Hello all
From time to time I run into phrases like "the shortcomings of the Nyquist theorem" or "misuderstanding or misuse of the Niquist theorem". Until I became interrested in audio, this seemed so straightforward and well-established, but now I'm beginning to question my knowledge. Not that I ever pretended that I was at such a high level, but at least I thought I understood what the Nyquist theorem was all about.
Also, this would cover the OS/NOS issue somehow. Anyone willing to discuss this?
From time to time I run into phrases like "the shortcomings of the Nyquist theorem" or "misuderstanding or misuse of the Niquist theorem". Until I became interrested in audio, this seemed so straightforward and well-established, but now I'm beginning to question my knowledge. Not that I ever pretended that I was at such a high level, but at least I thought I understood what the Nyquist theorem was all about.
Also, this would cover the OS/NOS issue somehow. Anyone willing to discuss this?
Yes, something is wrong. Maybe I forget the snubbers or the Black Gate , I don't know.pinkmouse said:
This is a completely different debate and has nothing to do with the sampling question.mr_push_pull said:
🙂
Konnichiwa,
It is very simple. The Nyquist Theorem is a mathematical theorem that states the conditions under which the complete original information may be retrieved from a sampled source. Like any serious "pure" mathematical theorem it is absolutely true, completely coherent and ABSOLUTELY not applicable to any parcticular actual reality.
Therefore the term "misapplication" for using Nyuists theorem to predict the actual ability of a system sampling a pseudo-random waveform (music).
Therefore you may discuss Nyquist untill you are blue in the face and you will be non the wiser.
Not interested.
Sayonara
mr_push_pull said:
It is very simple. The Nyquist Theorem is a mathematical theorem that states the conditions under which the complete original information may be retrieved from a sampled source. Like any serious "pure" mathematical theorem it is absolutely true, completely coherent and ABSOLUTELY not applicable to any parcticular actual reality.
Therefore the term "misapplication" for using Nyuists theorem to predict the actual ability of a system sampling a pseudo-random waveform (music).
Therefore you may discuss Nyquist untill you are blue in the face and you will be non the wiser.
Not interested.
Sayonara
Is it? If so, I could open another thread about it, but I don't think it is necessary. Why need 192KHz sampling frequency if 44.1KHz is enough?peranders said:
This is a completely different debate and has nothing to do with the sampling question.
Re: Re: I want to discuss the Nyquist theorem, anyone interrested?
Mr Kuei Yang Wang,
I opened this thread for a reason, not because I was bored. If I'm not looking for the answer in the right place, that doesn't keep me from realizing it and seek it somewhere else. In other words, there's no need to stick to the exact issue in the thread.
The least you can do is motivate yours statements like "Like any serious "pure" mathematical theorem it is absolutely true, completely coherent and ABSOLUTELY not applicable to any parcticular actual reality."
If you consider that I am not knowlegeable enough to understand the explanation, I will ask the moderators to close the thread, and I will seek the answer in the books.
Best Regards
Mr Kuei Yang Wang,
I opened this thread for a reason, not because I was bored. If I'm not looking for the answer in the right place, that doesn't keep me from realizing it and seek it somewhere else. In other words, there's no need to stick to the exact issue in the thread.
The least you can do is motivate yours statements like "Like any serious "pure" mathematical theorem it is absolutely true, completely coherent and ABSOLUTELY not applicable to any parcticular actual reality."
If you consider that I am not knowlegeable enough to understand the explanation, I will ask the moderators to close the thread, and I will seek the answer in the books.
Best Regards
mr_push_pull, don't get too bent out of shape by KYW's pontifications. That's an integral part of audio culture.
Note that people successfully use Nyquist criteria for all sorts of measurement activities that are much more critical than audio. In the real world, it works. My first exposure to the Nyquist theorem was in the context of infrared spectroscopy, where despite the misgivings of hifi mystics, the results are sufficient to understanding fine details of molecular structure.
Note that people successfully use Nyquist criteria for all sorts of measurement activities that are much more critical than audio. In the real world, it works. My first exposure to the Nyquist theorem was in the context of infrared spectroscopy, where despite the misgivings of hifi mystics, the results are sufficient to understanding fine details of molecular structure.
mr_push_pull
Nyquist works quite well if you only use it as a guideline and simply choose a sampling frequency 5-10 times the highest frequency in you signal. I've noticed this done in many engineering applications.
