I believe that you misread important posts of this thread.
You would have that to read the post #43, where, your doubt was answered clearly.

I don't see how that answers the question.

According to my experience, real-world music that reveals a difference when lowpassed at 16 KHz is not that frequent, thanks to spectral masking. But there is certainly some. One example is the first sample here, the one lowpassed at 16 KHz:

http://www.kikeg.arrakis.es/lowpass/

It's a sample extracted from a pop music cd, where there is a cymbal ringing just over 16 KHz. I can hear the lowpass at ordinary listening levels without any effort, using both monitor speakers and various kind of headphones (Sony MDR-7506, Sennheiser HD-580).

I've come accross at least another example of this type, but I have no samples available online. If you are interested, I'll post them when I have some time.

Edit: now it's two different samples that reveal a difference when lowpassed at 16 KHz.

From my experience, an instrument like harpsichord reveals without excessive difficulties a 16 KHz lowpass.

I thought it was established scientific fact, that humans can hear pure sinusodial signals up to ca. 20kHz. In that regard, I find it a hard claim that in musical content anything above 16kHz is allways masked.

That's a pretty amazing sample, I had no trouble ABXing 10/10 of the lowpassed version versus the original. On the other hand, I failed to ABX the 16kHz lowpass of ff123's Mustang Sally samples. Interestingly, my girlfriend (same age as me, 21) failed completely on this sample - she is convinced their is no difference. I blame that on the fact that she has been playing in an orchestra for six years.

Most of the time, it appears that data >16Khz is not important. However, in this sample provided by the poster, it has extraordinary HF content, which basicly resembles a sine wave for a signficant duration that is >16Khz frequency.

-Chris

Thank you. This sample seems to have an extraordinary type of HF content; essentially a relative long duration signal(synthetic cymbal?) of high amplitude that resembles a sine wave that is >16kHz in frequency. The perceptual test to which I referred to determine JNDs did not use this sort of signal. But your sample does show a superb example of the few times that the limit needs to be extended >16Khz. It is noted that the developers of redbook still decided that a bandwidth of about 22kHz was needed for a *safeguard* in the final standard. Maybe they feard this very type of sample would show up occasionally?

-Chris

Even at 39 it's easily abxable

I just encoded this sample (which is also very easily ABXable for me when lowpassed at 16kHz) with Lame 3.90.3 --alt-preset standard -Y, and according to the spectral view, Lame preserves most of the HF energy in the critical places; I can't ABX this encode, which shows that the -Y switch is very intelligent in its decision how to spend the few bits it can for HF content.
Here are the bitrates:
APS: 208 (can't ABX)
APS -Y: 199 (can't ABX)
APS --lowpass 16: 196 (very easy to ABX)

What I'm missing in this interesting discussion so far is the distinction between "production format" and "delivery format".
A production format is used to store audio (usually the output of one or more microphones) for future use in the production process. It is very likely that there will be subsequent processing and therefore overkill in audio quality is required (and legitimate imo).
A delivery format is used to provide the final (mastered) content to the consumer. Subsequent processing of the audio is not intended although it can't be completely excluded (radio broadcasting, consumer tools like EQ, dsp etc.). Therefore the quality requirements for a delivery format can be lower (no overkill).

Another item is the difficulty in separating the quality of a format and its implementation.
For DSD DAC's e.g. choice is rather limited at the moment and no matter how you compare models, there will be too many variables to draw objective conclusions.
If you want to listen to a DSD ADC, you'll need a DAC as well, thereby increasing the variables again. You're testing the implementation, not only the format.
Therefore I think that objective testing, which is relatively easy when you stay in the digital domain, becomes almost impossible when it comes to transducers. Good tests will be very time and budget consuming, probably exceeding the financial limits of this industry.

For me personally SACD is the best delivery format for surround audio at this moment. The hybrid format is great and several cd-plants can deliver the format (at least here in Europe).


Just my € 0,02

I am very interested in this forum, and you will have to excuse me for my lack of technical savvy on this topic. I am not quite up to speed on all of the lingo which is being used.

I look at this a little differently, and yet share some of the same views as some of you.

When I buy music, or movies. I objectively listen for all parts of it. I have been a musician for 2/3 of my life and grew up with an old school audiophile father. I can appreciate the different formats and for this reason I question the guys on here who soley resort to their math skills.

