Sampling: Ana vs. Dig

Cpyder

Fact: The Nyquist sampling frequency theorem says that if you have a continuos signal and you sample it at two times its highest frequency, the signal can later be reconstructed perfectly.

I present this to you: Leaving personal preferences aside, like 2nd order harmonic distortion heard with vinyls, (which is not part of the original signal and hence a distortion) CDs and digital sources can perfectly represent analogue/original recordings.*

Also, assume jitter can be avoided enough to make it negligible...

What's wrong with my statements? Anything?
** * **

zingo

I was recently talking with David Chesky and we agreed on the same thing. A digital copy of a song that is recorded perfectly, is played back exactly as recorded, perfectly. If you take the laser of a CD player out of the equation (jitter, etc) and play back a digital file off of a solid state drive, there would be nothing played except the original (perfect) file.

John K.

CP, you've simply re-stated the basic facts of digital sampling technology. As long as there are at least two samples of the waveform it's reproduced precisely as the original waveform. Some discussions on this topic indicate a misunderstanding of how sampling works, and appear to imagine that this a sort of "connect-the-dots" arrangement. Looking at a frequency near 20,000Hz where only the minimum required two samples can be taken and where they'd connect into a straight line(rather than the actual result, which is the audibly flawless reproduction of the original) should disabuse them of this notion. Mathematically, two samples can represent only one specific frequency and it's reproduced on discs such as CDs with a precision which analog formats such as LPs can't match.

DAC chips have long reached a state of technological maturity where they handle jitter and other digital issues with ease and the end results don't show the distortion which would result otherwise. Of course, this is another topic which is sometimes misunderstood and it's imagined that there's some mysterious effect apart from distortion.

reeltrouble1

of course listening to the bandwith of one frequency makes for an exciting experience for the simple-minded, lest one even consider an actual dymanic phrase, not to mention the use of interpolater's.

to be fooled by an schister is common, to follow one is a disgrace. all systems suffer from systemic anomolies, nothing is or can be perfect. an analog wave is the master having an infinite number of samples, just like the area of a circle, it is impossible to perfectly define.

RT1

Cpyder

reeltrouble1 wrote: »

of course listening to the bandwith of one frequency makes for an exciting experience for the simple-minded, lest one even consider an actual dymanic phrase, not to mention the use of interpolater's.

to be fooled by an schister is common, to follow one is a disgrace. all systems suffer from systemic anomolies, nothing is or can be perfect. an analog wave is the master having an infinite number of samples, just like the area of a circle, it is impossible to perfectly define.

RT1

"an analog wave is the master having an infinite number of samples, just like the area of a circle, it is impossible to perfectly define."

You do NOT need an infinite amount of points to represent the original signal. Discrete mathematics is some crazy ****, I know!

And I wouldn't say impossible, less you would like to disprove the Nyquist theorem yourself. I believe the only place the theorem fails is near the Nyquist frequency. Which is around 2X if the highest frequency is X. That's why the sampling rate of Redbook audio is 44,100 hz. Hence is there is any error around the upper frequencies, it will occur near 22,000. Which is inaudible to humans and also usually not in the original recording anyway (I believe).

madmax

If two times the sampling rate is achieved and the waveform is perfect then why do we need 128 times oversampling or whatever it may be?
madmax

reeltrouble1

let me try to rephrase, since the original recorded analog wave has an infinite number of samples it cannot ever be perfectly interpretated by any number of samples. the sampling rate of redbook is felt by many to be inadequate, I would suggest a reading and study of the work done by Mr. Robert Thomas.

The potential of the recorded analog vinyl signal is greater than the potential digital signal. A representation of the signal is by definetion not the signal.

RT1

heiney9

Nothing is wrong with your statement. You;ve sucessfully cut and pasted the Nyquist theorem. Now sit down and listen critically to analog and digital and tell me why there is a very real difference in sound. Theorem's are great, until you start listening to real music, in the real world.........then all the models, theories, lab tests, measurements pretty much go out the window.

Audio reproduction is not an exact science.........it never has been and never will be. Trying to define it you need to take in bits and pieces of tests, theorems, measurements, sound theories, human interpretations, biases, preferences, design topologies, etc, etc.....and on and on to begin to get a picture.

H9

DarqueKnight

Harry Nyquist and Claude Shannon are frequently misquoted and even more frequently understood.

