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Topic: Nyquist was wrong?! (Read 60219 times) previous topic - next topic
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Nyquist was wrong?!

Reply #25 –
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I thought Chemistry was difficult!!

If fact I used to find chemistry more difficult than these things...

Nyquist was wrong?!

Reply #26 –
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We discussed about all this some time ago: http://www.hydrogenaudio.org/forums/index....=ringing&st=50&

Actually, it was the Shibach EQ thread where you said this.

I did a search for "filter AND ringing" before posting, but I knew I should have also filtered by your username, KikeG. I mean, with 775 posts, I was sure you had addressed this issue before, I just couldn't find where.

Nyquist was wrong?!

Reply #27 –
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If fact I used to find chemistry more difficult than these things...


Yeah, so did I. I guess it just comes down to what you're interested in.

Anyway, this is a facinating topic. I'll have to come back to it after I take my next signal analysis class (this fall). It's funny though, because this topic relates to a lot of things. We were discussing Fourier series, as well as Nyquist's and Shannon's formulas in my networks class today; I was on top of it.

Nyquist was wrong?!

Reply #28 –
Quote
Actually, it was the Shibach EQ thread where you said this.

Yep, true, it seems that I made a mistake when cutting and pasting. I've corrected it, thanks.

Nyquist was wrong?!

Reply #29 –
Quote
I mean, read
the article.. you will see this guy is far from being stupid.

Am I missing something?!?!

He's trying to sell his stuff?

I'd propose that in the future this kind of thread gets renamed or split quicker. It contains a lot of usefull information, but my first reaction on seeing the title was 'sigh' and closing it.

Nyquist was wrong?!

Reply #30 –
Quote
He's trying to sell his stuff?

I'm afraid so. The pity is that surely some people bought it.

Either this Jan Meier thinks that he's smarter than Nyquist (when in fact he doesn't understand him), or he is just taking advance of people ignorance, or a mix of both things. I wonder how much he charges for his "analoger" tha tin fact is just a very simple analog delay line.

Be careful with those "audiophile"-style products and explanations!!

Nyquist was wrong?!

Reply #31 –
No, I'm not an idiot, I don't feel like an audio-guru either, and I don't like to sell equipment using "audiophile" style explanations. Actually, I have a PhD in physics and a profound professional experience in (digital) signal analysis.

Yes, the linear interpolation as shown in the article is a rather simplified one. Not because I don't understand, but because of didactic reasons. "Popular" articles always have to be written in such a way that the layman can understand without a throurough knowledge of the underlying theory. You always have to choose a certain balance between detail and simplification.

However, the beating effect is much closer to the truth than people at this forum seem to think. For a newer version of the article, with a slightly more elaborate discussion on the "beating" phenomenon I suggest people take a look at my home-page: www.meier-audio.com. Simply click at the "analoguer"-button and enjoy.

Cheers,

Jan

Nyquist was wrong?!

Reply #32 –
Quote
Yes, the linear interpolation as shown in the article is a rather simplified one... You always have to choose a certain balance between detail and simplification.

I'd say, in case of your article, it is balance between "wrong" and "right" explanation.

Quote
However, the beating effect is much closer to the truth than people at this forum seem to think.


I see you have tried to disguise the effect you talk with new fancy graphics and explanations. The fact is that they are still *wrong*. The beating you talk about is a nonlinear type of distortion. Sinc() filtering, which is the filtering used in DACs, won't cause any kind of nonlinear distortion, no matter how short the filter. A short filter will result just in a less sharp filter, but will cause *zero* distortion or beating. Beating is amplitude modulation, which translates into the addition of sidebands to the original signal. The inexistence of this phenomenon can be easily verified with any decent soundcard, just play and record a 20 KHz tone, and analyze it. Result? No beating or sidebands.

As to other assertions you do, good ADCs/DACs introduce minimal phase distortion at high frequencies, just see PCAVTech phase analysis of the LynxTwo, it is close to nothing. Maybe you SACD is one of those esoteric ones that in fact are not close no anything neutral. As to pre-ringing, I explained why it is not important in this case, at a previous post in this thread.