First off.
Who decides which sounds are, or aren't, important? It is my opinion that it is the complete sound which recreates the music, and omission of any of that data is therefore compromising the sound quality.

My father is 54, has over $150,000 invested in his setup and he still to this day goes for vinyl. I still remeber the first time I heard Dark Side of The Moon on vinyl.
The sound was far different from any other format I had heard it on, mainly because the records don't have the limitations of many of the other formats.
For this reason, I say that anyone who says you cannot "hear" the difference between the same recording on CD & SACD can kiss it. I believe hybrid discs are a great testament to this. I have a very modest setup in comparison to that of my father, but I am using sony es and nht 2.5i for fronts. Listen to the remastered Dark Side of The Moon on SACD/CD Hybrid, it was engineered by the ORIGINAL engineer and both recordings thus should be from the same source material. This to me provides an obvious win for SACD, as its' clarity and accuracy in representing the original audio is far greater than that of CD.

Off of that rant, I will say, I have not been able to obtain a recording in CD,SACD,and DVD-A. But to date SACD has best been able to make me feel as if it were live in my living room. Also, I find that a DTS DVD CD sounds just as good if not better that DVD-A (this of course depends on the source and engineer).
So, can anyone answer this. Why create the DVD-A format, when the DVD-V format does just as good.

For me, the choice is still SACD.

Good post, but can you ABX it? ABX is not about the maths, only the truth.

It has already been covered that the SACD/CD sides of DSOTM have different content.

This is exactly why people use ABX tests

The problem with this whole SACD/DVD-A/CD issue is, that we CAN't do any meaningful objective ABX test at our home "conditions". There are too many variables that could alter the outcome of such a test.

Let's say you have got two discs, one DVD-A the other SACD, with the same content, with the 'SAME' mastering, both originally recorded in analog and then transfered to the respective audio format with SOTA converters. Now you want to do an ABX test, but with which equipment? The processing of the digital signal and it's conversion into analog is so different in both cases that if the outcome of the test would be positive, then we can conclude nothing about the format, just about the used electronics.
A consumer can never approach the ideal state. With their use of some universal player and DVDA and SACD discs of the same material he or she can get some results, but it won't tell anything about the formats.

I won't discuss here which one of these formats is theoretically superior. Many heated words have already been spoken. As everybody knows, practice is very different from theory. A theoretically better method can yield poorer results in real-world use.

However one practical test could be conduced. Let's gather as many as possible DVD-A and SACD players of different price ranges and let's conduce an ABX test with identical source discs. This comparison could tell something about real possibilities of both formats in everyday employment.
The above test falsely entitled "practical" is quite difficult for normal consumer to achieve. So we are quite left in the dark...

Now to the even more sensitive issue - is there any ABXable difference between:
1) good-old 16/44.1 PCM and let's say 24/96 or even 24/192?
2) 16/44.1 PCM layer and DSD layer of the hybrid SACD disc?

I won't cover the first point, since I don't have much experience with such comparison and some tests have been already made (with negative results outweighting ).

The second point is practically feasible as a single or double-blind test. The necessary preconditions are:

- SACD player with DSD and PCM stages as much as similar (utilising the same DACs) with no conversion of the DSD bitstream to the PCM (bass management, etc.)
- Hybrid SACD disc derived from an original analog or DSD recording (analog prefered, to keep off any bias), with no usage of aditional effects in the PCM domain, overdubing, etc. with exactly the same material used for the PCM layer (this is absolute necessity - DSOTM and other discs with altered PCM layer is a joke for this test) and with the same loudness (very important). Classical recordings captured with few mikes and with few alterations on the engineer side are great candidates.
- Quick switching of the DSD/PCM layer in the SACD player. With the old players the layer switching could take for ages, but with the recent ones it's usually below 5 sec.

I've managed many single-blind listening tests consistent with the above scenario in my headphone setup (Modified Sony SCD-XA3000ES player, Dynahi headphone amplifier, HD650 headphones) with a help of a family member who switched randomly the layers.
Because of the TOS of this forum I cannot post any results of these tests, since there is no way how can I prove my claims in this virtual space (silly isn't it? - alternatively you can come by and see (listen) for yourself ). I'll do a little infringement and only say that the tests were in the case of original analog or DSD recordings mostly positive, in the case of PCM sourced discs I often failed.

