FYI: Digital Sampling

Cpyder

I really hope everyone on these forums is aware of what I'm about to tell you, but I've been far and wide around the internet and I seem to keep stumbling onto this misconception about digital music sampling... (So I will rant a little)

I've found that a great number of websites/forums/people seem to think that digital sampling of music is inaccurate because too few samples are taken to accurately represent a wave. A 10,000 Hz sine wave sampled at 44.1 kHz only has 4.41 discrete samples. I've found a lot of people assuming that you need to get close to an infinite amount of samples to approximate a wave because it, itself, is composed of an infinite amount of points due to the wave being analog in nature. They assume that when a computer circuit converts these 4.41 samples back into a continuous wave, it has to "guess" where the analog wave is between samples...

It does NOT have ANY guesswork to do.*

The computer algorithm does not have to guess where the wave is between points because it is aware of something that we don't think about when looking at pictures of digital samples. It knows there are no frequencies above 1/2 times the sampling rate. This is because this algorithm is based off of the Shannon-Nyquist sampling theorem - which states,

"...a bandlimited analog signal that has been sampled can be perfectly reconstructed from an infinite sequence of samples if the sampling rate exceeds 2B samples per second, where B is the highest frequency in the original signal."

In our example, the highest frequency allowed is 22.05 kHz. Because it knows this, there is only ONE way to draw the analog signal. ANY other way will involve frequencies higher than 22.05 kHz, so it doesn't even attempt to draw the waveform in that manner. I know this seems backwards and a little like voodoo, but in reality, that 10,000 Hz wave is actually oversampled. It has more samples than needed to perfectly represent it.

*The reason the asterisk is here is because in the real world, every signal will contain frequencies higher than 2B. And because of this aliasing will occur. But, I'm not discussing/arguing aliasing here. I'm simply explaining why digital sampling is not "inaccurate" for the reason that it doesn't use an infinite amount of sampling points to represent the original signal. You don't need infinite sampling points. Or anywhere near it. It does not matter if a plot of the sampled points doesn't look like the original wave to you. You are not converting it to an analog wave. A computer is and it looks plenty beautiful to its eyes.

There are other reasons why the theorem may fail, but with adequate sampling rates and sharp, near-brickwall filters, we can push almost all aliasing into the inaudible range. (I really want to say "all aliasing" here, but I have no sources to back this up.)

And once again, I'm writing this post because I feel there's too many people out there who think that there simply aren't enough samples to represent the anolog signal. I'm not here to argue aliasing with anyone. It's just that a lot of people I've run into on other sites solely cite the "stair-step" digital waveform as being "inaccurate" and not looking like the analog signal. They rarely cite aliasing which is the true problem here.

/Rant

Cpyder

Reserved for follow up

TroyD

My ears tell me that the higher the resolution....SACD or all analog, sounds better than standard CD. I really don't care what the computer thinks is 'beautiful'. If my computer were listening to my rig, maybe it would be a moot point....but that's not the case.

I'm more interested in the 'is' than the 'why'.....higher resolution sounds better, I know it and that's all that's important to me.

BDT

heiney9

Digital sampling IS an approximation of an analog signal. No algorithym is going to change the fact that only a certain number of samples are used to approximate the original signal. That is a fact. Whether one hears differences, good or bad, is where the debate lies. There are differences for sure to my ears.

H9

Cpyder

heiney9 wrote: »

Digital sampling IS an approximation of an analog signal. No algorithym is going to change the fact that only a certain number of samples are used to approximate the original signal. That is a fact. Whether one hears differences, good or bad, is where the debate lies. There are differences for sure to my ears.

H9

Problems can arise inside the ADC converter used to record the original signal and they can also arise within the DAC when you are playing back the original signal. But these are problems inherent to the physical devices and not a problem of the sampling itself.

Let's assume for a minute that these physical devices were ideal: jitter and noise are non-existent, the accuracy of the ADC is perfect etc, etc. These digital samples are NOT approximations of the original signal. They are all of the information needed to 100% perfectly reconstruct the analog waveform. The math is there. It works.

You are right in saying it is not 100% perfect. But once again, these errors are caused by the physical limitations of the hardware, and not because of the nature of sampling.

And that's the point I'm trying to get across. Digital recording is not less than perfect because we don't have enough samples, it's because the hardware has physical limitations. So we build hardware with tighter tolerances and we sample at higher frequencies and bit-depths to overcome the hardware's shortfalls. Digital sampling is not the enemy, but rather the hardware is.

At the end of the day, we must ask how tight do the tolerances need to be? How frequent do we need to take samples? At what depth do the bits need to be recorded at?

No studies to date confirm that people can distinguish between DVD-A and a down-sampled version equivalent to CD quality, I'd say we are pretty damn close to ideal. (At least in terms of sampling rate and bit-depth.) Hardware and the recording studio itself should now be the main considerations in improving digital recording technologies.

For anyone who claims to hear a difference between DVD-A and a CD release, that can usually be explained by the fact that they are usually mastered different. And if you think you can hear a difference between DVD-A and its down-converted CD equivalent, you need to contact a hgih-end audio publication because you can easily make thousands proving you can distinguish between the two.

heiney9

Believe me I completely understand as I've done a lot of research over the years on digital information, etc.

There is so much more going on than just the sampling of the information and there is a difference in sound between hi-rez and std. rez.

Ever listen to HDCD vs. Std. Redbook............I have, the mastering is exactly the same, except the HDCD does sound a little different. I'd be interested to hear how many hi-rez formats you've compared to std rez formats. Mine has been in the 100's, yours?