Quote
I have a PhD in physics and a profound professional experience in (digital) signal analysis.


This is just basic theory signal. I guess you need an introductory course, or just some real-world measurements that show any of this.

Edit: added more explanations.

Nyquist was wrong?!

Reply #33 –
Quote
No, I'm not an idiot, I don't feel like an audio-guru either, and I don't like to sell equipment using "audiophile" style explanations. Actually, I have a PhD in physics and a profound professional experience in (digital) signal analysis.

Yes, the linear interpolation as shown in the article is a rather simplified one. Not because I don't understand, but because of didactic reasons. "Popular" articles always have to be written in such a way that the layman can understand without a throurough knowledge of the underlying theory. You always have to choose a certain balance between detail and simplification.

However, the beating effect is much closer to the truth than people at this forum seem to think. For a newer version of the article, with a slightly more elaborate discussion on the "beating" phenomenon I suggest people take a look at my home-page: www.meier-audio.com. Simply click at the "analoguer"-button and enjoy.

Cheers,

Jan

I think the main argument against the analoguer in the posts above was not the linear interpolation in the explanation, but rather that it solves one 'problem' by introducing several others.

PS. I don't know about where you live, but here biomedical engineering is a quite different discipline from physics.

Nyquist was wrong?!

Reply #34 –
Quote
Yes, the linear interpolation as shown in the article is a rather simplified one. Not because I don't understand, but because of didactic reasons. "Popular" articles always have to be written in such a way that the layman can understand without a throurough knowledge of the underlying theory. You always have to choose a certain balance between detail and simplification.

That doesn't wash if the simplification is what introduces the problem you are trying to explain.

Nyquist was wrong?!

Reply #35 –
Quote
The inexistence of this phenomenon can be easily verified with any decent soundcard, just play and record a 20 KHz tone, and analyze it. Result? No beating or sidebands.

Should this apply if the 20 kHz tone is played by a different soundcard (clock shift -> beating) ?

Nyquist was wrong?!

Reply #36 –
Quote
The inexistence of this phenomenon can be easily verified with any decent soundcard, just play and record a 20 KHz tone, and analyze it. Result? No beating or sidebands.

I've analised the output of several CD players and DACs, using a tone 1kHz below nyquist, and an external spectrum analyser (an old HP machine which had 70dB range, and a frequency response from DC to either 100kHz or 200kHz - I forget which). They all showed this effect to some degree. Two of the DACs cost over $1000, so we're not talking cheap junk here!

As you reminded me, we've been through this before. Since we have, we must have discussed (and I'm sure you know) that a shorter filter gives rise to a less steep frequency domain response. The less steep response let's more of the nyquist +1kHz alias through - which beats with the 1kHz below nyquist tone.

Outside the theoretical limits, both sampling and quantisation are totally non-linear. They become linear over a specified range with correct filtering and dither.


FWIW I would rather perform the function of the analoguer using Cool Edit Pro (or a DSP board with 24-bit output) and a good DAC running 2 or 4x (e.g. 88.2kHz or 176.4kHz - it may oversample further internally). Having tried with CEP and the audiophile 2496 (which may not count as a good DAC) I can't say that I hear a difference, but (using a 21kHz sine wave) I can certainly measure one.

I must try ABXing the frequency response of the analoguer - I bet that the high frequency filtering of setting "5" is ABXable, using most normal DACs. This would probably improve the sound of most harsh recordings - but is it really any better than just EQing them to match your own personal taste? That's the fun of Cool Edit et al - we can all be audio engineers in our own bedrooms!


Cheers,
David.

Nyquist was wrong?!

Reply #37 –
2Bdecided:

We would have to distinguish between issues due to real-world implementation, ideal implementation, and theory. We could split this into 3 levels. In reverse order:

-In theory, when reconstructing sampled information in a pure, limitation-free, mathematical way, without quantization levels, there should be no problems (beating, noise, etc) at all, the reconstructed signal would be identicall 100% to the band-limited original signal. This is what Nyquist says, and I believe that Jan Meier agrees too, at least in his second version of the page.