Why is the theorem useful only under ideal circumstances? For one it assumes the measurements of the signal are perfectly taken and at exact instances. The voltage amplitudes in the digital audio scenario are only approximations and the time base is not perfect. It seems obvious to me that jitter plays correspondingly higher role at lower sampling rates. There is probably a lot more but even this shows that the minimum sampling frequency requirement is indeed sailing very close to the wind.
Nyquist works quite well if you only use it as a guideline and simply choose a sampling frequency 5-10 times the highest frequency in you signal. I've noticed this done in many engineering applications.
Why is the theorem useful only under ideal circumstances? For one it assumes the measurements of the signal are perfectly taken and at exact instances. The voltage amplitudes in the digital audio scenario are only approximations and the time base is not perfect. It seems obvious to me that jitter plays correspondingly higher role at lower sampling rates. There is probably a lot more but even this shows that the minimum sampling frequency requirement is indeed sailing very close to the wind.
Kuei... the radio equipment I design for a living uses a fast ADC to subsample a radio signal, gathering information from the resulting alias. It also uses all sorts of nyquist tricks in the digital domain (zero-stuffing followed by bandpass to do digital radio modulation, etc) in its operation. If Nyquist theorem was a "purely mathematical theorem" and "wasn't applicable to any sort of particular actual reality", then something tells me that I'd be out of work... 😀
Nyquist in its most blunt sense says "you can't represent a signal in the digital domain which has a frequency greater than half the sampling rate". This is a theoretical limit, no ifs/ors/buts. If your pet bat hears a 30KHz tone on the output of your CD player or if you see one there with a spectrum analyzer, then it's coming from your CD player and not the CD itself.
Now onto the practical world... Practically, you can't represent and *use* a signal within 5-10% of the nyquist frequency - I'll explain this in another post, as well as the difference between OS/non-OS and why one is "better" than the other, etc...
Right now, I've got work to do. Back in a few hours.
(edit: just realized that the thread starter was offering to give information - not asking for information. Oh well, I'll support and add to the discussion...)
Nyquist in its most blunt sense says "you can't represent a signal in the digital domain which has a frequency greater than half the sampling rate". This is a theoretical limit, no ifs/ors/buts. If your pet bat hears a 30KHz tone on the output of your CD player or if you see one there with a spectrum analyzer, then it's coming from your CD player and not the CD itself.
Now onto the practical world... Practically, you can't represent and *use* a signal within 5-10% of the nyquist frequency - I'll explain this in another post, as well as the difference between OS/non-OS and why one is "better" than the other, etc...
Right now, I've got work to do. Back in a few hours.
(edit: just realized that the thread starter was offering to give information - not asking for information. Oh well, I'll support and add to the discussion...)
Re: Re: Re: I want to discuss the Nyquist theorem, anyone interrested?
Konnichiwa,
This statement is motivated.
I merely point out that most "pure" mathethematical (information theory too) theorems are not applicable to reality.
Any good book on advanced math will tell you that pure math has limited if any applicability.
One of the fundamental limitations inherent to the Nyquist theorem is that in order to be accurate the sampled waveform must be unchanging, steady state in nature. In other words we need an infinitly wide window on an unchanging waveform.
The more sampled wavforms (I prefer the term wavelet) deviate from the above limitation the less accurate do the actual results match the theorem.
An extreme example would be a single cycle 22KHz sinewave "wavelet" sampled at 44.1KHz. This waveform would be minimally distorted by a comptelently designed lowpass filter yet once sampled and reconstructed would not be very recognisable as the original single cycle sinewave.
I doubt this makes anything much clearer. The best course is to leave math to the mathematicions and to stop listening to the man behind the curtain and to instead use ones own ears.
Sayonara
Konnichiwa,
mr_push_pull said:
This statement is motivated.
I merely point out that most "pure" mathethematical (information theory too) theorems are not applicable to reality.
mr_push_pull said:
Any good book on advanced math will tell you that pure math has limited if any applicability.
One of the fundamental limitations inherent to the Nyquist theorem is that in order to be accurate the sampled waveform must be unchanging, steady state in nature. In other words we need an infinitly wide window on an unchanging waveform.
The more sampled wavforms (I prefer the term wavelet) deviate from the above limitation the less accurate do the actual results match the theorem.
