Jan
It has been my experiences in design of ADC and sampling systems for data acquisition systems at Texas Instruments that Nyquist Sampling Theory has errors at high frequencies. As you approach 2 samples per period, errors can be considerable, we investigated the errors due to finite duration sampling of continuous signal and determined that this error can be considerable at the beginning and near the end of the sampling time window. These errors had a tendency to get larger at higher frequencies as they approach the Nyquist frequency ( fS / 2) for signal near the inside boundaries of the time window.
The easiest way to proved this is to build oscillators using a 16 bit DAC’s with EPROM lookup tables. Program the table with Triangle Waves and Sine Waves then measure the output after the aliasing filter, the proof is in there.
Nyquist Theorem's Consequences
It is worth noting that information about the signal V = V(t) at any given moment in time t n TS is distributed among all discrete samples { V[n] } with appropriate weights. Realistically, we are never presented with an infinite discrete time sequence and are therefore forced to perform the summation over a finite range. This is equivalent to a loss of information about the function V = V(t) not only before and after our time window (which is understandable), but also at the time points between the sampling points. This can introduce errors into the process of reconstructing.
KBK, the real problem with magnetic recording is that the particles are noisy when relatively large, but they have infinite print-through when they are too small. IE they change state almost by looking at them. ;-) This is the limit of analog recording, and perhaps digital magnetic recording.
I remember getting hammered by the alt.highend newsgroup, way back when the Internet barely or didn't really exist....we communicated via BBS. I stated that we needed something that could sample fast enough to do justice to a 100kHz signal, as a minimum, due to the fact that locational abilities of the human ear require this, amongst the 'learned crowd, ie. audiophiles. Therefore, the limits of human hearing, in this ONE single area, are above that 100khz limit (stereo signal, locational cuing, sensitivity and discernment of source point). What I said was.. that the minimum sampling rate should be at the nyquist minimum for 100khz reproduction, about 226khz sampling or so. Since we work in digital doubling, etc.. I figured it might be 256khz sampling. Now, nearly a decade later..what is Sony using as a archival system?????
Note to all you A-Holes from The Highend news group? I rest my case. 
!
Then, what about the temporal intermixing of harmonics? VERY critical.
So, this issue has been addressed via...SACD. Mostly, anyway. But..as an addendum, when I modded my clock in the way I did.. most of the complaints, ie, loss of that critical information...disappeared. Cymbals became VERY clearly discernible in all aspects of what exactly a proper cymbal sounds like. The theoretical and noticeable shortcomings of 44.1/16 bit where still there, but frighteningly lessened in terms of sheer discernible musicality. It was amazing the affect it had on it's musicality. I have a friend I work in loudspeaker design with. He stopped playing records for a few months when he received the unit I made for him. This is no simple task to do to a man who has 10K (mostly Jazz) albums, and makes a living by hearing temporal distortion and harmonics.
As for the grinding. We go as far as we need to go. The mill is totally custom in design, is all I can say. We don't need large amounts, so we don't make large amounts. Sometimes the pigments will be ground for 3-4 days. For example, this can double the effectiveness (amount of Cadmium pigment per liter of produced paint) of a Cadmium pigment, and it is definitely ecenomically worthwile to go through the effort. A small container of such can easily cost $K's dollars.
Note to all you A-Holes from The Highend news group?
I rest my case. !Then, what about the temporal intermixing of harmonics? VERY critical.
So, this issue has been addressed via...SACD. Mostly, anyway. But..as an addendum, when I modded my clock in the way I did.. most of the complaints, ie, loss of that critical information...disappeared. Cymbals became VERY clearly discernible in all aspects of what exactly a proper cymbal sounds like. The theoretical and noticeable shortcomings of 44.1/16 bit where still there, but frighteningly lessened in terms of sheer discernible musicality. It was amazing the affect it had on it's musicality. I have a friend I work in loudspeaker design with. He stopped playing records for a few months when he received the unit I made for him. This is no simple task to do to a man who has 10K (mostly Jazz) albums, and makes a living by hearing temporal distortion and harmonics.
As for the grinding. We go as far as we need to go. The mill is totally custom in design, is all I can say. We don't need large amounts, so we don't make large amounts. Sometimes the pigments will be ground for 3-4 days. For example, this can double the effectiveness (amount of Cadmium pigment per liter of produced paint) of a Cadmium pigment, and it is definitely ecenomically worthwile to go through the effort. A small container of such can easily cost $K's dollars.