- Going into a more real-world version of a DAC, we could consider a model that uses quantized, fixed-resolution sampled data, and digital reconstruction filters of fixed length, but that would have no real-wold analog parts inside that could cause any linear or nonlinear distortion or noise by themselves. This is how real-world DACs are, with the exception of the analog components inside them. A DAC of this kind can be perfectly modelled and simulated inside a computer.

Here is where things start to differ. Jan Meier says that in this case, there would be "beating" (nonlinear distortion) due to the use of fixed-length reconstruction filters. False. If you simulate a DAC inside a computer this way, it will still be distortion-free, given that you use dithering as needed. There would only appear quantization noise, depending exclusively on the data size of the samples at the adquisition (ADC) and the reconstruction (DAC) stages. Depending on the implementation of the filter, there would be for sure some images of the reconstructed signal (aliases, although it is not a proper definition of this) remaining above Nyquist frequency, specially if the filter is short and those images are not well attenuated. But, there would be still no distortion below the Nyquist frequency, just  reflected attenuated "images" of the signal, above this frequency, due to this possible limitation of the digital filters.


- Now, if we go into a real-world DAC, there is a possibility that due to the non-linear limitations of analog components, that ultrasonic remaining information ("aliases", or better say "images" of the signal over Nyquist frequency) could intermodulate with the reconstructed signal, appearing intermodulation products into the audible band (below Nyquist frequency). This is the only way that this beating can happen, due to analog limitations (linear and nonlinear distortion, noise) of real-world, solid-state, components. But this non-linearity has no direct relationship with the lenght of the filters used at the reconstruction process, or the frequency of the sampled signal, as Jan Meier tries to imply. It can be a non-direct consequence of it, but depends exclusively on the nonlinearity of the system, not the reconstruction sampling process, and will happen equally when playing lower frequency signals.


Now:

Quote
I've analised the output of several CD players and DACs, using a tone 1kHz below nyquist, and an external spectrum analyser (an old HP machine which had 70dB range, and a frequency response from DC to either 100kHz or 200kHz - I forget which). They all showed this effect to some degree. Two of the DACs cost over $1000, so we're not talking cheap junk here!


I find this quite strange. This is a loopback recording of my $150 card playing two tones of 19 KHz and 20 KHz.



As you see, there are minuscule intermodulation products at around -115 dBFS. However, those are result of the intermodulation of the two played tones, not of the tones plus aliased information over fs/2 (Nyquist frequency). See, the intermodulation products of those -12 dBFS tones fall at -115 dBFS. For sure, the intermodulation products of these tones with the aliased ones will be much lower, since those aliases will be of significant lower amplitude, due to the filtering of these frequencies over fs/2 that any DAC performs.

If I repeat that same measurement with a single 20 KHz tone, I bet that intermodulation products will be minuscule, if measurable at all. Maybe the effect you saw was due to the old HP anayzer you used?

Quote
Outside the theoretical limits, both sampling and quantisation are totally non-linear. They become linear over a specified range with correct filtering and dither.


Well, if you use proper dither, the system will be perfectly linear below Nyquist frequency, in the sense of that there will be just quantization noise added, but no distortion at all.

Nyquist was wrong?!

Reply #38 –
Quote
Here is where things start to differ. Jan Meier says that in this case, there would be "beating" (nonlinear distortion) due to the use of fixed-lenght reconstruction filters. False. If you simulate a DAC inside a computer, it will still be distortion-free, given that you use dithering as needed. There would only appear quantization noise, depending exclusively on the data size of the samples at the adquisition (ADC) and the reconstruction (DAC) stages. Depending on the implementation of the filter, there would be for sure some images of the reconstructed signal (aliases, although it is not a proper definition of this) remaining above Nyquist frequency, specially if the filter is short and those images are not well attenuated.


