ahem.., how do we arrive at and interpret the very first sample of, say, a steady sinus signal of the frequency at exactly fS/2, but whose samples are offset by a tiny fraction of a degree.. as far as I understand such a "sudden" jump at the first arriving sample isn't something a DFT would suddenly overlook and just continue on as if nothing happened there, wouldn't such case decay towards zero anyway as intended when reconstructing a signal, or am I missing something?
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No. What I am saying is that as we start to increase sampling above 2x, the window length needed for accurate reconstruction decreases. If just barely over 2x, a long window is needed. At 100x or 1000x, virtually no window is needed, as per RN's point.
Jn
No, you are not missing anything. I was explaining how to draw it on paper of reasonable length to show the ambiguity of 2x sampling, not a step gate function beginning, which certainly does introduce higher harmonics outside the current discussion.
Jn
I suspect most of the people who worry about high res aren't that bothered about sound stage accuracy anyway. But considering the 5us ITD and assuming the record and playback chain is perfect it seems the positional accuracy of the fleshy listening becomes the limiting factor?
'Strap me in wife, I want to listen to music'!
'Strap me in wife, I want to listen to music'!
That is why I analyzed w/r to a reference source. Not absolute positioning, but relative.
Jn
JN,
Think I see what you are getting at: If you want to measure with very fine grain frequency and phase resolution when very many frequencies and phases may be present then a very long FFT is needed.
When we talk in theory about the uniqueness of one sine wave (satisfying Nyquist), then we can uniquely identify it with say, three points.
On the other hand, if there are potentially infinite frequencies and phases (all satisfying Nyquist) to uniquely identify, then we need infinite points.
So, what is it you are trying to measure?
Think I see what you are getting at: If you want to measure with very fine grain frequency and phase resolution when very many frequencies and phases may be present then a very long FFT is needed.
When we talk in theory about the uniqueness of one sine wave (satisfying Nyquist), then we can uniquely identify it with say, three points.
On the other hand, if there are potentially infinite frequencies and phases (all satisfying Nyquist) to uniquely identify, then we need infinite points.
So, what is it you are trying to measure?
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I did, and I would rather think that JN is unable to admit a mistake. It's not a capital crime, you know. even if it's a recurrence.
As a side note, Nyquist does not predict how long the reconstruction will last; for sampling frequencies very close to the sine period, it may take a lot of time, the closer the longer. This, and the need for some room for the brickwall anti aliasing filter, are the reasons why the CD sampling is at 44.1KHz, not 40KHz.
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Such an audio signal would be a complete novelty.
Did it ever came to your mind that sines, also with the same frequency and shifted in phase add up to one new signal.
No problem at all to reconstruct this with Fsample > 2xFsignal.
Hans
Before to put-you *back* in my ignore list, because you are using personal attacks instead of arguments, and have not the slightest respect for your opponents, let-me answer you the same way:
You do not show the most basic experience in audio and psychoacoustics.
It advances the debate well, doesn't it?
And about signal theory, you did not understood that I was not talking about it, but about what you think that we can hear or not.
How can-you sample with accuracy a signal of half a period at, say 15kHz, with a sampling rate of 44.1 kHz. To get the right peak level you need lot of luck. As simple than that.
That what JN, RNM, Bimo and myself tried to share.
I hate to use this kind of authority arguments, but I found your stupid aggression amusing, addressed to somebody who have spend his professional life in the audio industry, in the beginning as a member of R&D department of a big French audio equipment manufacturer, then as a sound engineer and a studios technical manager(3 different music and postprod companies).
Was invited in several conferences to talk about new technologies in Audio, digital, Dolby surround etc.
Was chosen as one of the members of the interprofessional French commision that fixed the norms of audio (levels, format etc.) for TV, post prod studios and laboratories exchanges at the beginning of audio digital.
Was hired as a consultant by one of the important international (Japan based) company to participate to the development of a virtual editing machine, recorder etc.
Do you think you are more clever than all the people that took the decision to engage-me ?
I noticed you used the same kind of arguments with Jneutron, RNM, etc. and, in general, everybody that try to exchange with you not sharing your points of view.
The fact that you are not the only one acting this way, not the worse neither, does not justify anything and don't value you. Try to think honestly to this and ask yourself why.