Speaking on the temporal intermixing of harmonics.. I have jury-rigged a system where I can switch from the stock clock to the modded clock on my SACD/DVD-A player...on the fly.
This system is hooked into the Behringer DCX2496 (modified) Digital crossover on the digital input of the Behringer. This, on a prototype MTM Morel based sealed floorstander. The room has about 12-14 custom Tube trap patented absorbers, and modified associated amplification and wiring which I am intimately familiar with.
The results? When the clock is of the modded variety, it is as if the treble level was reduced by about 2 db or more, and with a notch filter reducing the highs in above the 5-10k range or so. Switch to the stock clock...and boom! Noise, hash, hardness and indistinct. Imaging, transient speed, harmonics are all smeared, etc..thus appearing elevated in output to the casual listener.
Once you've heard something like that and had it around long enough to see what it does, there is no going back.
Music, like with turntables.. goes back to being relaxing. Women LOVE the modded digital system..which speaks for itself, to those who know what digital audio equipment does to/for women...... It's basically the ultimate test. Ask a woman who has been around audio equipment all her life what she thinks of it. Then you'll know it's any good or not.
Yours and my opinion don't matter much. Her's does.
This system is hooked into the Behringer DCX2496 (modified) Digital crossover on the digital input of the Behringer. This, on a prototype MTM Morel based sealed floorstander. The room has about 12-14 custom Tube trap patented absorbers, and modified associated amplification and wiring which I am intimately familiar with.
The results? When the clock is of the modded variety, it is as if the treble level was reduced by about 2 db or more, and with a notch filter reducing the highs in above the 5-10k range or so. Switch to the stock clock...and boom! Noise, hash, hardness and indistinct. Imaging, transient speed, harmonics are all smeared, etc..thus appearing elevated in output to the casual listener.
Once you've heard something like that and had it around long enough to see what it does, there is no going back.
Music, like with turntables.. goes back to being relaxing. Women LOVE the modded digital system..which speaks for itself, to those who know what digital audio equipment does to/for women...... It's basically the ultimate test. Ask a woman who has been around audio equipment all her life what she thinks of it. Then you'll know it's any good or not.
Yours and my opinion don't matter much. Her's does.
I've Been Saying The Same For A Long Time............
"Music, like with turntables.. goes back to being relaxing. Women LOVE the modded digital system..which speaks for itself, to those who know what digital audio equipment does to/for women...... It's basically the ultimate test. Ask a woman who has been around audio equipment all her life what she thinks of it. Then you'll know it's any good or not."
Yeah, I have set up a very nice system in my long term GF's place, and if our relationship were to ever end I don't like my chances of getting it back.
"Yours and my opinion don't matter much. Her's does."
Yes, and if she doesn't like it, that expensive 'bloody stereo' represents a new car, and/or a new wardrobe and/or an overseas holiday denied her, and she will be sure to remind you.
Also be aware that if it sounds bad from the kitchen she may as well be stirring poison and curses both into your evening meal.
If she likes your stereo then she will probably love you too........works for me!!!
Calmness and 'niceness' in sound is what women far prefer above fine detail.
Remember women have the weird ability to listen to and memorize and then recall even years later multiple concurrent conversations in seemingly (to males!) impossible sonic environments .....Skinnyboy you have been warned !!!.
I usually willingly value women's subjective review of audio systems in preference to 'mere males' POV.
"Music, like with turntables.. goes back to being relaxing. Women LOVE the modded digital system..which speaks for itself, to those who know what digital audio equipment does to/for women...... It's basically the ultimate test. Ask a woman who has been around audio equipment all her life what she thinks of it. Then you'll know it's any good or not."
Yeah, I have set up a very nice system in my long term GF's place, and if our relationship were to ever end I don't like my chances of getting it back.
"Yours and my opinion don't matter much. Her's does."
Yes, and if she doesn't like it, that expensive 'bloody stereo' represents a new car, and/or a new wardrobe and/or an overseas holiday denied her, and she will be sure to remind you.
Also be aware that if it sounds bad from the kitchen she may as well be stirring poison and curses both into your evening meal.
If she likes your stereo then she will probably love you too........works for me!!!
Calmness and 'niceness' in sound is what women far prefer above fine detail.
Remember women have the weird ability to listen to and memorize and then recall even years later multiple concurrent conversations in seemingly (to males!) impossible sonic environments .....Skinnyboy you have been warned !!!.