If you have a real tone at 22kHz, and an image of that tone at 22.1kHz, the two will beat, won't they? If they're the same amplitude (unlikely in this case, but just imagine...), you'll see a classic beat waveform, with the amplitude envelope going from minimum to maximum in a regular pattern - in this case 100 times per second. Just what Jan shows on his site.

Quote
But, there would be still no distortion below the Nyquist frequency, just above, due to this possible limitation of the digital filters.


This is the key to the problem. What you say here is true. "If we look at this very carefully, and if we only consider frequencies below the nyquist limit, then they have not been harmed or changed in anyway." That's true - but in saying it, you are incorporating a perfect low pass filter into your hypothetical viewpoint.

"there would be still no distortion below the Nyquist frequency" = if I have a perfect filter, there is no distortion.

To "see" that there is no distortion, you have to look through a filter. In your viewpoint, you are removing all the components above 22.05kHz; then from this viewpoint, everything looks fine.

(If you use a spectrum analiser, with a long FFT setting, you can see that there are two tones - one above the nyquist limit, and one below - you're saying we ignore the one above - fair enough - but ignoring everything above a certain frequency is imposing a low pass filter on your view. That's not a useful way of looking at it...)


Now, back to reality: Let's say that we can hear 22kHz. I can't. I doubt most people can. But let's say we find someone who can. I think it's quite likely that, if your hearing extends to 22kHz, it'll also extend to 22.1kHz. Therefore, when you listen to the 22kHz tone, reproduced by this DAC which allows a (smaller) 22.1kHz image through, what you'll hear is a rough, beating tone, with a frequency of around 22.05kHz.


There you go - no analogue electronics involved, but a hiedous non-linear effect.



Quote
Quote

I've analised the output of several CD players and DACs, using a tone 1kHz below nyquist, and an external spectrum analyser (an old HP machine which had 70dB range, and a frequency response from DC to either 100kHz or 200kHz - I forget which). They all showed this effect to some degree. Two of the DACs cost over $1000, so we're not talking cheap junk here!


I find this quite strange. This is a loopback recording of my $150 card playing two tones of 19 & 20 KHz.


OK - first, I'm not talking about intermodulation - I'm just talking about the presence of the image tones.

Then, second, your looped back sound card doesn't work at a high enough frequency to capture the image tones of itself - the only way to do that it to run one soundcard playing at 44.1kHz, and another recording at (say) 96kHz.

Quote
If we repeat that same measurement with a single 20 KHz tone, I bet that intermodulation products will be minuscule, if measurable at all. Maybe the eefect you saw was due to the old HP anayzer you used?


You can see the beating between a 22kHZ and 22.1kHz tone on a 'scope. But I think we're talking at cross purposes - this all goes back to the fact that I think having an image tone is a bad thing (despite it being above nyquist) whereas you don't.

You're right - the effect at 20kHz is probably tiny.

(goes away, looks round the office, opens a box from university)

I've dug out the results of the experiment. I checked 3 DACs on a 'scope, and more using the spectrum analyser. All checked using 16-bit 44.1kHz test signals generated in CEP.

On the scope, I measured the beating, or amplitude modulation, in volts - peak to trough.

Meridian DAC, ref: 1kHz tone Vpp=6.4V
22.0kHz: 1.35V
21.0kHz: 0.32V
20.0kHz: <0.02V

Digilog DAC, ref: 1kHz tone Vpp=7.6V
22.0kHz: 2V
21.0kHz: 0.6V
20.0kHz: 0.1V
10.0kHz: ~0.02V

Sony DAC, ref: 1kHz tone Vpp=7.2V
22.0kHz: 0.96V
21.0kHz: 0.08V
20.0kHz: <0.02V

Then, on the scope, I measured the relative amplitudes of the real and image tones:

SME DAC
20.0kHz: +1.62dB > no image above -78dB
20.5kHz: +1.57dB > 23.6kHz: -50dB
21.0kHz: +1.24dB > 23.1kHz: -27dB
21.5kHz: -0.20dB > 22.6kHz: -13.31dB
22.0kHz: -3.95dB > 22.1kHz -5.09dB