An extreme example would be a single cycle 22KHz sinewave "wavelet" sampled at 44.1KHz. This waveform would be minimally distorted by a comptelently designed lowpass filter yet once sampled and reconstructed would not be very recognisable as the original single cycle sinewave.
I doubt this makes anything much clearer. The best course is to leave math to the mathematicions and to stop listening to the man behind the curtain and to instead use ones own ears.
Sayonara
SY said:
Same holds true for Shannon and Heisenberg. In fact Heisenberg appealed to the mystics of his day as a welcome relief from the bonds of a Newtonian universe.
Re: Re: Re: Re: I want to discuss the Nyquist theorem, anyone interrested?
That's not a sinewave, it's a transient. It *isn't* 22KHz, and if you've got the mathematical knowledge to toss in the "wavelet" word while knowing what you're talking about, you should know that the frequency components of such a signal will extend off into infinity.
Which means, a low pass filter *will* distort it.
(and at 22khz, a practical 44.1KHz ADC/DAC combination will distort the resulting distorted signal, unless the antialiasing/antiimaging filters are perfect, which they never are)
Oh no, not "first cycle distortion" again...Kuei Yang Wang said:
That's not a sinewave, it's a transient. It *isn't* 22KHz, and if you've got the mathematical knowledge to toss in the "wavelet" word while knowing what you're talking about, you should know that the frequency components of such a signal will extend off into infinity.
Which means, a low pass filter *will* distort it.
(and at 22khz, a practical 44.1KHz ADC/DAC combination will distort the resulting distorted signal, unless the antialiasing/antiimaging filters are perfect, which they never are)
Re: Re: Re: Re: I want to discuss the Nyquist theorem, anyone interrested?
I doubt if anything natural, let alone a musical instrument would produce anything like a single cycle of what looks like a 22KHz tone. Therefore if it happens, it is likely be an error, and can be safely ignored.
Kuei Yang Wang said:
I doubt if anything natural, let alone a musical instrument would produce anything like a single cycle of what looks like a 22KHz tone. Therefore if it happens, it is likely be an error, and can be safely ignored.
I think you are mixing things now. This is valid when you have an oscilloscope and want to catch a single sweep. The question is then how many samples do you require to be able to display a waveform which isn't repetitive.analog_sa said:
No, I don't want to teach, I want to learn. I'm not in the position to teach.
I think that a more fundamental question is whether the frequency-domain analysis approach is the right one.
I the past I've seen phrases like "the ability of the CD-A format to reproduce fast transients". In school they taught us that (I think there even is a theorem for this) that the magnitude and phase response of a linear system say everything about it, meaning that there can't be two different systems with the same magnitude and phase response.
So, if we have a certain system for which we know the freq/phase resp, we also know its transient response. And if we say that the freq response is OK in that specific context, but time response is not, it means that the, let's call it perceptor, doesn't analyze the signal only in the frequency domain. Does anyone know about any sampling that's done in the human ear?
I think that our ear and brain are able to distinguish well between tonal and non-tonal signals, and analyze them completely different, and this may be the key of the Nyquist issue. Meaning that our ear emphasises on the frequency content when it thinks that the signal is mostly tonal and on the time-domain content when the signal is non-tonal (drums for instance).
I could go on and on but I stop here for the moment, because I realized that I find it hard to give a coherent display of my vision on the subject. Or, even simpler, it might all be BS.
I think that a more fundamental question is whether the frequency-domain analysis approach is the right one.
I the past I've seen phrases like "the ability of the CD-A format to reproduce fast transients". In school they taught us that (I think there even is a theorem for this) that the magnitude and phase response of a linear system say everything about it, meaning that there can't be two different systems with the same magnitude and phase response.
So, if we have a certain system for which we know the freq/phase resp, we also know its transient response. And if we say that the freq response is OK in that specific context, but time response is not, it means that the, let's call it perceptor, doesn't analyze the signal only in the frequency domain. Does anyone know about any sampling that's done in the human ear?
I think that our ear and brain are able to distinguish well between tonal and non-tonal signals, and analyze them completely different, and this may be the key of the Nyquist issue. Meaning that our ear emphasises on the frequency content when it thinks that the signal is mostly tonal and on the time-domain content when the signal is non-tonal (drums for instance).
I could go on and on but I stop here for the moment, because I realized that I find it hard to give a coherent display of my vision on the subject. Or, even simpler, it might all be BS.
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