Obviously, as you stated, if the mastering is very different then the results will be different.

This subject has been debated ad nauseum on this forum and I am not interested in rehashing everything. Do a search and you'll see other comments on this issue. I don;t have the time, energy or interest in discussing it furthur.............been there done that. There are analog sources that sound fantastic and there are analog sources that sound like doo doo, same goes for digital sources.

H9

headrott

I disagree whith your statement that sampling is not the problem and that hardware is. The sampling is done by the hardware involved, so one dictates the other right? A sample is inheriantly not as good as the original source and in the case of trying to make a digital version of an analog sine wave by taking samples of it and extrapolating all the parts in between the samples creates flaws. That's logic. Not only that, but as H9 pointed out, my ears and others' ears let you know that there are flaws in the digital samples. That's factual.

Greg

Cpyder

heiney9 wrote: »

Believe me I completely understand as I've done a lot of research over the years on digital information, etc.

There is so much more going on than just the sampling of the information and there is a difference in sound between hi-rez and std. rez.

Ever listen to HDCD vs. Std. Redbook............I have, the mastering is exactly the same, except the HDCD does sound a little different. I'd be interested to hear how many hi-rez formats you've compared to std rez formats. Mine has been in the 100's, yours?

H9

Hi-Rez formats I frequently listen to are DVD-A, Blu-ray audio (TrueHD and DTS-HD Master Audio), vinyl rips in 192/24 or 96/24 and some source material in 24-bit such as the Beatles remasters.

Probably not you specifically, but I still get the feeling that many people think the shortfalls of digital are the fact that in between samples, nothing is "recorded." Nothing is recorded, but this is not a problem. (It is only a problem at higher frequencies where aliasing can occur) Because the computer running the algorithm knows what the absolute highest frequency can be, and this means there is a limit to how "curvy" the wave it's constructing can be. And because of this, there is only one way to construct this line. Any other "line" it draws either has too high of frequencies or doesn't touch all of the points, and hence it does not draw that "line."

Now, aliasing is a problem. But like I said originally, most people opposed to digital sampling don't state aliasing as a primary problem. They state that there is information missing in between samples. There isn't. A good example is of recording a straight line. Sure you could take a high-def picture of it and store it that way (This would be similar to analog) Or you could record any 2 points. With those two points you know everything you need to draw the line later. Perfectly. This is exactly how digital works. No information about that line is missing, even though you only know 2 points.

And why does aliasing exist? Because of the physical limitations of the hardware (or software). Brick wall low-pass filters do not exist, so aliasing will occur. But this is not a problem of sampling, but rather of the hardware. Because if your low-pass filter attenuates sharply enough and at high enough frequencies (which can be allowed due to oversampling), any aliasing should be inaudible to any listener.

Cpyder

headrott wrote: »

I disagree whith your statement that sampling is not the problem and that hardware is. The sampling is done by the hardware involved, so one dictates the other right? A sample is inheriantly not as good as the original source and in the case of trying to make a digital version of an analog sine wave by taking samples of it and extrapolating all the parts in between the samples creates flaws. That's logic. Not only that, but as H9 pointed out, my ears and others' ears let you know that there are flaws in the digital samples. That's factual.

Greg

Why do you state that your ears let you know there are flaws in digital samples. Because it's different than analog sound? Why do you assume since there is a difference, analog must be the more accurate sound? How do you know with absolute confidence that digital is not better?

We all know that if you listen to a record enough, the upper frequencies get destroyed. 2nd order distortion is also introduced, along with a louder noise floor. Clearly these things are not in the original recording. So while is perfectly okay to prefer vinyl to CD, you should not assume because CD sounds different than vinyl, that it is digital recording errors that are to blame. The exact same argument could be made in favor of digital. That in not using sound logic.

madmax

Sounds like smoke and mirrors to me.
madmax

Cpyder

I love magic!

Cpyder

Want a good laugh? It takes about 8 responses before someone chimes in and tells the OP he's ignorant and misinformed. Which means those other 7 have absolutely no idea how sampling works.

http://www.buzzlife.com/forums/showthread.php?t=79877

Jer.War

You got a point. Here at Club Polk it doesnt take long to call someone ignorant, and insult and belittle them for not having all the facts. Such a warm learning environment. I read alot more than I post and too often a thread is reduced to people argueing things based soley on opinion. Let's keep it fun......Or else I'll start a bunch of cable and amp threads for LSI and watch this forum BURN!!!!
(Just kidding, but seriously, don't take this stuff too seriously, turn the volume down and RELAX!)

Cpyder

Jer.War wrote: »

You got a point. Here at Club Polk it doesnt take long to call someone ignorant, and insult and belittle them for not having all the facts. Such a warm learning environment. I read alot more than I post and too often a thread is reduced to people argueing things based soley on opinion. Let's keep it fun......Or else I'll start a bunch of cable and amp threads for LSI and watch this forum BURN!!!!
(Just kidding, but seriously, don't take this stuff too seriously, turn the volume down and RELAX!)

Agreed. Let's do keep it fun. I may be interpreting your response wrong, but I'd like to make clear I wasn't insulting anyone here at Club Polk. I probably was a little harsh on the people from the other forum I cited though.

Jer.War

Just adding my two sense (probably worth more like 1.5 cents to be fair
This forum is definately one of the more civil, and thats why I frequent it the most.
Cheers