may be better at attempting to explain what's going on than was done for that particular article.
Smart does not equal an ability to explain. But given that I've lectured on digital signal processing at the post-graduate level, I'm not without some qualification in the area.
As I said earlier, if you find me wrong or harsh, that's your right.
But my bottom line stands - it's a wonder that CDs work.
From an earlier post - perhaps yours, it's impossible to tell with an AC -
mean, you get a piece of graph paper with 65,535 blocks vertically and 41,100 blocks horizontally, and plot the samples, and you literally have a picture of the waveform. It doesn't get much simpler than that, so where's the misunderstanding?
The expanded form for the Fourier transform of a single impulse is a circle scaled to voltage in the S plane. Phase response - the angular progression from point to point is constant - so we describe that as having minimum phase. Plotted as phase vs. frequency, it's a straight line with a nonzero slope. Magnitude however, is that constant distance from the origin. Plotted as magnitude vs. frequency, it's a straight line with a slope of 0 - it's literally a flat line from DC to infinity.
That particular point is called the Dirac delta function - after the physicist of whom you may have heard.
And if one point cannot be band-limited, then no number of additional points can be band-limited.
A sine wave - ok, I'm being specific and sine waves are, in fact, imaginary - so a cosine wave, then, analytically, has but one frequency. The very fact of sampling that one wave - and then calculating it's frequency components - leads to an unlimited number of frequency components out to infinity - not just one. And only by the most ideal case possible will one particular frequency ever be sampled such that it appears as a single frequency point within the Nyquist criteria - 1/2 of the delta-time sampling rate. Under that condition, it will appear at (K*Nyquist_criteria) + actual_frequency - and in our case, the next occurrence won't happen until past 22.05 kHz.
Under ideal circumstances - controlled by fate, totally uncontrollable by electronics or design. And for any given sampling - it's incredibly rare. In the real world what really happens is that any given frequency component - any single frequency, in other words - is smeared to a peak at or only near that frequency, with additional frequencies at plus or minus a (hopefully small) margin about that frequency.
Engineers have poorly chosen the word aliasing for this - the frequency aliases as other frequencies. And they window it, they anti-alias filter it - but there ain't no such thing as a free lunch, so it's a battle that cannot be won.
Again - what could be simpler than that picture of a waveform on your graph paper?
Well - steps are much simpler than curves.
So for each quantization value of the signal, the voltage is held constant for 1/44100 second, then changed to the next step level for the next 1/44100 second and so on. However - amplifier circuits have something called a slew rate - the rated ability to change voltage over time. If a circuit can slew quickly, it may have a tendency for overshoot - partial solutions for that exist, but again - TANSTAAFL.
Both of those critical points, I covered in my original post - but evidently, I didn't explain them there any better than laughably, because you were left with the impression that you can get a picture of a waveform by sampling it - and you simply cannot.
It's entirely possible that the only reason that CDs can work in first place is all of the slop in transitioning voltages in the amplifiers in the first place.
No wizardry is required. Each sample is 16 bits - that's vertical resolution. The 44.1 kHz is horizontal resolution. It does indeed take (16 bits / sample) * (441000 samples / second) * 2 channels to get 1411.2 kbps for stereo.
As wikipedia says, that's the bit rate.
Maybe I'm just having a bad day. Bit rate is a significant parameter. And perhaps the fact that sampling is a signed 16 bit integer is a significant parameter.
But the wikipedia article, I personally found lacking - it's just a raw data dump, leaving the uninitiated susceptible to confusion. I found the decomposition of terms - rather than learnable references for DSP and PCM - laughable. So, I derided it as I did. Maybe I could have done better in my criticism of the article.
I tried a number of sampling schemes with a number of program sources on my system. Then had the sources switched for me (electronics are in another room from my speakers, so it was blind). On some material, I could hear significant differences from the original - where the original was an audio CD - sampled in the first place.
That's not scientifically acceptable - but perhaps it's a probative anecdote.
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Frankly, I believe all you're hearing is your own confirmation bias.
