192 khz vs 48 khz poll

[kumakuma]

Since you know how it works, please explain to me how if a rare bird noise is made between T50.1 and T50.9 and samplings are only at T50 and T51, how that sound is reproduced.

 

In your hypothetical example, wouldn't the noise only need to be 1/48,000 of a second in duration to missed, assuming a sampling frequency of 48kHz?

[Mike Mcsweeney]

In your hypothetical example, wouldn't the noise only need to be 1/48,000 of a second in duration to missed, assuming a sampling frequency of 48kHz?

The question wasn't about what is audible, it was about the accuracy of the reproduction....you can have millions of inaccuracies in a very short time depending on how complex the signal, of which none would be audible.

[kumakuma]

The question wasn't about what is audible, it was about the accuracy of the reproduction....you can have millions of inaccuracies in a very short time depending on how complex the signal, of which none would be audible.

 

Then I guess your answer to the question is "True"?

[Mike Mcsweeney]

Then I guess your answer to the question is "True"?

 

Of course...that is what i selected...quite obvious to me. I did state in the thread "false", when i forgot how the question was worded...

 

But yes, of course the answer is true...you can ALWAYS improve the accuracy of the reproduction by increasing the sample rate (given my stipulation of perfect circuitry that doesn't cause distortion in effort to increase the sample rate).

[kumakuma]

Of course...that is what i selected...quite obvious to me. I did state in the thread "false", when i forgot how the question was worded...

 

But yes, of course the answer is true...you can ALWAYS improve the accuracy of the reproduction by increasing the sample rate (given my stipulation of perfect circuitry that doesn't cause distortion in effort to increase the sample rate).

 

Actually I think you are wrong. Think of a sine wave for a sound with a frequency of 24 kHz. A sampling rate of 48 khz might not catch the beginning of the sound if it falls between samples but it will catch the upward slope of the wave and be able to determine mathematically exactly where the sound started based on the next sample. You just need enough samples to be able to determine the shape of the curve, not an infinite number.

[Mike Mcsweeney]

Actually I think you are wrong. Think of a sine wave for a sound with a frequency of 24 kHz. A sampling rate of 48 khz might not catch the beginning of the sound if it falls between samples but it will catch the upward slope of the wave and be able to determine mathematically exactly where the sound started based on the next sample. You just need enough samples to be able to determine the shape of the curve, not an infinite number.

 

You are entitled to your incorrect opinion. your arguments have been repeated several times...i don't hear any more this time than the other 100 times. consider my examples...even you suggested that the tone that was lost in my example would only be 1/48,000 of a second....forget the numbers or how audible....just realize it is less accurate.

 

I cut and paste from someone else, which i think may show it better than i illustrated:

Nyquist theorem adresses A ONE signal while music is ever changing (notes, harmonics, transients, reverberations, what have you) :

----------

A signal can be so complex that you would need to sample it billions of times in a second, and it would still be possible that you have an incomplete reproduction. It would take an infinite number of samples to achieve a perfect reproduction.

 

Perhaps you can explain why DSD sounds so much better for complex waveforms. Do you really think that some of these DSD downloads would sound the same if you downsampled them?

 

Or do you think DSD files don't sound better?

[Paul R]

Okay Miska, I get this. I don't think I know as much as you about these things, but have looked at such. But you are describing something above the nyquist frequency. And something not found in musical signals.

 

Are you purposely trying to force an erroneous conclusion, or do you really not understand that Miska is providing a concrete example of why a higher sample rate can be used to produce a more accurate signal? Higher sample rate can equal less distortion in both the time and frequency domain.

[Jud]

The question wasn't about what is audible, it was about the accuracy of the reproduction....you can have millions of inaccuracies in a very short time depending on how complex the signal, of which none would be audible.

 

Hi Mike. It's simple, if you have a million waves in a second, then you need a sample rate over 2 MHz. If you want to say that you have a million "inaccuracies" or waves or what have you in a second and that 48kHz is an inadequate sample rate to show what's going on, you're obviously right.