Sony DAC
1.00kHz: +2.21dB
10.0kHz: +2.37dB
15.0kHz: +2.19dB
20.0kHz: +1.98dB > no image above -78dB
20.5kHz: +1.54dB > 23.6kHz: -51.5dB
21.0kHz: +0.12dB > 23.1kHz: -31.01dB
21.5kHz: -2.92dB > 22.6kHz -18.11dB
22.0kHz: -8.11dB > 22.1kHz: -9.45dB

CardD+ sound card
1.00kHz: -4.05dB
10.0kHz: -4.14dB
15.0kHz: -4.22dB
20.0kHz: -4.34dB
20.5kHz: -4.38dB > 23.6kHz: -66dB
21.0kHz: -4.52dB > 23.1kHz: -40.15dB
21.5kHz: -5.62dB > 22.6kHz: -22.03dB
22.0kHz: -9.76dB > 22.1kHz: -11.17dB

Digilog DAC:
1.00kHz: +2.96dB
This DAC has terrible filtering - even the 1kHz tone gives:
~43kHz: -57.8dB
~45kHz: -59.2dB
~87.2kHz: -60.4dB
~89.2kHz: -60.7dB
Similar rubbish for 10 and 20k, then for the main ones:
20.5kHz: +2.62dB > 23.6kHz: -21.59dB
21.0kHz: +1.88dB > 23.1kHz: -12.67dB
21.5kHz: +0.41dB > 22.6kHz: -6.74dB
22.0kHz: -2.05dB > 22.1kHz: -2.69dB

Meridian DAC
1.00kHz: +1.74dB > ~43kHz: -66.9dB (I hadn't checked this high for the other DACs before the one above)
10.0kHz: +1.32dB > ~34kHz: ~64dB
15.0kHz: +1.67dB > 29.1kHz: ~-65.5dB
20.0kHz: +1.54dB > 24.1kHz: -52.7dB
20.5kHz: +1.08dB > 23.6kHz: -29.75dB
21.0kHz: -0.01dB > 23.1kHz: -18.61dB
21.5kHz: -2.03dB > 22.6kHz: -11.21dB
22.0kHz: -5.25dB > 22.1kHz: -6.08dB



At the time, I dumped these numbers into Excel and plotted graphs of the image rejection filter response in each of these DACs - not quite the brick walls I was expecting before I performed these measurements. The Digilog DAC from Musical Fidelity was very old, but both the Meridian DAC and the SME DAC were recent, and generally thought to be excellent.


I did these tests because of an AES paper by Richard Black (I think) who suggested that these image frequencies were a real problem. He doubted that we could hear them, but he pointed out that they are not harmonically related to anything within the true audio spectrum - hence any intermodulation caused by amplifiers or speakers could create some nasty inharmonic components within the audible range. I'm not sure the numbers add up to a huge problem for typical music, but he had a point - it is possible that there is an audible effect.


Cheers,
David.

Nyquist was wrong?!

Reply #39 –
Quote
If you have a real tone at 22kHz, and an image of that tone at 22.1kHz, the two will beat, won't they? If they're the same amplitude (unlikely in this case, but just imagine...), you'll see a classic beat waveform, with the amplitude envelope going from minimum to maximum in a regular pattern - in this case 100 times per second. Just what Jan shows on his site.

Not exactly. The output of a DAC goes through a filter (in practice, it's one digital filter with over-sampling plus an alalog filter) that makes sure there's nothing left above 22.05 kHz. Depending on your hardware, it may start cutting at 20 kHz to achieve that (in which case, you'll likely lose the 22 kHz tone), as long as nothing's left above Nyquist frequency. Now for your example, it's quite possible to make a filter that would have its transition band between 22.01 and 22.05 kHz, in which case you'd get the signal correctly. In the case of a normal soundcard, trying to play a 22 kHz tone would probably result in no output at all.

Nyquist was wrong?!