Not sure how that was - I didn't know what the source was being switched for comparison. It was simply - ok, agree to these passages on this music at these time points - switching was done in another room by another party.
The routine included included many "switches" with no actual change of source. I reliably reported no difference on those. In the cases where I could I hear the differences - different samplings were indeed present. There were no cases of reported improvement with lower sampling.
And I did limit my earlier comment to only some program material.
Dude - I didn't want to hear a difference - I wanted to save storage. I took close to three hours on that, and made it as fair as I knew how.
Try it for yourself.
I don't say it requires expensive equipment - but I don't believe you'll hear a difference if all you run is junk and listen to Britany Spears at full volume. Otherwise, I invite you to try it out. With a variety of program sources.
On some source material - I could not tell a difference.
Your claims against me are too harsh by half. I already stated that I heard a difference on some material only.
Traveling Wilburys, Trip Wamsley, Stanley Clarke, various classical, various acoutic, various electric.
BTW - I tried several MP3 and AAC sampling rates for this. I found better range, tonal and dynamically, in the AACs - except when I couldn't tell a difference.
No prob on the 45 mill - I simply assumed that was what happened. Unlike some forums, this one doesn't give you an edit button, and people make a federal case out of the lamest things instead of cutting a little slack. I especially liked the idea that we needed help in the form of some 1200 HDTVs to graph a single second of CD audio. So we could _understand_ digital audio. Golly, that was helpful. Never mind that the same guy correcting your 45 mill got it as 41.1 k.
As for mods - didn't mean to sound too harsh on that. I've been following /. since a few months after its inception, and generally keep up. Lost my low-numbered acct when I forgot my password - and they no doubt mailed my password to the email account that was no more. Got a new id, and got flamed the first day for not waiting and lurking and then saying something intelligent. :P
What was it we used to say? Life is short and slashdot karma is cheap?
I meta-mod and mod when I get the chance, which is less often than when I'm offered points. I take modding seriously and that means it takes time and the efforts to not look at the id and to put away one's own opinions on a subject. I think people get fans - or memes do - and some mods operate in packs. I'd go thru a stretch where I'd get a +5, insightful for saying a ham sandwich is tasty and then a few days later get modded at troll or flamebait for posting a link to an article that _supported_ TFA.
Well before /. there was another saying - on the internet, no one can tell if you're a dog. But some of us can tell who belongs in an RL conversation and who needs to be 86'd.
Woof!
Cheers!
Some audiophiles are prima donnas.
Sound is simply a sense, and like vision, it can be a form of trainable observation. One day you're listening to Birdland by Weather Report and you become unhappy with the bridge to the cacophony - so you go looking for weak spots causing it - whether it's your speakers, a scuff on a CD or something else.
All I care about is the music. It's why I leave my electronics out of sight - I don't want to see or think about how I'm getting it. Takes longer speaker wire. So what. So you like MP3s in a car. What's wrong with that? My opinion, as long as it's better than radio, I'm winning. Stuff where I couldn't hear a difference - or one to speak of - I listen in the house to AACs, and save the storage for those recordings where it makes a difference.
Nice to exchange with someone who isn't all dogmatic about it.
Well, why not? The sideband frequencies will never appear at (lower than) 1/2fs because we band limited the signal before sampling it.
No problem. I've seen more than a few filter designers who've tried to get rid of the complex conjugate by not really understanding that were looking at invalid transform results. Better designers never had that problem - but in my generation there were few of those.
I'm taking a systemic approach, the DAC can only operate properly if the data it is fed obeys certain constraints. Not every possible combination of bits can be 'legally' reconstructed as a waveform!
Well, I'm pedantic, but I'm not a peasant about it. :) Throughout, I'm presuming real-world and reasonable constraints.
Do you mean amplitude quantisation error or timing errors (jitter)? There will *always* be amplitude errors, but they can (and indeed must) be removed with 1/2lsb dither.
I apologize. I had simply thought that all readers would be clear with my choice of terminology - completely my bad.