Forget about the PCM layer on a SACD.



This is an interesting example. If you record the analog signal that comes from the DSD layer to a cd, with eg a stand alone cd recorder, then you must conclude that this PCM version is far better (maybe indistinguisable from the SACD) than the PCM layer on the SACD!! If you ask me the PCM layer of the SACD is the 20th anniversary edition and not the 30th anniversary.

Regards,
Jacco

If there's any audible difference (equipment aside) between DVD-A and SACD, then surely DVD-A has to be the better one, simply because it has more data. It might not sound better, but I can't see how it could sound worse. By good I mean more accurate, of course.

No offense intended, but I think you might want to reconsider your logic.

The accoustical accuracy of the media cannot be determined merely by the size of the data disc. Liken this to a computer program.

If two programmers write two completely different programs to perform the exact same function, the programs will not necessarily be the same. Much data can be erroneous. Your program will only be as good as the person who wrote it, and will only be efficient as the person who wrote it.

Who really cares about the capacity of the media in terms of data? Quite frankly, I'm not considering this when I listen to my music, nor do I care about the size of the files that comprise it. Give me media the size of laser-disc, I dont care. That will only effect production/distributions costs. I WANT GREAT SOUND, not an effecient compression.

Earlier in this forum, it is referenced from technical docs that DVD-A is the more effecient of the two, but lacks in certain aspects. See post #9.

SACD may sound better because of different mastering and 5.1 channel distribution, not because it has greater resolution. In fact, DSD is not better than 44.1 KHz PCM, just read this: http://sjeng.org/ftp/SACD.pdf
And that is the answer to everything. 8)

Careful. Just because it was mastered by the same engineer does not in any way mean it was mastered the same. It is virtually impossible to do so. First, the mastering tools available for the DSD environment are different from those available for PCM. Second, traditional PCM mastering involves normalizing and limiting in ways that are actually illegal in the SACD scarlet book - the disk would be rejected. The result is that mastering engineers on SACD are actually forced to use less compression and allow more dynamics. It is not to say that the PCM mastering engineer couldn't do the same, but they don't HAVE to, so they don't.

The result is that SACD disks often use more dynamic range, have less compression, and sound that way. But they don't have to...

Nika

I understand this, that is why I referenced the Dark Side of The Moon Hybrid. Both layers are 30th anniversary remasters done by the original engineer.
Multi-Channel aside, compare the two 2 channel recordings.

The reason I referenced the CD was to address earlier posts by people who try to use the "scientific limitations of the human ear" to excuse the fact that they are unable to distinguish between CD and SACD.

As far as I understood the dynamic range is about 30 dB larger for SACD, but it is not distortion-free. Due to the inability of proper dithering.

DVD-A has even more dynamic range and can be made distortion-free.

Regards,
Jacco

Jacco...

you seem very knowledgeable on DVD, so I'll ask you. What is the technical difference in DVD-V and DVD-A in terms or the capabilities?

From page #4:

Where it boils down to is the data rate, resulting in a limited amount of high resolution multi channel playback for DVD-V. Not all DVD-V players can handle even the stereo high resolution track. With DVD-A you can go up to 6 channels 24 bit 96 kHz lossless audio.

I truly believe that 16 bit 44k1 is good enough and it should be possible to put a 6 channel 16 bits 44k1 stream on a DVD-V, taking away the necessity of SACD and DVD-A.

Regards,
Jacco

True. But this statement does not relate cd with sacd in the sense that 44k1 PCM is better than DSD. It is more efficient.

Regards,
Jacco

This is still, however, to imply that the two releases are identical other than the fact that one is encoded to DSD and the other to more traditional PCM. This is an assertion that I do not believe it safe to make.

And even if it were, a gentleman above pointed out various other reasons that an AB test between the two cannot be conclusive with respect to the formats themselves - only to the very specific (and heavily variable laden) equipment and situation that was tested.

Nika

Jacco,

do you know of any DVD-V recorded in high res? I would like to locate these and play some!

We have to specify a frequency range before we can discuss dynamic range. SACD has only 6dB of dynamic range if we talk about the broadband capabilities of the system (from 0Hz to 1.411MHz) but in narrow frequency bands the dyanmic range is much greater. For example, in the audible region of 0Hz to 20kHz the dynamic range is often somewheres between 108dB and 120dB. If we look at, say, up to 100kHz of frequency range (though I don't know why we would) the dynamic range drops precipitously.