I usually willingly value women's subjective review of audio systems in preference to 'mere males' POV.
Just take a look at the thread "RIAA amplifier inside the tonearm"
One would say: It's stupid - then give some reasons
Another one starts with : digitalize the signal right after the pick-up !
No one talks about the processing that the signal has to subdue.
I think of TT and vynil and I think: Ahhhh, Analog ! Straight, little processement of the sound, just find the flaws of the system and correct them.
One would say: It's stupid - then give some reasons
Another one starts with : digitalize the signal right after the pick-up !
No one talks about the processing that the signal has to subdue.
I think of TT and vynil and I think: Ahhhh, Analog ! Straight, little processement of the sound, just find the flaws of the system and correct them.
c'mon...!
I don't care ( should I? ) what technique is used since you have the media in your hands. What should you do ? If your mother didn't give you breast milk but solubizable powder, do you feel less mammal ?
Arer you going to eat only junk food because milk powder have just alienated you from your body ?
Ok, not a great parallel, but, bring Scott ! I love that guy !
I don't care ( should I? ) what technique is used since you have the media in your hands. What should you do ? If your mother didn't give you breast milk but solubizable powder, do you feel less mammal ?
Arer you going to eat only junk food because milk powder have just alienated you from your body ?
Ok, not a great parallel, but, bring Scott ! I love that guy !
Sampling Theorem is incorrect
Ok.
The sampling theorem IS INCORRECT.
I wrote several articles (in russian) from 1992...2000 about fundamental flaws of digital processing and later - about the incorrectness of sampling theorem itself.
Here the reprints on Interet (in russian):
1). И это - неправильно!
publication date: Sep 1, 1997 publication description "Class-A" magazine
publication description : Mistakes in digital sound systems. Improvements of high-end audio.
Pages 20-22.
? ??? - ???????????!
2). А вот это - правильно!
publication date Jan 1, 1998 publication description "Class-A" magazine
Высококачественный ЦАП (цифро-аналоговый преобразователь) с частотной модуляцией и цифровой обработкой сигнала.
Pages 20-23.
3). "Правдорубная мастерская"
publication date: Dec 21, 1999 publication description "Computerra" magazine.
publication description : About mistakes in sampling theorem, digital sound and digital signal processing. Also about problems in modern Intellectual Property Law concepts.
Компьютерра: Правдорубная мастерская
In short: the sampling theorem is a tautology as defined in mathematics, because it defines the "spectra" as a Fourier serie. A Fourier serie itself is defined for periodic signals (functions) ONLY, because the Fourier serie is a periodic function.
There is a theorem called in russian literature "Ageev theorem" which contradicts the sampling theorem and defines the adequate sampling WITH High-pass filter (supressing lower frequencies) as a suitable method of sampling ONLY. Several prominent russian radio- and math- scientists called sampling theorem "a tautology" long time ago.
This is a very complicated matter, so do not expect an easy explanation from me.
I sent A HUNDRED letters to various US/Japan electronics companies as well as to AES (to Elizabeth Cohen), but they ignored all of them.
As I understand, You need "some reason" and "to find the flaws".
Ok.
The sampling theorem IS INCORRECT.
I wrote several articles (in russian) from 1992...2000 about fundamental flaws of digital processing and later - about the incorrectness of sampling theorem itself.
Here the reprints on Interet (in russian):
1). И это - неправильно!
publication date: Sep 1, 1997 publication description "Class-A" magazine
publication description : Mistakes in digital sound systems. Improvements of high-end audio.
Pages 20-22.
? ??? - ???????????!
2). А вот это - правильно!
publication date Jan 1, 1998 publication description "Class-A" magazine
Высококачественный ЦАП (цифро-аналоговый преобразователь) с частотной модуляцией и цифровой обработкой сигнала.
Pages 20-23.
3). "Правдорубная мастерская"
publication date: Dec 21, 1999 publication description "Computerra" magazine.
publication description : About mistakes in sampling theorem, digital sound and digital signal processing. Also about problems in modern Intellectual Property Law concepts.
Компьютерра: Правдорубная мастерская
In short: the sampling theorem is a tautology as defined in mathematics, because it defines the "spectra" as a Fourier serie. A Fourier serie itself is defined for periodic signals (functions) ONLY, because the Fourier serie is a periodic function.