I'm unconcerned - for the sake of this discussion and the points I was putting forth - with quantization error. One chooses 8, 12, 16 or 24 bits largely by convention and the application and ya just live with it. I'm not overconcerned with 2^16 quantization levels being insufficient because I'd expect it to match or exceed the noise of the analog components (microphone, mixers) in the original analog recording. In other words, you have to start somewhere, and with dithering, filters and a certain uncertainty that the input signal is indeed perfect - as I express it - ya just live with it.
But timing jitter. I've not heard not that term in quite some time. If you'd caught my earlier reference, I did say that there's a reason that the PDF is related to LaPlace transforms (I _believe_ I remember mentioning it in this thread) - and I therefore, not without foundation, refer to that as sampling error.
It had simply never occurred to me that modern readers would read that quantization error, so I apologize.
Have you ever tried this experiment:
Have a friend give you some exponentially damped cosine waves at audio frequencies and then the same with a few raised cosine pulses summed in and have them give you that as the analytical function - as a blind experiment, let someone else choose that. Ensure that the function is piecewise continuous and give it a start point offsetting it from zero time by some irrational value multiplied by the sampling rate. Run the function, sample at 44.1 kHz, transform it, and compare to analytic results. Next - using the same functions - sample at 317 kHz and compare to 44.1 kHz and to analytic results.
You may be surprised.
This was illustrative of the crux of my sampling argument - and I thank you for not quoting wikipedia's sample theory pages to tell me about what I don't get and have instead responded kindly and intelligently.
People have built dacs with simple one pole R/C filters, or no filter at all, but they do sound a bit harsh. I suspect this is not due to the ultrasonic side bands being audible, but to the way they may cause IMD in amplifiers and tweeters.
That is all I needed in the way of correction on filter use for this application. Again, thanks.
In directly, it illustrates one part of my point - that sampling itself, played back - is wrong. After that, the argument reduces to ADC/DAC quality and the filters.
And I simply have chosen to ring the dinner bell that once the sampling - time jitter by your terms - is screwed up, then filters cannot correct that.
Is there any way the output from an ideal DAC can be analysed to tell that source is a DAC rather than a band limited analog signal+noise?
Crediting that all reasonable conditions exist for this experiment then under most signals - perhaps I'll go so far as to sa
If you are capable of improving the article and refuse to do so, then you're in no position to complain about the state of the article.
I've already pointed that finger at myself and have stated my regret more than once for the harshness of my criticism.
Does it occur to you that it's incredibly difficult to satisfy the tremendous amount of AC posts in this thread?
Also, there's no "voting process for knowledge" involved in Wikipedia. Editors don't vote on facts. It's meant to be based on research from reliable sources, and yes, sometimes there's voting on which details are worthy of inclusion - but you seem kind of resentful of how Wikipedia works, perhaps because you misunderstand its policies?
No, I'm not resentful, I'm simply worn out by it.
That's what the statistics say.
What statistics?
Your argument is basically, "well, I'm not average".
I never once said that. I did say this:
http://slashdot.org/comments.pl?sid=1435342&cid=30018954
And I did say this:
http://slashdot.org/comments.pl?sid=1435342&cid=30020646
The one consistent thing about 'audiophiles' is that they insist that they can hear the difference.
Ah. I even said this:
http://slashdot.org/comments.pl?sid=1435342&cid=30020358
Next time, kindly respond to where I'm coming from, not just where you want to accuse me of coming from.
My arguments and positions were specific whereas yours are generalized - exactly my complaint.
Hope this helps.
Yes, for continuous functions with unlimited time sampling, gee, that's completely true.
And for transients? Where you cannot control where the transient will actually be sampled?
Once again -
Have a friend give you some exponentially damped cosine waves at audio frequencies and then the same with a few raised cosine pulses summed in and have them give you that as the analytical function - as a blind experiment, let someone else choose that. Ensure that the function is piecewise continuous and give it a start point offsetting it from zero time by some irrational value multiplied by the sampling rate. Run the function, sample at 44.1 kHz, transform it, and compare to analytic results. Next - using the same functions - sample at 317 kHz and compare to 44.1 kHz and to analytic results.
