Analogue playback Wander

jkeny

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I was asked this on another thread but didn't get a chance to fully offer my thoughts

Linn Jitter.jpg

Let's have you explain to analog audiophiles why the above low frequency random jitter is not bothersome to them even though its level is orders of magnitude higher than in digital.

This is a question that is often posed & deserves some attempt at a cogent answer
So to restate the question - analogue playback is so prone to wander & drift & yet is not particularly noticeable, how then can digital audio jitter at much lower levels of wander & drift be so noticeable?

Even though there is substantial confusion shown in the above notations on the graph, I will not even deal with these but try to deal with the core of what's being stated
Here's one possible answer:

- wander & drift in analogue is fundamentally different to the same terms used when talking about jitter. In analogue wander/drift is the shifting of all frequencies by a set value caused by many things which effect the rotational speed of the platter, for instance. The important point about this type of drift/wander is that it affects the whole audio spectrum equally - all frequencies drift/wander in the same direction & by the same amount. It's a macro effect & at macro timings. Because this is a macro phenomena & not a sample by sample determination (it's analogue) this wander gradual, not instantaneous - it doesn't shift timing suddenly in one direction & stop suddenly or reverse direction suddenly - see jitter wander below. So a change in speed happens over an extended period of time

- wander & drift when talking about jitter is a completely different & more complex phenomena. A clock that wanders causes spectral impurity in the reproduced tones - in other words the frequencies fluctuate. But this fluctuation is caused by each sample being off by whatever the mistiming of the clock is when the sample is being converted to an analogue value. The next sample will have another random amount of mistiming in plus or minus direction so we end up with a series of samples all converted with mistimings which make up the waveform. The result is a slightly (hopefully) skewed waveform than what it should be. The point is that this clock mistiming is happening at the micro level of each sample conversion & it's a function of the mistiming of the clock at this conversion point. This mistiming is not a macro trend, as in the analogue playback where the whole waveform is shifted by the slowing down or speeding up of the platter from its ideal speed - this mistiming is a micro trend which can go plus for one sample & negative for the next sample. This is what's happening at the micro level. So when all the samples of a waveform have been converted to analogue with a clock which suffers wander/drift, we end up with a reconstructed waveform which is skewed in both amplitude & frequency (or phase). This skew in frequency is the spectral impurity that clock wander causes - it's nothing like the speed drift that analogue suffers from.

So, in essence there are many mistakes made in this comparison - the first & most egregious is that a graph of a single tone is used as representative of what happens with multitone dynamically changing music. The second & obvious mistake is just interpreting the word "wander" as a definition that means the same thing in both scenarios. And the third mistake is not being able to analyse beyond first order thinking

Now it is necessary to apply psychoacoustics & understand auditory perception in order to comprehend how these two very different signal waveforms will be perceived in a dynamically changing signal stream we call music. It's obvious from empirical evidence that they are perceived very differently & one is more intrusive than the other.

Hopefully whenever someone uses this well-worn & mistaken comparison, this answer might be helpful to an understanding of why it is mistaken?
 

Don Hills

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... analogue playback is so prone to wander & drift & yet is not particularly noticeable, how then can digital audio jitter at much lower levels of wander & drift be so noticeable?

In practice, it can't. I have a party piece that I perform on occasion when the subject of LP vs CD comes up. I play the 1 KHz tone from a test LP, and the same tone from a test CD. The differences are not subtle. It's an interesting example because it's a case of the longer you listen, the more differences you identify. The lesson is that the same audible degradations are occuring in all music that you play on that turntable, yet they are difficult to identify on most (musical) sources.

... In analogue wander/drift is the shifting of all frequencies by a set value caused by many things which effect the rotational speed of the platter, for instance. The important point about this type of drift/wander is that it affects the whole audio spectrum equally - all frequencies drift/wander in the same direction & by the same amount. It's a macro effect & at macro timings. Because this is a macro phenomena & not a sample by sample determination (it's analogue) this wander gradual, not instantaneous - it doesn't shift timing suddenly in one direction & stop suddenly or reverse direction suddenly - see jitter wander below. So a change in speed happens over an extended period of time ...

It's quite clear from the graph you quoted that if "wander/drift" as you define it were the main cause, there wouldn't be any components greater than a couple of Hz from the fundamental. There are significant components out to 50 Hz, so there is a lot more happening.