Reply #40 –
jmvalin,

Have you read the rest of the thread? 

Actually, just the rest of the post that you quoted will do - especially the part where a 22kHz tone comes out of a soundcard at only 5.71dB less than a 1kHz tone - that's hardly "no output at all". :;


Hope this doesn't sound harsh - I'm just trying to stop the thread discussion from looping back to the start!


And though it sounds like I think I know all the answers, I actually learn something more about this subject every time it comes around - so I'm not having this discussion with KikeG to say "I'm right, you're wrong" because I've learnt things from what he's said in the past. Just hads to put this bit because it's very easy to sound argumentative in typed things when you don't mean to be.

Cheers,
David.

Nyquist was wrong?!

Reply #41 –
Quote
Actually, just the rest of the post that you quoted will do - especially the part where a 22kHz tone comes out of a soundcard at only 5.71dB less than a 1kHz tone - that's hardly "no output at all". :;

Well, it has nothing to do with 44.1 kHz not being enough to sample a 21 sine wave. It just shows that the DAC's you analyzed aren't behaving the way a "standard DAC" ought to do. I'm guessing that they just didn't really bother filtering the exact way because you don't really hear above 20 kHz anyway. I don't think it's really worth discussing what each individual DAC does.

The main thing here is that people keep saying "Nyquist was wrong" when they're just completely mis-interpreting the sampling theorem. So far I've seen:

- I use linear interpolation between samples and it doesn't look like the original.
- My soundcard doesn't work with a 22.0499 kHz tone.
- I can sample a 1 MHz tone at 50 kHz and still get perfect reconstruction, Nyquist was wrong. (no you can just compensate the aliasing which is OK as long as you don't have other stuff in the baseband)

Nyquist was wrong?!

Reply #42 –
this is obviously cannot be a discussion whether nyquist was right or wrong. this discussion is basicly a 'theory vs. practice' discussion..
theory : nyquist wasn't wrong. the sampling function is a one-to-one function iff (if and only if) the sampling-rate is equal or higher than twice the bandwidth of the source signal.  in this case (one-to-one), there exist an inverse function.
practice : implementing the inverse function (reconstruction filter) is a problem.


i wonder what's your opinion about an alternative approach :
process your digital signal through a digital upsampler from 44.1khz to 88.2khz (cs8420, for instance, can do this directly on spdif traffic),  and then use a lousy anti-aliasing reconstruction filter with cut-off frequency at 88.2khz.


edit : typo

Nyquist was wrong?!

Reply #43 –
Quote
i wonder what's your opinion about an alternative approach :
process your digital signal through a digital upsampler from 44.1khz to 88.2khz (cs8420, for instance, can do this directly on spdif traffic),  and then use a lousy anti-aliasing reconstruction filter with cut-off frequency at 88.2khz.

Well, of course you can get almost as close to the Nyquist limit you like by spending more on hardware. As for up-sampling, that's of course the logical thing to do, although you still need a sharp filter at 22 kHz. The only difference is that the filter can be implemented numerically, which is easier. In theory, you could have a transition band of only 1 Hz. The down side is that the (huge) filter would introduce a delay of several seconds.

Anyway, I still don't understand the point of this thread.

Nyquist was wrong?!

Reply #44 –
This thread deserves to be pinned one and for all times IMHO. What i do understand is that even the most intelligent experts here are slowly coming to the point where i have been at almost 5 years ago ( and i dont understadn at least half of what is said here, being a low-level electrical engineer with bad results in the DSP courses  :

Its much easier to drop the old 16/44.1 standard and concentrate on 24/96 instead, to make sure we have a digital frontend that is superior to the human ear under all circumstances, instaed of discussing endlessly if maybe 16/44.1 iss good enough or not, and then tweaking the old standard with expensive equipment to make the best out of it.

F..ck ( censored ), any crappy DVD can hold up to 5 hours of 24/96 recorded Stereo music today, so whats the bloody point in defending the usage of 16/44.1 still ? The necessary ADC/DAC's to record in 24/96 are no miracles anymore, and for low cost equipment you simply downsample to 16/48 and the user of this unit will still be more than happy .....