 

On the other hand, it's also mathematically provable under idealizing assumptions that if the highest frequency of interest is under 24kHz, a 48kHz sample rate will specify the waveform equally as well as anything higher. In the real world that sample rate won't specify a 23kHz waveform perfectly, *but not because of too few samples*. Rather, we're now talking about filter characteristics, and sample rate is far from the sole determinant of filter performance (though it can certainly help).

[sdolezalek]

Mike: I really don't think you are helping yourself here, in part because you are making two different arguments; one of which most of us think is just flat wrong and the second of which is probably correct.

 

As to the first, in order for a sound to be AUDIBLE by humans, its wavelength is such that it cannot physically start and end in the gap between 48 khz samples. To do that, the sound would have to have an extremely short wavelength and would therefore be of a frequency greater than 20,000Hz (beyond audibility). Thus 48 khz sampling will capture all the sounds we can hear because it is frequent enough to bisect all wavelengths of just less than 24,000. Logic might imply that you could have a 400 hz tone that only lasts 1/50,000 of a second, but physics says it can't be.

 

As to your second argument, which I believe goes more to whether there are things that could be picked up by more frequent sampling that either are recognizable by humans or (because of other things we do with the soundwave) become audible to us (such as time shifts or other effects that filtering might introduce), I would think most people here would at least admit to the possibility, if not outright agree.

[Daudio]

You are entitled to your incorrect opinion. your arguments have been repeated several times...the other 100 times...

 

 

 

** Troll Alert **

[Paul R]

Actually I think you are wrong. Think of a sine wave for a sound with a frequency of 24 kHz. A sampling rate of 48 khz might not catch the beginning of the sound if it falls between samples but it will catch the upward slope of the wave and be able to determine mathematically exactly where the sound started based on the next sample. You just need enough samples to be able to determine the shape of the curve, not an infinite number.

 

Actually, you need a sampling rate greater than the highest frequency you wish to reproduce. And you do need an infinite number of samples to achieve perfect reproduction. It is also true that the more samples you have, the more perfect your reproduction. However, the fact is that in the audible frequency range, for a intents and purposes, the reproduction is perfect enough.

 

Whether or not the difference between a reproduction at 48,000 samples per second and 192,000 samples per second is, all by itself, audible is very questionable. It is much less questionable if you add in the technical facts surrounding the recording and playback of material at those same rates though.

[Jud]

Those waves. That is a superposition of at least two components. What "Nyquist says" applies to the highest-frequency component.

 

Thanks, I didn't know that and the information is much appreciated.

[sandyk]

An interesting read. Hopefully it hasn't already been linked to ?

 

http://www.wescottdesign.com/articles/Sampling/sampling.pdf

[kumakuma]

Perhaps you can explain why DSD sounds so much better for complex waveforms. Do you really think that some of these DSD downloads would sound the same if you downsampled them?

 

Or do you think DSD files don't sound better?

 

DSD material often sounds better because it is a better mastering of the original source material. I have tried converting DSD files to high resolution PCM files and they sound identical to my ears.

[Mike Mcsweeney]

Mike: I really don't think you are helping yourself here, in part because you are making two different arguments; one of which most of us think is just flat wrong and the second of which is probably correct.

 

As to the first, in order for a sound to be AUDIBLE by humans, its wavelength is such that it cannot physically start and end in the gap between 48 khz samples. To do that, the sound would have to have an extremely short wavelength and would therefore be of a frequency greater than 20,000Hz (beyond audibility). Thus 48 khz sampling will capture all the sounds we can hear because it is frequent enough to bisect all wavelengths of just less than 24,000. Logic might imply that you could have a 400 hz tone that only lasts 1/50,000 of a second, but physics says it can't be.

 

As to your second argument, which I believe goes more to whether there are things that could be picked up by more frequent sampling that either are recognizable by humans or (because of other things we do with the soundwave) become audible to us (such as time shifts or other effects that filtering might introduce), I would think most people here would at least admit to the possibility, if not outright agree.

 

I didn't say "most", I said many...even in this poll there is near a 50/50 split....so regardless of who is correct and who is wrong, obviously many people are incorrect (wink)...I also was only paraphrasing the individual i quoted... read the posting i replied to.

 

I also never spoke to what is audible. I only spoke to accuracy.