DVD-A with good converters has approximately the same dynamic range in the audible band but above the audible band (again, why do we care?) it is greater.

Indeed, DSD has inherent distortion problems, especially noticeable with low level signals due to the lack of dither in the feedback loop of the delta sigma modulator.

Nika

I found this quote from "Why 1-Bit Sigma-Delta Conversion is Unsuitable for High-Quality Applications, Stanley P. Lipshitz and John Vanderkooy" very interesting indeed (originally pointed to by Mo0zOoH).
It suggests that if successful ABX tests are performed to show that DSD sounds different from PCM, then it would be worthwhile repeating the test with a low pass filter before the amplifier. It is well understood that inaudible high frequency signals can cause audible distortion in tweeters and power amplifiers.

Yes, of course. And if you use an analog one (as recommended by Sony) then you end up with phase distortion which should be audible.

And if you use a digital, linear phase, low-pass filter to do the same then you end up with....

No offense intended, but I think you might want to read up on the Nyquist theorem.


Excuse me? Post #9 (from Garf) does not mention anything about DVD-A lacking in certain aspects. Quite the contrary, Garf clearly stated his preference for DVD-A.

Just to try to put this one to bed, indeed whether or not the result is correct, the logic expressed by tgoose is suspect. We cannot say that just because one format uses more data that it will inherently sound better. Reductio ad absurdum: a 192bit 10kS/s sample rate will sound better than 24 bit 48kS/s.

DVD-A uses more data but this unto itself cannot be used as an indicator of whether or not it is superior to competing formats. Coastalalbum was correct to call this logic into question.

Nika

When I read it back, what I said isn't quite what I meant. Reading the technical info a bit, what I meant isn't right either, but it's more right than what I said .

I was saying it based on an idea that it'd be possible to losslessy convert DSD to some sort of linear PCM - if it were, it would have both a lower bitrate and sample rate than high end DVD-A, and so, forgetting any resampling problems incurred (or put another way, assuming the sample rate is a factor of DVD-A's sample rate), it wouldn't be possible for it to sound better.

Hmph, that's even less sensical than before.

coastalbumm,

No, but I suppose you search for lossless DTS disks. However, it can be the case that these disks are not compatible with all DVD-V players.

In practise this is the case at 80 kHz or so. Other players such as the DVD963SA uses an even dramatic filtering: they use different filters for the Front and Surround/Center/LFE channels. One with a cutoff of 50 kHz and the other with 40 kHz. Unbelievable.

Right. Up to 20 kHz I would say, because I cannot hear signals above 20 kHz at normal listening levels. Furthermore, the 120 dB in the audible range should be seen as a system specification. I have seen with my own eyes that such a converter is designed as such, without stating that every DSD converter is made like that! Also the distortion is kept out of the audible range, but it is not removed especially at frequencies closer to Nyquist.

Regards,
Jacco

Stanley P. Lipshitz and John Vanderkooy disagree, as you should well know!

Cheers,
David.

Oh yes, pardon me. I was not talking about a standard 2 level quantised system such as DSD as it is posed in the beginning. After the paper of Lipshitz and others it became clear that we have been "mislead", so to speak. After that improvements in DA converter design are proposed (I am not fully aware of the technical inside details) to overcome the distortion problem in the audible range. These distortion components are not removed (as well as the noise modulation) but can be made as small as wanted.

This is a far cry from the originally claimed super-audio performance. Also I made big mistakes in the beginning, you can read them elsewhere on this forum. DVD-A systems are better, in theory. In fact, every 3 or 4 bits quantizer based PCM system is in theory better in the sense of distortion and noise modulation provided that they are properly dithered.

Regards,
Jacco

I'm not sure if you guys have finished arguing the range of human hearing. here is a link.

http://www.norsonic.com/web_pages/human_hearing.html

Also, babies and small children are the only peple who can hear 20hz-20K

the rest of us have lost some hearing.

On the contrary, records have the severe limitations. But, you can not compare two different formats fairly using standard commercial releases/versions of the same albums. They will probably be different. Nothing guarantees they will be the same.



Nice.

Let's examine the difference(huge compression differences) between Diana Krall's "The Look of Love" CD track samples vs. SACD track sample.