You may be surprised.
I have to agree you really have some things confused or missing from your understanding of DSP.
Yes. In some areas, that is true. Not quite as many as I'm being accused of in this thread, but why quibble? Fundamentally, you're right.
The use of higher oversampling at the DAC spreads the DAC quantization error out across a wider frequency band, providing less in-band noise and allowing a simpler (lower order) reconstruction filter for the DAC. This is not equivalent to oversampling at the ADC.
I am more experienced at ADC - no practical field experience at DAC.
The audio domian is not the only place that digital signal processing and sampling are used.
Roger that, Houston.
This stuff works and is robust.
You're welcome.
The new digital workstations used for professional mastering are all either 24 or 32 bits and when i listen to tracks being played back on those systems that are sampled even at 24bit/96khz they sound nothing short of amazing.
Cool.
One of my DVD players I got specifically because of its SACD capability - and have yet to hear a single one of those recordings. :-(
How does what you're listening to compare with that? Any projections for when that will hit the consumer market?
Of course it is - it's a measurement of a voltage level at a given moment in time. The only question is how accurate is that measurement?
Ah. That's what you meant.
OK, then you're trying to describe quantization error. It's not the only question. Sampling error is more important.
Apology not required.
Gracious of you to the max - but it's hereby given as offered.
Mom always said there's no good excuse for bad manners - so, my bad.
This snippet may clarify my response to some of your criticisms - http://slashdot.org/comments.pl?sid=1435342&cid=30022018
Or - it could make it worse. Either way, I wrote it, so I bought it. :)
I do get confused by the threading when it gets deep, I guess.
Cheers!
Man, if you do lectures in this stuff, I'd hate to be one of your students.
OK.
The signal is band limited to 1/2 fs BEFORE it is quantised, and so the aliasing frequencies are not "at plus or minus a (hopefully small) margin about that frequency.", but instead ALWAYS above 1/2 fs. So these can be filtered off in the reconstruction filter. (And this is trivial nowadays with oversampling DACs).
I am completely familiar with this filtering fact - and some of its myth.
Are you aware that you're trying to justify that you can filter the complex conjugate of the sampled signal? I ask that in complete candor, and without sarcasm.
I'm also familiar that at many schools, aliasing is the term given specifically to the misunderstood components of the other half of the S plane. In such a case, you were likely taught to use the terms, "frequency estimation error" or "frequency component leakage" where I am identifying that as another form of an alias. Am I correct?
Now - I am not arguing against anti-aliasing filters, per se. Their value is well-established for many applications. I do argue that much of the math used to teach them is not sufficiently rigorous.
As for reconstruction filters, yes, I understand what you're trying to get to and how I ignored that completely. However - I honestly wonder to the extent that speaker diaphram momentum was taken into account - and if the reconstruction filter was needed as much as believed. Again - a bit of speculation, but given that few perform decent speaker measurements, and given that that momentum term is already contributing to smooth any hypothetical staircase, I thought that the whole reconstruction point wasn't that big a deal.
Except, you're of the school that sufficient oversampling applies. Me, too - but to a more limited point. It suggests you'll getter better confidence of your low-frequency estimates (relative to the sampling rate).
Remind me, if you will, as to how oversampling at the DAC weighs higher than oversampling at the ADC. (No sarcasm intended if that was a simple typo on your part - and if not, it's an honest question.)
The slew rate of amplifiers has NOTHING to do with this.
Then I stand corrected and thank you.
I agree that samples are not signals.
It's a good starting point for clarity.
The "waveform" you see when looking at a collection of samples in a wave editor has little to do with the analog waveform that leaves a DAC.
And with sampling error, I question how well that analog waveform that left the DAC resembles the analog waveform that went into the ADC.
And it is precisely upon this point that I am so unforgiving.