 

The rest i either agree with, or i don't have the knowledge to remark. I am not above suggesting i am probably the biggest novice here...(wink wink)

[Jud]

Actually, you need a sampling rate greater than the highest frequency you wish to reproduce. And you do need an infinite number of samples to achieve perfect reproduction. It is also true that the more samples you have, the more perfect your reproduction. However, the fact is that in the audible frequency range, for a intents and purposes, the reproduction is perfect enough.

 

Whether or not the difference between a reproduction at 48,000 samples per second and 192,000 samples per second is, all by itself, audible is very questionable. It is much less questionable if you add in the technical facts surrounding the recording and playback of material at those same rates though.

 

I want to try to be precise here. Because Nyquist's idealizing assumptions do include infinite time/samples, it is true even if you have a 2 Hz sample rate applied to a wave of less than 1Hz frequency, that an infinite *number* of samples is necessary to provably specify the waveform completely. But you do not need an infinitely fast sample *rate*. In fact it is provable that given an infinite number of samples in each case, a 1MHz sample rate would not specify a 1 Hz waveform any better than a 3 Hz sample rate.

[Mike Mcsweeney]

here is a good read...although it is quite lengthy, it is in comparatively simple language

 

Music and Computers

 

I have only brushed through a couple chapters, but to me, the most interesting, and where i think the difference would be most notable would be in this chapter.

 

http://music.columbia.edu/cmc/musicandcomputers/chapter1/01_04.php

[RobbieC]

I cut and paste from someone else, which i think may show it better than i illustrated:

Nyquist theorem adresses A ONE signal while music is ever changing (notes, harmonics, transients, reverberations, what have you) :

----------

A signal can be so complex that you would need to sample it billions of times in a second, and it would still be possible that you have an incomplete reproduction. It would take an infinite number of samples to achieve a perfect reproduction.

 

Mike,

 

In some ways you are right: "A signal can be so complex that you would need to sample it billions of times in a second...."

 

However, in esldude's scenario he asks whether content below 20 kHz would be more accurate. This is an important part of the question. Even the most "complex" waveform that contains frequency components below 20 kHz contains those components uniquely. Those components aren't going to change whether you sample at this rate or that if we hold that the curve (waveform) is unique. If you limit yourself to thinking about whether or not it is possible to identify those components accurately (those below 20 kHz) it may help.

 

I am one of the few that frequent this forum who is "qualified" more or less to talk about the intricacies of the maths involved as I have a degree in mathematics and specifically studied Fourier among other things. For instance, there are ways around a requirement that something be infinite. Let me give a little background: there are four kinds of so-called Fourier transforms. 1) Fourier transform, 2) Fourier series, 3) Discrete Time Fourier Transform and 4) Discrete Fourier Transform. Of the four, the one most "applicable" to a piece of music that has been digitized from the layperson's point of view would be the DTFT. This is because the DTFT is used for those curves (waveforms) that are discrete (meaning sampled) and aperiodic (meaning does not repeat infinitely such a piece of music with a clear beginning and end). But the DTFT is not the correct choice for analyzing music as it is impossible to calculate by computer (intractable). The DFT, on the other hand, is completely doable. The DFT requires that the curve be discrete and periodic (meaning repeats to infinity). Infinite, oh no. So what the mathematician does is take all the samples of that piece of music and repeats them end to end over and over and over again. Voila! I now have an infinite number of sample points. (We don't really repeat them over and over; we just know that the results of the transform applies to such a construct.) Because the results of the DFT is also periodic (always) I still only have to work with a finite number of points.

 

Also, please note that the state of understanding in mathematics is sufficiently advanced to handle the question as posed by esldude and that the Shannon-Nyquist Theorem is not limited in any way to applying to a "single signal" or pure tone if that is what you meant in the quote above. I wouldn't want you to be misled by that quote.

[Teresa]

...in order for a sound to be AUDIBLE by humans, its wavelength is such that it cannot physically start and end in the gap between 48 khz samples.

 

I have read the initial impact of percussion instruments is 1,000 times louder during the first two millionths of a second and dies down after that, and of course the fundamental frequency of all percussion instruments are in the audible range or we couldn't hear them. That is why percussion has much more impact live than it does in the home as our equipment is not fast enough (transient response).

