I would only need to take the samples with an interchannel timing accuracy better than 2 to 5 microseconds. Not? What am I still missing?
Much thanks,
Chris
You made a statement “sampling a 1KHz sine at 2 [and change] KHz doesn’t uniquely reconstruct the sine” and some blurb about “amplitude modulation”, you need to prove it. Extraordinary claim requires extraordinary proof.
Otherwise, as myself and Scott mentioned, approaching the Nyquist limit requires asymptotically infinite time to reconstruct the sine, but that’s irrelevant. You still need only two points per period.
I can only guess you are talking about stereo? So, what has this to do with the sampling period? Really.
Proof. Unfortunately, measurement of interchannel delay of a specific instrument or vocal in a complex two channel musical playback is not very simple.
It would be easier to test if red book is capable of retaining 2 uSec accuracy for any arbitrary musical signal. Actually, I would want 500 nSec accuracy, as I'm a measurement kinda guy. I prefer measurements at least an order of magnitude beyond what I'm looking for.
Jn
Just making a statement the overlap and add FFT filter works fine.
Try this sometime digitize a 10kHz sine with phase rotating slowly in time at 44.1kHz and look at the result, I don't see any problem with phase resolution. Sampling is in two dimensions amplitude and time.
I fear you have more to understand than I can provide using one finger on an IPad.
Your shoot from the hip tactics are not serving you well here. Perhaps you should step back and find some good content on human hearing capability. I speak only on what has actually been measured by some, confirmed by others.
Google ITD, IID, nordmark, many others I would spell terribly from home..
Jn
His usual method. His unique argument is "You are incompetent".
No exception in any of his inputs. A very scientific approach.
All the misunderstanding in this controversy that I think totally stupid is the prerequisite that our hearing is 20-20 000 Hz bandwidth limited. (nothing at 21 000) and that the music is constituted of a combination of sinusoidal signals long enough in time to satisfy Mr Nyquist.."the sum of an infinite series".
Nobody pretend that 44.1 is an horror. Lot lot of people (me included) find an improvement with 48-96. On several aspects of sound reproduction. Especially the transients, how curious!
why do they want to deprive us of it, those who never listen and wave their school books?
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A better test. Sample two 10khz sines, one .1hz away from the other, verify the phase difference of the reconstructed pair matches that of the analog at the 2 to 5 uSec level.
Then push a 50 hz signal on one channel, and again verify the phase difference of the two 10k signals.
Do it using a simple s/h, then an 8 or 16 deep reconstruction math package.
Jn
I’m sure I do. So, what is the relationship to sampling period?
BTW, here’s an interesting exercise for you. Draw a 1KHz sine and check what samples you got acquired with a 2.1KHz sampling frequency after 5mS, 10mS,..., 100mS,... Do these samples more and more better approximate the sine? Is it now clear that the closer the sampling frequency is to the Nyquist limit, the longer it takes to get the same level of accuracy? And yes, a greater sampling frequency will accelerate the approximation process; but the original sine can still be uniquely rebuilt with only two points per period.
Now I'm really not following you. Surely (and don't call me Shirley) you're talking more about the bandwidth limitations of Red Book than about issues related to sampling per se.
If we could agree that Red Book is a standard from the 1980s, and limit our discussion to not include any bandlimiting, before or after sampling, and only talk about sampling itself, could we agree that (ideally) perfect reconstruction from samples is possible (plus the noise of dither, plus a delay) for any arbitrary dithered signal that doesn't violate Nyquist?
And if not, why not?
Much thanks, as always,
Chris
Talking of politeness, Mr. Insults ?
Just a question for you:
Who is more qualified to judge the accuracy of the reproduction of his instrument. The musician, that do not even heard about Nyquist ? Or the mathematician that do not even heard his instrument ?
You should go to the concert, it seems that the music softens the manners.
Or go back to your books, you wouldn't hear (understand) anything.
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No.
Take a sine, sample at zero degrees and 180 degrees every period. The reconstruction is zero signal.
At 90 and 270, it is full amplitude.
Now start at zero and sample every 179 degrees. The reconstructed waveform starts at zero, and will be full amplitude after 45 periods. Then it will drop to zero after another 45 periods.
Jn
I'm really not following. The last couple of days I have been playing with measuring the phase difference between the left and right channels on a test LP at 1kHz. There is no problem doing 0.1 degree at 16/48 which is ~250nsec. Do you want me to post the plots?
No, you still don’t get it. Sample after every 179.9 degrees. Now how many periods you need to get the same approximation as for 179 degrees? But after a period of 179.99999999999999999........ degrees?
I can’t do anything better to explain it, other than quote: http://www.wescottdesign.com/articles/Sampling/sampling.pdf Please pay attention to the “What Nyquist didn’t say” section, it addresses all of your questions and confusions.
Do you guys read carefully in English? You need many cycles to construct such a waveform with 2 samples per cycle. Are we listening to constant tones or to transient and non-constant tones?
As far as I can tell, it was a marketing spec to look like it will do fine in the 1980's when CD came out. Like TEK tried but with research EE's it did not fly. TEK had to reduce the BW claimed or go to higher sampling rates to have accuracy to the BW spec'ed. Espec for single-shot event data.
You dont have to negate Nyquist to know the minimum for a continuous frequency of 2 samples wont be adequate for music signals.
More clues ---> https://www.mouser.com/pdfdocs/Tektronix12_things_to_consider1.pdf
THx-RNMarsh
As far as I can tell, it was a marketing spec to look like it will do fine in the 1980's when CD came out. Like TEK tried but with research EE's it did not fly. TEK had to reduce the BW claimed or go to higher sampling rates to have accuracy to the BW spec'ed. Espec for single-shot event data.
You dont have to negate Nyquist to know the minimum for a continuous frequency of 2 samples wont be adequate for music signals.
More clues ---> https://www.mouser.com/pdfdocs/Tektronix12_things_to_consider1.pdf
THx-RNMarsh
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You're saying some change is happening to a high frequency signal. If the rate of change doesn't cause any new frequency components that violate Nyquist, then it can be sampled and reconstructed without error. If the rate of change is high enough to cause a violation of Nyquist, then errors will occur.
These discussions seem eternal, and fuzzy violations of Nyquist lurk behind pretty much all that I've seen. It only works right if you play by the rules, and the rules are strict.
All good fortune,
Chris
These discussions seem eternal, and fuzzy violations of Nyquist lurk behind pretty much all that I've seen. It only works right if you play by the rules, and the rules are strict.
All good fortune,
Chris
The Nyquist-Shannon(-Kotelnikov-Whittaker) theorem states that the sampling frequency must be more than 2 times of the signal to be sampled, arguably one could near that limit infinitesimally, but getting back to CD audio one have to remember that 20 kHz is the highest frequency allowed, the remaining 2.05 kHz is actually a transition frequency band left for the filters to take care of anything above 20 kHz in order to best avoid aliasing anomalies.
However nowadays the ADC's are so much better and the higher the sampling frequency the better as the more lax the filter can be done prior to ADC.
However nowadays the ADC's are so much better and the higher the sampling frequency the better as the more lax the filter can be done prior to ADC.
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To accurately measure the frequency of a signal, we need a sampling rate of at least twice the highest frequency in the signal. This concept is known as Nyquist's theorem. To get the shape of the signal, you will need a sampling rate of at least ten times higher than the highest frequency in the signal. Jan 8, 2019
THx-RNMarsh
THx-RNMarsh
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