CD:


SACD:


The CD version is purposely designed to be bad/different in this case, as compared to the SACD version. The dynamics were squashed so that they could increase loudness as far as possible. But, many CDs seem to be designed to be purposely bad these days. Not a problem with the format. A problem with the morons mastering to the format.

-Chris

I don't believe we can say for certain that the CD version is purposely designed to be bad/different. The CD version is not limited by modulator overload. It is possible to clip a compact disk even when all of the samples are legal - the signal, when reconstructed, can exceed full scale even though the samples don't. Since D/A converters can't reconstruct above full scale, it is therefore possible to create a compact disk with "illegal" content in that the signal "clips" all over the place when reconstructed despite adhering to redbook standards and having no "digital overs" by definition. This phenomenon happens far more often when significant compression/limiting (and of course normalizing) is used. With all of the compression used in CD mastering and with the loudness wars still happening there can be no surprise that CDs suffer from a potentially "brittle," distorted sound. Not only is the compression and heat itself fatiguing to the ears, but the distortion on top of it can be troublesome. This is again not inherently a limitation of the format (the CD itself) but is really more a limitation of the way in which it is utilized. Of course I don't think any mastering engineer would complain if the redbook standard were suddenly to change to prevent inter-sample digital overs, essentially forcing the industry to adopt either a quieter level on the disk or more dynamic range.

[pause and digest that]





[/pause and digest that]

Funny, that's exactly what the SACD format does. It has a mathematical formula in it (if you will) that prevents digital overs between samples so that the modulator never has to try to reconstruct a signal that could cause it to overload. In the SACD "scarlet book" this is determined by any 28 consecutive identical sample values (28 1s or 28 0s in a row). Such a signal, when reconstructed, is equivalent in the example above to exceeding full scale and clipping the converters.

Therefore, the SACD does not allow that hyper-compression and limiting that CDs can (illegally) allow, forcing the mastering engineer to take one of two approaches:

1. Either hyper compress it and limit it but then turn it down a respective amount (essentially defeating the entire purpose of limiting it in the first place, no?), or
2. Let it breathe and allow it to have the dynamics.

Which choice do you think mastering engineers are taking? We can look at the Diana Krall track above as an indicator. Can there be any surprise that people generally prefer the SACD version of tracks to their hyper-compressed, distorted, (inter-sample) clipping CD tracks? Is this an inherent benefit to SACD or just a misuse of CD?

Nika

The CD was definately compressed more than the SACD, as can be seen in the waveforms. This, in my book = bad, as an automatic qualification. And it had to be purposely designed to sound different. The compression difference is subtantial(enough to be easily seen in waveform windows). It's not as if the compression happened all by itself on the CD: a mastering engineer dialed it in to be that way on purpose. You refer to the errors of some DACs, and how they differentiate when approaching 0dBfs. It is easy to prevent the anomolies that can occur from different DACs when they approach 0dBfs: don't allow signals to come close to 0dBfs. Keep peak signals 0.3dBfs or lower. If the recording was modified(compressed/limited) in the first place to try and be as loud as possible on the CD, but was left alone for the SACD; then it was purposely designed to sound different between the two examples.

-Chris

Chris,

I think the difference in our opinions has to do with intent. It is most likely that the two pieces were mastered independently. The CD version may have been mastered first, but even if it wasn't, it was mastered the typical way CDs are mastered, with no intent of TRYING to get it to sound like the SACD. So it was overcompressed just like the rest of CD mastered material on the market today.

The SACD version was mastered probably with the intent of getting it as hot as possible, but the restrictions in this force it to maintain more dynamic range when it was.

I really think it is unlikely (am I an optimist?) that some record exec said, "Hey, master this one well and make this other one sound better." I think there was probably no intent of getting them to sound different or to skew toward the SACD version. It is more likely, I believe, that that's just the way it came out.