 

Remember just because something vibrates so many times per second does not mean they last for a full second, and many happenings in music are extremely fast. Thus many believe that sampling frequency is more important for speed (fast changes) than for the extended frequency range.

 

Back to that initial percussion strike that lasts two millionths of a second, all equipment will time smear that some, either by completely missing the initial impact and reproducing the fade down due to it being between samples or making the initial impact too long. The more often the waveform is sampled, the more accurate it is.

 

One of the many reasons I voted true.

[Mike Mcsweeney]

Mike,

 

In some ways you are right: "A signal can be so complex that you would need to sample it billions of times in a second...."

 

However, in esldude's scenario he asks whether content below 20 kHz would be more accurate. This is an important part of the question. Even the most "complex" waveform that contains frequency components below 20 kHz contains those components uniquely.

 

I will be the first to admit that most of this mumbo jumbo is way over my head, and i get lost quickly when some of you engineers start talking.

 

Regardless of all that, let me give another example. I doubt even two elephants have the exact same sound.

Suppose there are one billion elephants each making their "music" at the same time, where the pitch fluctuates dramatically.

Of course this is totally hypothetical, and an impossibility, but to take it to extremes, will help me understand more.

 

1. What would the resultant composite analog waveform look like (besides a mess-grin), that was a composite of all 1 billion elephants at a several different pitches, and at various distances from one another.

 

I am sure there is no recording device that could accurately capture such a composite signal, but if there was...

 

2. What would be required to convert the original composite signal perfectly such that nothing is lost, whether audible or not.

 

I just find it difficult to believe that without an infinite number of samplings, you would ever be able to "accurately" reproduce such a signal without an infinite number of samplings?

 

I am sure you will lose me in your explanation very quickly, and i am also certain, that i doubt i would ever believe differently. I think that we underestimate the gift of our ears.

[RobbieC]

Suppose there are one billion elephants each making their "music" at the same time, where the pitch fluctuates dramatically.

Of course this is totally hypothetical, and an impossibility, but to take it to extremes, will help me understand more.

 

1. What would the resultant composite analog waveform look like (besides a mess-grin), that was a composite of all 1 billion elephants at a several different pitches, and at various distances from one another.

 

I am sure there is no recording device that could accurately capture such a composite signal, but if there was...

 

2. What would be required to convert the original composite signal perfectly such that nothing is lost, whether audible or not.

 

I just find it difficult to believe that without an infinite number of samplings, you would ever be able to "accurately" reproduce such a signal without an infinite number of samplings?

 

I am sure you will lose me in your explanation very quickly, and i am also certain, that i doubt i would ever believe differently. I think that we underestimate the gift of our ears.

 

Mike you are again correct when you say one would not be able to reproduce the composite signal "perfectly" such that noting is lost, audible or not. This is indeed an impossibility for all intents and purposes as the noise in the signal has the potential for astronomical bandwidth and our sampling technique does not have enough bandwidth.

 

However, if we restrict ourselves to discussing a real world signal as it applies to human hearing there are some interesting things we can do. We can now state a limit to the amount of dynamic range we want to consider as well as a limit to the amplitude and frequency content of the signal. Why? Because human beings have a limit to what frequencies they can hear, to how much amplitude they can tolerate or even detect, and to what details they can detect given they are receiving a masking signal (discussion of phase left out for simplicity). Together, those four things would describe a real world signal perfectly: 1) spectral content, 2) amplitude of that content, 3) phase of that content and 4) dynamic range. The last one, dynamic range, is not what most people here think of when they hear the words dynamic range. In this context it simply means the difference between the highest amplitude component in the signal and the lowest detectable given that there will always be noise in the signal. The noise itself can then be treated as a sort of single component if the noise is approximately white and Gaussian. ("White" and "Gaussian" are not the same thing.)

 

By treating the noise separately, it is possible to focus on whether or not the four necessary parts of capture are attainable. I would and have argued that they are indeed attainable. Digital capture techniques are advanced enough to satisfy all four requirements for "perfect" signal capture when we take into account that we need to capture up to no more than about 120 dB component amplitude, up to about 20 kHz spectral max, and about 30 dB of dynamic range (phase is not restricted).