The Nyquist criteria is that *any* frequency *less* than 1/2 fs can be *completely* reconstructed. A frequency of exactly 1/2fs cannot have it's amplitude and phase components reconstructed.
Or, you could have said - with greater simplicity - that the real axis is crossed at DC and 1/2 dt. You say *less* - I said *within* - yes, you'd have hated to have had me - or not.
...brush up on sampling theory.
Yes. I agree. I recommend it as a daily activity, myself.
This parallel discussion may be slightly interesting to you - http://slashdot.org/comments.pl?sid=1435342&cid=30020132
You are assuming that there is one AC, perhaps some of us are not just here to wind you up.
OK. Despite the fact that I earlier stated that I couldn't tell if there was more than one AC I was talking to... I'll just take that one lying down.
I believe that to plagarise I would have to be passing it off as my own work.
Agreed - I choose the wrong word. Kindly correct me - were you copying that from somewhere, or trying to phrase something that you believe that you know?
Reference please, AES?
No, you'd find it in the IEEE Journal of Radiation Effects, and then a related work published by the Applied Computational Electromagnetics Society.
Digital signal processing existed long before the AES got seriously into it.
At least one of my algorithms was implemented in one of the earlier HP digital oscilloscopes - and that model was used to get results in more than a few AES papers, AFAIR. As was the Nyquist criteria tech note that I'd re-written for HP. And I'm proud to say that I never got a nickel for that (and no, I never worked for HP) - that was just free and open before that was popularly known.
If you're a practitioner in the field, I will kindly and sincerely apologize - when you correct your post with discipline.
BR, Patchy the Pirate
Incidentally, to faithfully plot one second of CD audio at HDTV 1080p resolution, you'd need a display 22 units across by 61 units high.
Absinthe is illegal here in the US.
By the way - the ability to reconstruct filtered signals perfectly - that's from one of my seminal papers in a peer-reviewed journal.
trouble is that *perfect* filters are not available to us...
Unless you'd like a digital one, for specific applications - that's the topic of the follow-on paper I did.
...higher sample rates take the strain of these two filters making them easier to design...
That's a bastardization and I did not write that.
Too bad you only found derivatives of my work - and too bad you didn't even understand that much.
If you ever decide to stop being an AC, you can call yourself Polly The Parrot.
cheers!
I think that you are missing some filters!
Not really.
Filters are the reason that PCM audio can work.
Nope.
One filter to band-limit the analog input signal and try and avoid aliasing during sampling...
The idea that you can avoid aliasing during sampling is the most often quoted, and most completely wrong, statement by undergraduates. Some never get past that C and yet find work writing that stuff in later life.
Go to the graduate library, and begin by reading anything you can find by Cornelius Lanczos.
...one filter on the output of D/A to remove frequency images.
And do that lookup for Lanczos' work right after you've taken any elementary classes in physics, calculus and electrical engineering.
If these filters are *perfect* then everything works hunky-dory - at least in the sense that the filtered input signal can in theory be reconstructed.
You can't even plagiarize at all close to well.
That pokey feeling is the fork I just stuck in you - you're completely done now.
Under that condition, it will appear at (K*Nyquist_criteria) + actual_frequency - and in our case, the next occurrence won't happen until past 22.05 kHz.
It was late when I wrote that, so this correction is offered - the above equation holds true for even K. For odd, it's ((K+1)*Nyquist_criteria) - actual_frequency.
Obviously.
Ah. You're under the impression that I care about you.
And I do. I really, really do.
Because I think of the children.
Especially when they're so cute.
In short, cutting off information about 15k makes no difference in how we experience the audio, much like a camera not recording ultraviolet doesn't affect a photograph.
True, but only trivially so - very few sources have significant content above 16 kHz anyway. Except for triangles, some violins, some harpsichords and some synthesizers.
MP3 encoding is pointed at reduced sampling - and then betting on psychoacoustics. You can get close that way - that's why it was accepted by people in the first place. Add in that a great many people listen through low fidelity equipment, and the margin for MP3 improves.
But sampling in any form introduces error - and given the right program content and decent equipment in a decent environment - one can hear differences.