On my side, I just try to understand as much as possible what are the important technical aspects that can satisfy our listening impressions in this make believe (illusion) game that is audio reproduction.
Observation (subjective by essence), analysis (not always accurate, even Einstein), application.
It seems you, as many contributors here, are stuck to the last point, referring to literature on the first two ones. The literature i'm talking about is subject to a lot of controversies. It is not included in the tables of the law that a God would have given us at the top of the mountain.
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The problem is that a sine wave has the one and only frequency in spectrum only if it has infinite duration. Some people do not realize that the sine wave turned on at some defined instant or turned off at some defined instant is not frequency limited anymore and does not have a single line in spectrum. So it may easily violate Nyquist criterion. Therefore "first cycle distortion" and similar nonsense. Technically it is a single frequency only in case that we analyze between turn-on and turn-off instants and we have time enough for the windowed or synced spectral analysis.
Wasn't that guys name Kotelnikow? Along with the Whittakers quite ahead and maybe the reason why Shannon wrote in his paper that the fact (i.e. Nyqist frequency limit and sampling theorem) is well known in the communication field.
But Shannon also wrote about the preconditions that can't be met in reality for the sampling process to work as flawless as in theory. And neither for the reconstruction process, at least I've had problems with my ideal sinc functions. 🙂
If the reconstructions relies on a series of amplitude weighted sinc functions (nonideal) then it will take some time to get the real result if the sampling did take place at unfortunate time marks (with respect to the original signal wich was sampled)
But Shannon also wrote about the preconditions that can't be met in reality for the sampling process to work as flawless as in theory. And neither for the reconstruction process, at least I've had problems with my ideal sinc functions. 🙂
If the reconstructions relies on a series of amplitude weighted sinc functions (nonideal) then it will take some time to get the real result if the sampling did take place at unfortunate time marks (with respect to the original signal wich was sampled)
What do you mean by "with accuracy"? Did you watch all the video TNT posted earlier? Re: "peak level" are you still talking about transients?
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I understand that you feel this way. Be certain that I challenge your technical insight - I'm sure we could have a nice chat about music etc. Now, I don't think this statement in any way will make you change your view of me. I would happily rest in your ignore list. I will not put you on mine as I don't want to ignore you - I want to protect the fact searching world from you.
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That was the original point the theory involves a limit. On another issue unless you eliminate the possibility of high frequency IM in your choice of speakers or headphones any perceptual tests of these effects are a waste of time.
Mark,
I point out the trade off between very low sampling rates and the accuracy of measurement.
Syn08,
When presented with accurate information, I have no issue admitting error.
You have been glossing over what I have been saying all along, that is why I asked you to actually read my posts.
Finally, you repeat what I have been saying, that the closer to 2x you get (from above), the longer it takes. I said that quite a few posts ago.
PMA,
He is the best at what? In not presenting well, you and I agree.
If you mean in terms of intelligence or technical knowledge, I have said nothing in that regard. Please discontinue strawman arguments.
Hans,
I did not say add two equal frequency phase shifted sines, you present a strawman argument as well.
What I said is that there are an infinite number of sines that can be represented by sampling at exactly 2x. And sampling just slightly faster requires very long data lengths.
Scottjoplin,
Sampling I discuss is knowledge learned in the 1975 timeframe.
ITD/IID is something I researched in 2004. IIRC, it was Jon R of aa fame who first pointed out Nordmark to me.
I point out the trade off between very low sampling rates and the accuracy of measurement.
Syn08,
When presented with accurate information, I have no issue admitting error.
You have been glossing over what I have been saying all along, that is why I asked you to actually read my posts.
Finally, you repeat what I have been saying, that the closer to 2x you get (from above), the longer it takes. I said that quite a few posts ago.
PMA,
He is the best at what? In not presenting well, you and I agree.
If you mean in terms of intelligence or technical knowledge, I have said nothing in that regard. Please discontinue strawman arguments.
Hans,
I did not say add two equal frequency phase shifted sines, you present a strawman argument as well.
What I said is that there are an infinite number of sines that can be represented by sampling at exactly 2x. And sampling just slightly faster requires very long data lengths.
Scottjoplin,
Sampling I discuss is knowledge learned in the 1975 timeframe.
ITD/IID is something I researched in 2004. IIRC, it was Jon R of aa fame who first pointed out Nordmark to me.
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