There is a theorem called in russian literature "Ageev theorem" which contradicts the sampling theorem and defines the adequate sampling WITH High-pass filter (supressing lower frequencies) as a suitable method of sampling ONLY. Several prominent russian radio- and math- scientists called sampling theorem "a tautology" long time ago.
This is a very complicated matter, so do not expect an easy explanation from me.
I sent A HUNDRED letters to various US/Japan electronics companies as well as to AES (to Elizabeth Cohen), but they ignored all of them.
Yes, it does matter.
If the signal is not limited from the bottom (poor or absent High-pass filter) or the jitter occurs, or if the signal is complicated (poly-harmonic), then the DAC (and earlier the ADC) restores the signal incorrectly. When I say "incorrectly" I mean "mathematically incorrectly", so there is no way to restore it correctly at sampling frequencies lower than say 1500 kHz.
What is "incorrectly"? Distortions?
NO.
This is the main problem: the DAC (and ADC) dynamically shifts the whole spectrum a bit lower or higher.
This is a kind of jitter but here (in math foundations of digital sampling) it depends on the complexity of a signal itself. This is what causes the health hazard to humans and a headache - the jitter of the whole musical spectrum.
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Ok, it doesn't matter!
I was praising the virtues of analog, not the contrary !
Talking about processment, that is the big IF...
Contrary to analog, where the signal has to be resumed and amplified, with digital there is no "signal" but just information, bricks to build the signal.
That is the big difference.
I was praising the virtues of analog, not the contrary !
Talking about processment, that is the big IF...
Contrary to analog, where the signal has to be resumed and amplified, with digital there is no "signal" but just information, bricks to build the signal.
That is the big difference.
You have never heard the analogue.
The conclusion - You have never heard the analog.
Only the vinyl records made earlier than 1955 (spread of high-frequency biasing of magnetic tapes by Sony) are pure analogue. They dont have coarse voices, for example early Ella Fitzgerald records with beautiful voice modulation. Later one are all coarse.
Sorry, probably I get you wrong. But the problem in electronic recording is even deeper, and situation is even worse: the high-frequency biasing on magnetic tapes provided the sampling of analogue signal (not digitazing but analogue sampling).
The conclusion - You have never heard the analog.
Only the vinyl records made earlier than 1955 (spread of high-frequency biasing of magnetic tapes by Sony) are pure analogue. They dont have coarse voices, for example early Ella Fitzgerald records with beautiful voice modulation. Later one are all coarse.
I can only agree (and at the same time disagree) with you: it is perfectly possible to use HF bias to get rid of many level-related distortions.
Somewhere in the forum, I described a (working) method of using a raw, unbiased class B OP stage to amplify audio signals without noticeable Xover distortion by adding a sufficient HF bias to the signal.
Certainly something you would not like, but it actually works (for me).
I never used it actually, because I think there are better methods of eliminating Xover distortions, and maybe it appeared to work because the input material was only processed that way (I don't think I ever heard a true analog signal according to your standards, and if I did, I didn't notice it).
Unfortunately, I was not able to find the posts in question for the moment, but I will try again later.
Anyway, I was simply duplicating the HF bias method of recording in another heavily non-linear reproduction means, and it did work.
In fact, it made a linear transfer possible in the dead-band through a mix of analog and PWM, exactly like HF bias of magnetic recording.
Unilateral (DC) bias is also possible for mag rec, but you lose 1/2 of the dynamic range, and increase the background noise.
That is the equivalent of class A for amplifiers.
Chose your evil.....
In section 19 of his paper, http://www.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf , Shannon doesn't state whether he uses Fourier series or Fourier transforms. Fourier transforms are defined for non-periodic signals.
His discussion of functions that are limited in time as well as in frequency is mathematically incorrect, though, because these don't exist according to the uncertainty principle. Still, signals can roll off so quickly in time and frequency that you can regard them as approximately bounded in time and frequency.
That is the main point. Kotelnikov (in published work with early priority), and Shannon use the word "spectra" ("spectrum") in the meaning of Fourier serie, because the proof of "sampling theorem" is made by Fourier transform (and with Wiener works).
This is a pure theoretical mahematical illusion. For non-periodical signals the Fourier transform should be infinite in time: spectra is infinite to the lower band down to zero frequency and the analogue restored signal will never sound out of DAC, because the time lag of Low-pass filter should be infinite, with infinite number of samples. This is the main error of theorem.
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