Close enough for rock and roll? Probably.
But why bother with MP3 in the first place? They're patented and out of date. If you're going to accept a lossy format, why not AAC, at the very least?
But in all of the arguments for or against audibility of lossy formats, such as MP3, one other factor is left out - using which encoder? More than one exists for MP3, so you can't really characterize MP3 by bit rate alone unless we can jointly agree on which encoder will be used in the first place.
I, for one, am in no position to do that.
And another point you raise about the ultraviolet - we all seem to agree that we don't see at that wavelength. But if you're calling for any double-blind tests, how about an ear check for all participants and sorting the hypothetical results further with that criteria.
People get their knickers in a bunch about physical criticisms - but how many people working next to jet engines, operating construction equipment, firing guns regularly, or lovers of loud head-banging music actually can hear anything above 8 kHz?
If 99% of your test subjects don't hear above 8 kHz - and 1% do - would that study prove that MP3 is inaudible compared to non-lossy digital - or would it prove it only for the hearing-imparied?
What are the ranges of hearing for the adult population? At one time, Bell Labs used to publish that - and it varied by age, gender and environment. I haven't seen such study results for many years.
So, until you qualify the MP3 encoders and until you specify music program content and specify the test subjects' hearing range - I'm not sure that you'll make solid points with your MP3 argument.
And you're going to need several double-blind tests to really prove anything - because there are more variables than you seem to be counting.
You clearly have little idea how digital audio is actually implemented and only a vague notion of the theory.
That's what my friends coworkers in the audio industry used to tell me - after they got very drunk. I'll be sure to turn in my patents.
Have fun with your little staircase graphs.
The wikipedia gods love me - http://en.wikipedia.org/wiki/Digital_audio
Like most grads, they still have aliasing completely wrong, but the top of the page is simply hilarious.
Quit while you're ahead - those words just aren't in your vocabulary, are they?
aliasing doesnt have anything to do with sampling (e.g. quantization errors) either in frequency or amplitude). aliasing is simply an unwanted side effect of not having enough sampling resolution
Correct that it has nothing to do with quantization errors - but absolutely incorrect that aliasing can be cured with higher sampling rates. It simply cannot - discretization error is unavoidable unless you get to Plank time.
I've attempted to explain further here - http://slashdot.org/comments.pl?sid=1435342&cid=30020106
It's a fantasy that increased sampling rates gets rid of aliasing. Only dumb luck in sampling does that - and that will self-limit to occasional frequencies in time.
Have a friend give you some exponentially damped cosine waves at audio frequencies and then the same with a few raised cosine pulses summed in and have them give you that as the analytical function - as a blind experiment, let someone else choose that. Run the function, sample at 44.1 kHz, transform it, and compare to analytic results. Next - using the same functions - sample at 317 kHz and compare to 44.1 kHz and to analytic results.
You may be surprised.
Finally the one thing that i never hear the analog audiophile types talk about (keep in mind i have nothing against it: if you prefer analog good for you) is that the same quantization errors that apply to digital audio also apply to analog...
Right on, and I'm glad you mentioned it. Only, to be canonically correct, I'd state it mo' more better as "...noise errors that apply to digital audio also apply to analog..." But FWIW, I think you covered the point admirably in your follow-on statements.
So. What is noise?
It's uncertainty in the signal. There's a reason in the maths that probability functions and LaPlacian equations have similarities. And uncertainty tends to increase as we go up in frequency.
Now, considering the playback medium - what are the choices? Hysteresis phenomena with tape playback or lateral acceleration problems with a stylus in a groove.
For all of its woes, I'm terribly happy with CD audio. It's good enough to really enjoy decent performances on an intimate performance - even with an inverted mike (or something in that feed) on the sax - (Dave Brubeck Quartet, Take the A Train).
And I'd be even happier at twice the sampling rate - not to eliminate aliasing - but to further reduce sampling error - because, no, I'm not happy with a 4 stairstep equivalent at 11 kHz.