 

If we capture all those components of the signal that fall under the above limits and then upon reconstruction add random white noise back in, then for all intents and purposes we have recreated the signal indistinguishably from the original (within those bounds). One would not even be able to identify by measurement the original from the copy (meaning mathematical equivalence had been achieved).

 

That said, the issue of stereoscopic hearing has not been addressed. The above holds at least for a single point source. And don't get me started on digital filters. Digital filters' imperfection destroy the above statement of mathematical equivalence (as does the accuracy and precision of our capture equipment, or lack thereof compared to perfection).

[RobbieC]

And don't get me started on digital filters. Digital filters' imperfection destroy the above statement of mathematical equivalence (as does the accuracy and precision of our capture equipment, or lack thereof compared to perfection).

 

I say "don't get me started on digital filters" not because I don't like them--quite the contrary--but because they are a favorite subject of mine and I fear getting too technical should I go there.

 

Also, someone should nail down the definition of "accurate" as it pertains to the original post.

[wgscott]

Yes : the point is complexity and how to approach it.

 

There are many things to take note of when reading Nyquist theorem. Notably that it doesn't care about human hearing but about the frequency range : if the mikes feed a 50 K range you need to sample at 100.

 

And that's just to keep the static view whereas music is ever-changing : common sense applies perfectly : Nyquist theorem adresses A ONE signal while music is ever changing (notes, harmonics, transients, reverberations, what have you) : let's say ok what you get at 44 k allows to perfectly reconstruct all the collected data at that time up to 22 k ; but it's a different signal that the one you collect whatever fraction of time later : common sense applies ; the more moments you capture, even though 44 K is enough for reconstruction up to 22 k, the closer you are to the breath of music in time

 

 

That is a very interesting point of view that I had not thought of. Since all ideas are equally meritorious, I will just mention that I really like vanilla.

[esldude]

I say "don't get me started on digital filters" not because I don't like them--quite the contrary--but because they are a favorite subject of mine and I fear getting too technical should I go there.

 

Also, someone should nail down the definition of "accurate" as it pertains to the original post.

 

Well accurate as in accurate. Least difference between original signal and reproduced signal. We'll say imagining microphone to AD with no processing and straight back to DA.

 

Now on the other hand, would you please start a thread on digital filters. Please, pretty please with a cherry on top. Or discuss it here in my thread.

 

I don't have the knowledge to decide on some of the stuff Miska says. One thing Miska is talking about impulse response or response to above band signals. I just don't see anything to 'ring' the filter in music. I also don't measure those sorts of effects with equipment except single sample pulses. It therefore seems unlikely to me music has any transients or other pulses to ring the filter with the input filtering in place. Am I wrong about this?

 

So if you have knowledge of the filtering which you seem to have, discuss it, inform us, deign to answer our foolish questions please. And if I may put in a plug for Miska, he is most generous in deigning to respond to us. Or at least I have found him to be so. And Miska, if you read this, it isn't that I don't believe you, more I don't understand you (my fault I am sure not yours) so any further comments you could make would be welcome also.

 

And if I may be somewhat presumptuous. At least for myself and a few others, we seem to agree that if there is a difference in low vs high sample rate accuracy for sub 20khz signals, it is to be found in effects of filtering to achieve Nyquist conditions.

 

That is the point of this thread. To illuminate the idea that high rates are just better because there are more points of sampling to work with being the wrong picture in people's minds about how this works.

[Miska]

I don't have the knowledge to decide on some of the stuff Miska says. One thing Miska is talking about impulse response or response to above band signals. I just don't see anything to 'ring' the filter in music. I also don't measure those sorts of effects with equipment except single sample pulses. It therefore seems unlikely to me music has any transients or other pulses to ring the filter with the input filtering in place. Am I wrong about this?

 

Anything in the input that exceeds filter's pass-band will result in ringing. Higher the filter order, more it rings. Only first order filter doesn't ring. Music content doesn't abruptly stop at 24 kHz, you can see it in the measurement results I sent, or by analyzing many hi-res recordings.

 

For perfect transient response you should use only first order filter, you can calculate how high sampling rate you would need to avoid aliasing with first order anti-alias filter with 24 kHz f_c.