Nika

Call me paranoid, but the fact that record companies would be glad to phase out CDs sooner rather than later due to missing DRM/copy protection capabilities AND the fact that CD audio is already overkill for 99% of people on 99% of all equipment AND the fact that SACDs can be sold with a higher mark-up makes it very likely for me that CDs are screwed up on purpose to fool people into buying SACD/DVD-A

Yes, there appears to be a difference in our interpretation of intent. But what does not help, is that about a year ago, I had some e-mail discussions with a recording engineer(Michael Bishop) regarding a CD release(Tierney Sutton, Album: Dancing In The Dark) that he engineered. I was concerned about the horrible sound quality. By horrible, I mean that it was very compressed and even had *audible digital clipping(!) on some parts of the recordings(clipping readily available on waveform windows, very audible hash/static sound where these clips occur, and the voltage overshoot[exceeding 0dBfs] on clipping from a CD player DAC is confirmed with a digital scope). This behaviour was confirmed to exist on two different copies of the CD, obtained several months apart, and from different states. Back to the discussion with the engineer: Mr. Bishop disclosed that the CD version was 'compromised' so that it would sound as loud as popular CDs, if playing one after another in a disc changer, for example. He denied that the CD was clipped in any spot -- but a simple exam of the ripped CDDA data demonstrates that portions are clipped--no question. Now, please consider that this record company in question is Telarc. An audiophile label! This has biased me, and I automaticly assume the worst now.

-Chris

* TOS #8 violation is possible with this claim. But an ABX is not possible in this situation, so please allow this exception. Since a DBT was not possible, I did this: I listened to a few suspect tracks and wrote down the time positions where I believed to hear digital clipping. I then checked the waveforms using these written down time positions, to discover that the waveforms were clipped at the positions I wrote down. I will upload a clip of one of the worst occurances on the CD, but I can't at the moment. I can't access my ftp(internet problems) at the moment.

Update: I have now uploaded a sample section from the album referenced above:

www.linaeum.com/downloads/misc/ts_ditd_t10_clipsample.wav

DVD-A is nothing but a CD, with the same idea and principles of signal coding, just with increased parameters. SACD has different principles, and it is closer to analog recording. It was designed for recording studios to store there tape archives and for audiophile listeners. Studios never used and will never use CD or DVD-Audio for serious backups.

That's a bold statement and I disagree. This loudness war has started long before these new formats were known.
Perhaps you're underestimating the importance of having the music sound as loud as possible.
Even in the old, analog times, mastering engineers tried to push the medium to its limits, partly for signal to noise reasons, but also for increased impact when played next to competitors music.
With all other things being equal, a louder version of a track is usually preferred over the softer one. Engineers know this and try to go as far as possible, even if this means increased distortion.
Just do the test yourself. Make a playlist of say 10 of your favorite songs and reduce the level of just one somewhere in the middle by 3 or 6 dB and play the entire(!) list again. The softer song will sound different and, probably, less interesting. Not by itself, but in the context.
Consumers are now used to randomly play thousands of different tracks on their mp3-jukebox and it's the task of a mastering engineer to make sure his/her version sounds as good as possible to 99% of the people. A difficult task.

Digital clipping can be shown on a good digital peak-level meter with calibrated overload indication. The number of consecutive clipped samples (full scale) is an indication for the amount of audible clipping. No clipped samples means the audio can be reconstructed with a good DAC.
One or more FS samples indicate clipping, but it doesn't have to be audible.
I'd gladly check your files for digital clipping and even try to remove the clipping if you like. The music will be softer then, but that's exactly the mastering engineer's dilemma.

I agree that there are other (and certainly equally important) factors that affect the loudness of CDs, but still the companies have good reasons for pushing SACD/DVD-A. Their main selling point is that they sound much better than CDs, which is plainly wrong. They may sound better with some kinds of music on high-end systems and with experienced listeners, but it's really ridiculously little advancement which in no way justifies changing systems on the part of consumers as it was the case with Vinyl vs. CD. So if an album is released simultaneously on CD and SACD, the record company has to make sure that the SACD version sounds better in order to justify its existence. Since this is only possible by making the CD worse than it could be, even with musical genres that are usually not much affected by the loudness race, they do it. At least that's what I would do if I were in their place

ok, so, the debate rages on between formats... ive a question then.

What would be the idea way to try to represent analogue sound in a digital medium? How can we duplicate, with optimal results, real sound in digital format?

SACD is the first step to do that.
You can find technical info regarding SACD's coding in the web.

Well the truth is that PCM is actually a very ideal format. The problem is that many knowledgeable fools make fantastic pages like this that make people misunderstand the way PCM works.
Remember maths class when you find that there is only one parabola that can fit through 3 given points? Well PCM is working on this principal, using the sampled points to guide a continuous waveform. It is -not- the jagged and "digital" (but good enough) approximation that is often described.