But I am happier with that than the work of dealing with a head amp, moving coil cartridges and a multiple tonearm turntable mounted on a massive plinth, a ritual of pre-play cleaning - and no repeat playback on rare vinyl or at least a half-hour for cooling, because the stylus contact pressure does soften the vinyl - and before CDs came along, I did just that.
All I can say is - don't knock it 'til you've tried it. Then knock it. :)
I know a lot of people who insist that analog sounds better - and I've known them for decades - and many of them haven't heard live acoustic music in decades and I know for a fact have never in their lives heard a record played with even a clean stylus.
But some people do know what decent analog sounds like compared to live acoustic sources, and they prefer it to digital music. To each their own.
My intention was not to denigrate the fine work done by Red Book. I was just overly frustrated at having to once again explain this sort of thing, and I'm too lazy - or something - to contribute to wikipedia to improve things. (Or, I just don't believe in a voting process for knowledge - there's no democracy in physics, right?)
That's a triangle wave.
You wish. :-)
That's the first point at 0 volts for 1/44100 sec, the peak held for 1/44100 sec, 0 volts for 1/44100 of a second, and then the negative peak at 1/44100 second - it looks like a triangle if you connect the dots like in school - but that's a control function for electronics, so it ends up as 4 steps representing that particular frequency.
So, you see - it only gets worse, the better you understand what's going on.
As for 16 bits vertical, I've asked whether any electronics can accurately measure line voltage divided by 65535. That's like, serious millivolts. Lot of bits are being thrown away in both directions. Don't believe me? Stand back, and turn up the volume.
16 analog-to-digital converters are well within our tech. If we model amplitude vertically and time horizontally, it's cool that they've attempted to mitigate vertical error with such high sampling - and then counterpointing that with amplifier response time for each quantization level - pretty cool, actually. But the time sampling, well - as I keep repeating, it's a wonder than CDs work as well as they do.
I think you'll be interested in my parallel response, so in case you've missed it - http://slashdot.org/comments.pl?sid=1435342&cid=30020106
Now, while I've railed a bit against the Red Book wikipedia entry - perhaps too harshly - I find this one particularly delicious:
http://en.wikipedia.org/wiki/MP3
The authors make no bones about it - the entire MP3 approach is to exploit psychoacoustics. The algorithms for this, and other codes, are quite fascinating - and all in all, they do a pretty good job.
But the bottom line for MP3 audio - 1) psychoacoustics, 2) not all MP3 encoder algorithms are equal, irrespective of bit rates, 3) the algorithms are adaptive to the input waveform because they know that it's lossy and they try to limit that.
Why do I call that delicious? Because that's what Vincent Price would call this insanely scary reality:
All you have to do in any of these articles to be modded as 5, funny, or 5, insightful, is to bray like a jackass that MP3 after a certain point is just so good that humans simply can't hear any better - and anyone who thinks differently is some kind of audiophile - you know - a psycho .
The irony can't get much thicker than that.
But psychoacoutics may be a perfect science - ask Bose. Those products are perfect too, aren't they?
Oh - and not any mods are paying attention - but just in case - Bose radios wired with Airport Express using AirTunes is one way to go for the guy that started this thread with his question. Now I can laugh some more if I'm modded off-topic - which I am. :-P
It's not 45 million, it's 41,100 for CD audio. And ALL samples are instantaneous...
No, the sampling is not instantaneous - by definition.
Anyway, I only suggested it as a way to visualize how straightforward PCM audio is on CDs. earlymon just wants to sound like he's smarter than the average Wikipedia editor.
Close, but no cigar. In this case, I may be better at attempting to explain what's going on than was done for that particular article.
Smart does not equal an ability to explain. But given that I've lectured on digital signal processing at the post-graduate level, I'm not without some qualification in the area.
As I said earlier, if you find me wrong or harsh, that's your right.
But my bottom line stands - it's a wonder that CDs work.