The mere feeling of being on the safe side does justify the using of higher sampling rates already IMHO, especially with respect to the fact that its technically feasible today  !! There is only one reason why DVD-Video with 24/96 has not found broad usage already, and that is because Chesky was the only one to release music on this standard, while Panasonic and SONY are still trying with huge amounts of money to push SACD and DVD-A .. sad but true  .... every crappy DVD-player out there ( and there are billions already ) has to be able to play 24/96 audio tracks on DVD-Videos ( somehow ), that makes it even more sad ....

Nyquist was wrong?!

Reply #45 –
Quote
This thread deserves to be pinned one and for all times IMHO. What i do understand is that even the most intelligent experts here are slowly coming to the point where i have been at almost 5 years ago ( and i dont understadn at least half of what is said here, being a low-level electrical engineer with bad results in the DSP courses  :

Its much easier to drop the old 16/44.1 standard and concentrate on 24/96 instead, to make sure we have a digital frontend that is superior to the human ear under all circumstances, instaed of discussing endlessly if maybe 16/44.1 iss good enough or not, and then tweaking the old standard with expensive equipment to make the best out of it.

F..ck ( censored ), any crappy DVD can hold up to 5 hours of 24/96 recorded Stereo music today, so whats the bloody point in defending the usage of 16/44.1 still ? The necessary ADC/DAC's to record in 24/96 are no miracles anymore, and for low cost equipment you simply downsample to 16/48 and the user of this unit will still be more than happy .....

The mere feeling of being on the safe side does justify the using of higher sampling rates already IMHO, especially with respect to the fact that its technically feasible today   !! There is only one reason why DVD-Video with 24/96 has not found broad usage already, and that is because Chesky was the only one to release music on this standard, while Panasonic and SONY are still trying with huge amounts of money to push SACD and DVD-A .. sad but true  .... every crappy DVD-player out there ( and there are billions already ) has to be able to play 24/96 audio tracks on DVD-Videos ( somehow ), that makes it even more sad ....

Hey, keep in mind that with Speex, I'm still trying to convince people to switch from 8 kHz to 16 kHz  . My opinion is that 96/24 is overkill. While I agree that 44.1 kHz might not be enough (even then, I'm not completely sure), 48 kHz should be enough. It's not only a matter of storage but processing too. In many cases, processing at 96 kHZ is just 100% overhead. As for 24 bits, I think it's usful if you're going to do some processing, but just for playback, I don't think it makes much of a difference when taking into account compression (even at high bit-rate) and the rest of the sound system. I have yet to see a power amp (or even a 24-bit soundcard) with 144 dB SNR.

Nyquist was wrong?!

Reply #46 –
2Bdecided:

Ok, I must admit I've been trying to explain the wrong thing, and that didn't totally understand what this beating effect consisted of. What mislead me was Jan Meier suggestion of that this was an audible phenomena and for that reason, I assumed it happened below Nyquist frequency. My explanation holds true if you assume that signals above 20 KHz or 21 KHz are not audible. But, as you say:

Quote
This is the key to the problem. What you say here is true. "If we look at this very carefully, and if we only consider frequencies below the nyquist limit, then they have not been harmed or changed in anyway." That's true - but in saying it, you are incorporating a perfect low pass filter into your hypothetical viewpoint.


That's all true, from the point of view of the whole signal, there is distortion. But assuming that our "natural" lowpass filter will filter out all frequencies close to Nyquist frequency and above, it still holds.

Quote
If you have a real tone at 22kHz, and an image of that tone at 22.1kHz, the two will beat, won't they?
...
There you go - no analogue electronics involved, but a hiedous non-linear effect.


True. Doing a short-time analysis of the signal, as our ear does, in this case there would be obvious amplitude modulation.

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OK - first, I'm not talking about intermodulation - I'm just talking about the presence of the image tones.


Now I see. For the reasons explained before I thought this was an intermodulation problem, so I just analyzed below Nyquist frequency.