The famous Nyquist and Shannon sampling theorems are concerned with two concepts that are commonly thought to be interchangeable, but are not:

1. Signal RECOVERY, and,

2. Signal RECONSTRUCTION.

For perfect signal recovery, Nyquist said that the sampling frequency need only be equal to twice the highest frequency contained in the signal or fs=2B Hz.

For perfect signal reconstruction, Nyquist said that the sampling frequency must be greater than twice th highest frequency contained in the signal or fs>2B Hz. Furthermore, Nyquist said that the sampling sequence must be infinite so that the sampling interval, or space between samples, will go to 0.

Now, if the sampling sequence is not infinite and the sampling interval is greater than 0, then continuous information in the signal that occurs between samples cannot be reconstructed.

As the sampling rate increases, the sampling interval becomes smaller and smaller (moves closer and closer to 0) and the reconstructed waveform becomes more similar to the original signal...but it will not and never will be a "perfect" reconstruction of the original signal as long as the sampling rate is below infinity.

Another important point overlooked in popular discussions of Nyquist's theorems is that Nyquist was concerned with "BAND-LIMITED" signals, or, in other words, signals without harmonic overtones. Music signals are definitely not band-limited.

We know that there are only twelve notes in the Western musical scale. However, musical instruments produce fundamental tones and overtones (harmonics) that are multiples of the fundamental tone. A sampling rate that is adequate to only capture the fundamental tones produced by a musical instrument will not be adequate to capture all the instrument's higher harmonic tones.

For example, the highest orchestral instrumental fundamental tone tops out around 15,000 Hz. The second harmonic of this is 30,000 Hz, which is 10,000 Hz beyond the upper limit of human hearing. However, even though human hearing is, on average, band limited to a range of 20 to 20,000 Hz, humans can feel tones below 20 Hz and above 20,000 Hz. This is why some people with high frequency hearing impairment can differentiate between two recordings that only differ in high frequency content that they can't actually hear...but can feel.

This is also why digital playback systems with higer sampling rates generally sound better.:)

BlueFox

DarqueKnight wrote: »

Furthermore, Nyquist said that the sampling sequence must be infinite so that the sampling interval, or space between samples, will go to 0.

Reminds me of calculus.

Cpyder

I believe the signals can have harmonic overtones just as long as they aren't at frequencies above the Nyquist frequency. Correct?

I'll have more to say later. Time to go workout.

DarqueKnight

....

unc2701

Think of it this way:

Draw a circle (we'll assume that it's prefect). In order to get an exact replica of that circle, you need just one piece of information: its radius. There's an infinite number of points along the circle, but it can be complete captured with just that single piece of information.

Now, let's redraw that circle. The single piece of info tells you everything, but instead of dragging a continuous line around the paper, you make dots. The higher the rate, the closer you get to a circle, but no matter what, you're stuck with dots.

So, with a high enough sampling frequency, you can capture all the information under 20 khz, and with an even higher one you can get the information in the harmonics, but the playback will never give you that continuous function.

rru2s

Thanks for that summary graph, very interesting.

I think harmonics above the human range of hearing are not going to make or break musical appreciation. However, that being said, I would imagine that one of the aspects missing from this discussion is what happens when you apply an algorithm to an overlay of a couple dozen primary frequency notes played by a half dozen instruments all at once, combined with another dozen important harmonics. Clearly, the lower ranges won't suffer much, but the higher ranges, consider that the interpolation process can be "fooled" into missing the proper slope between frequency hills and valleys, that to a discerning ear, might make the difference between reproducing the correct signal as an overlay of 3 high frequencies, versus an approximated overlay of only 2 high frequencies. This type of thing is common in modeling. Sometimes two very different pattern sources can, over a very small interval, yield almost the same behavior. In the case of music, I think that multiple instrumental notes might not sound as good if they were reproduced so as to sound more like a different combination of notes was being played.

Cpyder

This is a pretty good read.

http://www.audioholics.com/education/audio-formats-technology/exploring-digital-audio-myths-and-reality-part-1

It explains how a correctly sampled piece of music can be perfectly reconstructed from the digital realm by filtering out frequencies higher than the Nyquist frequency/2. It also shows some of the pitfalls of digital audio such as the representation of saw tooth and square waves. These types of waves cannot be perfectly represented because they contain components with frequencies that are near infinite, so no sampling rate is sufficient.

madmax wrote: »

If two times the sampling rate is achieved and the waveform is perfect then why do we need 128 times oversampling or whatever it may be?
madmax