From an earlier post - perhaps yours, it's impossible to tell with an AC -
mean, you get a piece of graph paper with 65,535 blocks vertically and 41,100 blocks horizontally, and plot the samples, and you literally have a picture of the waveform. It doesn't get much simpler than that, so where's the misunderstanding?
The expanded form for the Fourier transform of a single impulse is a circle scaled to voltage in the S plane. Phase response - the angular progression from point to point is constant - so we describe that as having minimum phase. Plotted as phase vs. frequency, it's a straight line with a nonzero slope. Magnitude however, is that constant distance from the origin. Plotted as magnitude vs. frequency, it's a straight line with a slope of 0 - it's literally a flat line from DC to infinity.
That particular point is called the Dirac delta function - after the physicist of whom you may have heard.
And if one point cannot be band-limited, then no number of additional points can be band-limited.
A sine wave - ok, I'm being specific and sine waves are, in fact, imaginary - so a cosine wave, then, analytically, has but one frequency. The very fact of sampling that one wave - and then calculating it's frequency components - leads to an unlimited number of frequency components out to infinity - not just one. And only by the most ideal case possible will one particular frequency ever be sampled such that it appears as a single frequency point within the Nyquist criteria - 1/2 of the delta-time sampling rate. Under that condition, it will appear at (K*Nyquist_criteria) + actual_frequency - and in our case, the next occurrence won't happen until past 22.05 kHz.
Under ideal circumstances - controlled by fate, totally uncontrollable by electronics or design. And for any given sampling - it's incredibly rare. In the real world what really happens is that any given frequency component - any single frequency, in other words - is smeared to a peak at or only near that frequency, with additional frequencies at plus or minus a (hopefully small) margin about that frequency.
Engineers have poorly chosen the word aliasing for this - the frequency aliases as other frequencies. And they window it, they anti-alias filter it - but there ain't no such thing as a free lunch, so it's a battle that cannot be won.
Again - what could be simpler than that picture of a waveform on your graph paper?
Well - steps are much simpler than curves.
So for each quantization value of the signal, the voltage is held constant for 1/44100 second, then changed to the next step level for the next 1/44100 second and so on. However - amplifier circuits have something called a slew rate - the rated ability to change voltage over time. If a circuit can slew quickly, it may have a tendency for overshoot - partial solutions for that exist, but again - TANSTAAFL.
Both of those critical points, I covered in my original post - but evidently, I didn't explain them there any better than laughably, because you were left with the impression that you can get a picture of a waveform by sampling it - and you simply cannot.
It's entirely possible that the only reason that CDs can work in first place is all of the slop in transitioning voltages in the amplifiers in the first place.
Again - hope this helps.
I'm well aware that's from the Red Book.
No wizardry is required. Each sample is 16 bits - that's vertical resolution. The 44.1 kHz is horizontal resolution. It does indeed take (16 bits / sample) * (441000 samples / second) * 2 channels to get 1411.2 kbps for stereo.
As wikipedia says, that's the bit rate.
Maybe I'm just having a bad day. Bit rate is a significant parameter. And perhaps the fact that sampling is a signed 16 bit integer is a significant parameter.
But the wikipedia article, I personally found lacking - it's just a raw data dump, leaving the uninitiated susceptible to confusion. I found the decomposition of terms - rather than learnable references for DSP and PCM - laughable. So, I derided it as I did. Maybe I could have done better in my criticism of the article.
If you find me harsh or wrong, that's your right.
http://en.wikipedia.org/wiki/Red_Book_(audio_CD_standard)
Sorry - my bad. Guilty as charged.
And there is also the issue - was the hypothetical 256 kilosample/second MP3 made from the analog original or resampling the sampled source.
If interested, my other post in this thread may be useful - http://hardware.slashdot.org/comments.pl?sid=1435342&cid=30018812
I tried a number of sampling schemes with a number of program sources on my system. Then had the sources switched for me (electronics are in another room from my speakers, so it was blind). On some material, I could hear significant differences from the original - where the original was an audio CD - sampled in the first place.
That's not scientifically acceptable - but perhaps it's a probative anecdote.