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this all goes back to the fact that I think having an image tone is a bad thing (despite it being above nyquist) whereas you don't.


The measurement data you have provided is very interesting. I have done some quick audibility tests based on the image rejection data, but with audible test tones of 15 KHz instead. According to those, assuming that we could hear above 20 KHz, this beating effect would be audible just near 22 KHz. At 21.5 KHz, the attenuation of the images is of around 15 dB, and 1.1 KHz over the original tone. In this case, my tests suggest (using 15 KHz plus 16.1 KHz "image" tone, both audible by themselves in my case) that the image tone wouldn't be audible, because the beating effect dissapears when the frequencies are distant enough, and because the image gets masked from the original tone.

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At the time, I dumped these numbers into Excel and
I did these tests because of an AES paper by Richard Black (I think) who suggested that these image frequencies were a real problem. He doubted that we could hear them, but he pointed out that they are not harmonically related to anything within the true audio spectrum - hence any intermodulation caused by amplifiers or speakers could create some nasty inharmonic components within the audible range. I'm not sure the numbers add up to a huge problem for typical music, but he had a point - it is possible that there is an audible effect.


I think this could only be verified via blind tests. I think that over 16 KHz or so, many of the audible content of music is usually of percusive type (drums, cymbals, transients, etc) and of inharmonic content then, too. On the other side, this beating effect would happen just over, say, 21.5 KHz (being pesimistic), where usually ADCs start rolling off and there's less signal content recorded. I think very plausible the idea that intermodulation products due to high-frequency image signals would be small in comparison with the intermodulation effects on this non-harmonic percusive content over 16 KHz.

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And though it sounds like I think I know all the answers, I actually learn something more about this subject every time it comes around - so I'm not having this discussion with KikeG to say "I'm right, you're wrong" because I've learnt things from what he's said in the past.


Thanks, I'm happy to have helped you on those occasions. That same thing has happened to me sometimes from you in the past too, and has happened in this this particular case.

Nyquist was wrong?!

Reply #47 –
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While I agree that 44.1 kHz might not be enough (even then, I'm not completely sure), 48 kHz should be enough.

I still think that, given limitations of human hearing, 44.1 KHz is enough. Maybe for some 0.1% of young bat-eared people there could be a difference using a higher sampling rate, and just on critical material. But even in this case, the difference I believe would be very subtle. Still, I would only be convinced form a rigorous, repeatable, blind test.

Nyquist was wrong?!

Reply #48 –
KikeG,

Hey - I think we agree!

Cheers,
David.

Nyquist was wrong?!

Reply #49 –
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While I agree that 44.1 kHz might not be enough (even then, I'm not completely sure), 48 kHz should be enough.

I still think that, given limitations of human hearing, 44.1 KHz is enough. Maybe for some 0.1% of young bat-eared people there could be a difference using a higher sampling rate, and just on critical material. But even in this case, the difference I believe would be very subtle. Still, I would only be convinced form a rigorous, repeatable, blind test.

Stumbling across this discussion, I just had to jump in on some of what's being discussed.


1. Filter ringing / Impulse response

Any filter, may it be analog (electronic), digital or even mechanical, will ring around fc. The steeper the filter, the longer the impulse resonse (ringing) will be. Symmetric filters (only realizable in the digital domain) will have even distribution of pre/post ringing, creating a flat phase response.


2. Audibility of filter steepness

As it has been stated in this thread, it should be impossible to hear filter ringing with fc beyond human hearing. This is INCORRECT. It might be tempting to think so. The human hearing cannot hear steady-state sines over 20kHz. This has been concluded in millions of hearing tests all over the world. However, when listening to impulse responses, we have to take into account what is analyzing these sounds. The human ear has its own set of filters, analysis windows. Analyze a long enough impulse response with an auditory model and you will find that these filters are indeed triggered. This is why we can hear steepness of filters even when fs=96kHz and fc=47kHz.


Cheers,

Martin Saleteg
N i n j a F X