Oversampling is done because it allows a cheaper equipment/DACs to do the same job as more expensive options. You don't need to use as complex of algorithms with proper oversampling. And I don't want to say that 44.1kHz is the "perfect" sampling rate. That's why I started this discussion. I'd like to hear what you think. Mathematically 44.1kHz is sufficient to perfectly reproduce audible frequencies. But there are pitfalls which may require a higher sampling frequency when crossing over (with John Edward) from the theoretical world to the real world.

heiney9

Cpyder wrote: »

This is a pretty good read.

http://www.audioholics.com/education/audio-formats-technology/exploring-digital-audio-myths-and-reality-part-1

It explains how a correctly sampled piece of music can be perfectly reconstructed from the digital realm by filtering out frequencies higher than the Nyquist frequency/2. It also shows some of the pitfalls of digital audio such as the representation of saw tooth and square waves. These types of waves cannot be perfectly represented because they contain components with frequencies that are near infinite, so no sampling rate is sufficient.



Oversampling is done because it allows a cheaper equipment/DACs to do the same job as more expensive options. You don't need to use as complex of algorithms with proper oversampling. And I don't want to say that 44.1kHz is the "perfect" sampling rate. That's why I started this discussion. I'd like to hear what you think. Mathematically 44.1kHz is sufficient to perfectly reproduce audible frequencies. But there are pitfalls which may require a higher sampling frequency when crossing over (with John Edward) from the theoretical world to the real world.

FAIL on both quoting from Audioholics and about oversampling being done because of "cheaper" dac's as well as the rest of your thought process.

Cpyder

heiney9 wrote: »

FAIL on both quoting from Audioholics and about oversampling being done because of "cheaper" dac's as well as the rest of your thought process.

First, just because Audioholics doesn't worship speaker cables as a religion is no reason to dislike them.

And also,

"In practice, oversampling is implemented in order to achieve cheaper higher-resolution A/D and D/A conversion. For instance, to implement a 24-bit converter, it is sufficient to use a 20-bit converter that can run at 256 times the target sampling rate. Averaging a group of 256 consecutive 20-bit samples adds 4 bits to the resolution of the average, producing a single sample with 24-bit resolution."

And...

"It aids in anti-aliasing because realisable analog anti-aliasing filters are very difficult to implement with the sharp cutoff necessary to maximize use of the available bandwidth without exceeding the Nyquist limit. By increasing the bandwidth of the sampled signal, the anti-aliasing filter has less complexity and can be made less expensively by relaxing the requirements of the filter at the cost of a faster sampler. Once sampled, the signal can be digitally filtered and downsampled to the desired sampling frequency. In modern integrated circuit technology, digital filters are much easier to implement than comparable analog filters of high order."

You'd best go change wiki, and every other site out there that has this wrong.

Cpyder

Also, "Noise reduction/cancellation. If multiple samples are taken of the same quantity with a different (and uncorrelated) random noise added to each sample, then averaging N samples reduces the noise variance (or noise power) by a factor of 1/N. See standard error (statistics). This means that the signal-to-noise-ratio improves by a factor of 4 (6 dB or one additional meaningful bit) if we oversample by a factor of 4 relative to the Nyquist rate (i.e. a β of 4) and low-pass filter."

shack

Quoting wiki and Audioholics...

Damn...it must be undisputed fact!

dkg999

There might be some good info on Audioholics, however anything from the site is tainted with their reputation of being first cousins to the flim-flam man at the fair.

I do find the theory and discussion fascinating. What intrigues me is that no matter what all the theories are in reproducing sound, we are still limited (or maybe not so limited) by how the human hearing and brain functions interpret it. Why is it that on average I am more pleased by the sound of a vinyl LP than by the same work on digital/CD media? In comparing them analytically, sometimes the differences aren't readily noted. So is it the way my brain is wired and the method of reproduction is not as important? We could sit around a campfire and discuss this for hours!

Cpyder

"In common usage, oversampling is the process by which the sampling rate of a digital
audio pulse code modulated (PCM) data stream is increased to allow digital filtering to
largely replace analog filtering in reconstructing the original analog audio signal. In the
early days of CD playback, it was discovered that the analog reconstruction filters then
used in CD players were expensive, cumbersome and prone to various forms of
overload and distortion. It was soon recognized that these high-order analog
reconstruction filters, also known as anti-imaging filters, could be replaced by a digital
filter operating at a large multiple of the original sampling rate. Virtually all CD players
today employ an 8-times oversampled digital filter driving the digital-to-analog converter
(DAC)." -From DRA Laboratories

From Audiosonica: http://www.audiosonica.com/en/course/post/223/Digital_Audio-Oversampling

And from Principles of Digital Audio By Ken C. Pohlmann



Who do you want me to cite?

dkg999

Cpyder - you're at ISU if I remember right. Prof Messenger (if he's still there) in the music dept used to do some work on music reproduction, acoustics, and how listeners perceive music reproduction IIRC. You might see if any of his research or papers are in the library.

heiney9

Cpyder wrote: »

Who do you want me to cite?

Don;t need you to cite anyone or anything. I've done a lot of reading over the years and numerous posts right here in the forum about this subject. It can;t be covered in one theorem here or there or a few quotes from here and there. It's a very complex process with far too many variables to generalize.

I have no horse in this race............pontificate all you want, but do realize Wiki and Audioholics are considered to be on the same level as the National Enquirer or the Star or any other tabloid out there.

Again far, far to many design variables to pin down an nice neat, fit in the box, type discussion about digital reproduction. If you think you can define it simply, you obviously have more to learn.

H9

Cpyder

dkg999 wrote: »

Cpyder - you're at ISU if I remember right. Prof Messenger (if he's still there) in the music dept used to do some work on music reproduction, acoustics, and how listeners perceive music reproduction IIRC. You might see if any of his research or papers are in the library.

Yeah, he's still here. I'l definitely check that out. Thanks! Are you an ISU grad?

Cpyder

heiney9 wrote: »

Don;t need you to cite anyone or anything. I've done a lot of reading over the years and numerous posts right here in the forum about this subject. It can;t be covered in one theorem here or there or a few quotes from here and there. It's a very complex process with far too many variables to generalize.

I have no horse in this race............pontificate all you want, but do realize Wiki and Audioholics are considered to be on the same level as the National Enquirer or the Star or any other tabloid out there.

Again far, far to many design variables to pin down an nice neat, fit in the box, type discussion about digital reproduction. If you think you can define it simply, you obviously have more to learn.

H9

I do have a lot more to learn. And that's why I'm here, talking to you and posting my little heart out trying to eat up as much information as possible.

You hurt me though. Wiki is the love of my life. lol. No, I see how it can be wrong, but at least for featured articles (oversampling not one of them) it's pretty damn accurate.

dkg999

Cpyder wrote: »

Yeah, he's still here. I'l definitely check that out. Thanks! Are you an ISU grad?

Yep, way back in 1983! Major in business admin, minors in Econ and CompSci, focus on transportation/logistics. I'm back in Ames a couple of weekends a month, still have many friends in town, and the farm and family farm is about 20 miles southeast of Ames.

vc69

dkg999 wrote: »

I do find the theory and discussion fascinating. What intrigues me is that no matter what all the theories are in reproducing sound, we are still limited (or maybe not so limited) by how the human hearing and brain functions interpret it. Why is it that on average I am more pleased by the sound of a vinyl LP than by the same work on digital/CD media? In comparing them analytically, sometimes the differences aren't readily noted. So is it the way my brain is wired and the method of reproduction is not as important? We could sit around a campfire and discuss this for hours!

There exists some research that addresses that very question. It was done some years back and I am going to have to do some digging to find it. The gist of it was, that under MRI or CT imaging observation (i can't remember which) the human brain activated differently and measurably depending on what kind of music was played for the subject and what the source material was (analog or digital). I sure wish I could find it readily. It was a really interesting read. It was proof that our brains percieved a difference in the source even if our conscious mind could not.

Fongolio

The bottom line is my ears prefer analog to digital. SACD and DVD-Audio come close but analog wins everytime. Unless my records are really scratchy.

madmax

Modern electrical trickery is evil.
madmax

reeltrouble1

yes MM it is, the work being done by the engineers at Meridan and Onkyo (go figure) is interesting, I cant exactly recall in the moment but I think the fellow from Meridian is named Kragen, quite noted in audio circles. Anyway, development of so-named apodizing filters which eliminate pre-ringing that occurs with digital music signal is interesting, pre-ringing is likened to a guitar string that starts to vibrate prior to being struck, this sound does not occur in real time but the phenomenon does occur with typical digital brick-wall filters which makes it quite discernable to the human ear, anyway this techology seems to hold promise amongst those who have heard hi-fi systems with the apodizing filter technology, I seem to recall the filter is actually not a part of the DAC.

RT1

madmax

I'm afraid.
madmax