... wander & drift when talking about jitter is a completely different & more complex phenomena. A clock that wanders causes spectral impurity in the reproduced tones - in other words the frequencies fluctuate. But this fluctuation is caused by each sample being off by whatever the mistiming of the clock is when the sample is being converted to an analogue value. The next sample will have another random amount of mistiming in plus or minus direction so we end up with a series of samples all converted with mistimings which make up the waveform. The result is a slightly (hopefully) skewed waveform than what it should be. The point is that this clock mistiming is happening at the micro level of each sample conversion & it's a function of the mistiming of the clock at this conversion point. This mistiming is not a macro trend, as in the analogue playback where the whole waveform is shifted by the slowing down or speeding up of the platter from its ideal speed - this mistiming is a micro trend which can go plus for one sample & negative for the next sample. This is what's happening at the micro level. So when all the samples of a waveform have been converted to analogue with a clock which suffers wander/drift, we end up with a reconstructed waveform which is skewed in both amplitude & frequency (or phase). This skew in frequency is the spectral impurity that clock wander causes - it's nothing like the speed drift that analogue suffers from. ...

The "micro" fluctuations you describe manifest themselves in the audio output as noise, just as they do for analogue. And when plotted in a graph just like the one you quoted, they look very similar (although at much lower levels). The same distribution curve, indicating the same "macro" effects that you attribute to analogue. "Micro" sample-to-sample differences produce HF noise, not "close in" (LF) jitter.

... Now it is necessary to apply psychoacoustics & understand auditory perception in order to comprehend how these two very different signal waveforms will be perceived in a dynamically changing signal stream we call music. It's obvious from empirical evidence that they are perceived very differently & one is more intrusive than the other. ...

And if you actually try my party trick, it should be very clear which one is more intrusive than the other. "Psychoacoustics and auditory perception" clearly explains why analogue (LP) playback of music doesn't sound as bad as the "party trick" implies it should.
 

jkeny

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In practice, it can't. I have a party piece that I perform on occasion when the subject of LP vs CD comes up. I play the 1 KHz tone from a test LP, and the same tone from a test CD. The differences are not subtle. It's an interesting example because it's a case of the longer you listen, the more differences you identify. The lesson is that the same audible degradations are occuring in all music that you play on that turntable, yet they are difficult to identify on most (musical) sources.
Perhaps I should have been more precise in my words.
Yes, I'm sure analogue playback is much more noticeable when single tones are being played yet when music of some complexity is being listened to, it's my experience that clarity & sound stage are improved with low close-in jitter clocks. Now perhaps this is also the effect that is noticeable with a more stable platter speed - I don't know, I'm not that familiar with TTs - perhaps some analogue guys can answer this?

It's quite clear from the graph you quoted that if "wander/drift" as you define it were the main cause, there wouldn't be any components greater than a couple of Hz from the fundamental. There are significant components out to 50 Hz, so there is a lot more happening.
I'm not following you exactly - the graph I posted was one that I copied over form another thread to show that analogue playback wander/drift (although it was annotated as random jitter & deterministic jitter which is damn confusing when talking about analogue playback)

The "micro" fluctuations you describe manifest themselves in the audio output as noise, just as they do for analogue. And when plotted in a graph just like the one you quoted, they look very similar (although at much lower levels). The same distribution curve, indicating the same "macro" effects that you attribute to analogue. "Micro" sample-to-sample differences produce HF noise, not "close in" (LF) jitter.
Is close-in phase noise not going to produce micro sample to sample differences? If it is then your claim that "Micro" sample-to-sample differences produce HF noise, not "close in" (LF) jitter." is wrong because the FFT plots don't show HF noise for oscillators with close-in phase.

And if you actually try my party trick, it should be very clear which one is more intrusive than the other. "Psychoacoustics and auditory perception" clearly explains why analogue (LP) playback of music doesn't sound as bad as the "party trick" implies it should.
I think this is where FFTs can lead us astray - just because two plots look the same in an FFT doesn't mean that the underlying dynamic signal is the same.

I've also used this analogy before - an FFT is like a long exposure photo - objects that don't move get enhanced in the pic; objects that do move are very dim by comparison, maybe even invisible depending on the speed of their movement & their brightness to start with.

An FFT doesn't tell us much about the underlying dynamics of a changing signal - it just emphasise the things that are not fluctuating much & raises their significance. Therefore we have to be careful about FFTs & the conclusions we can draw from them. As I said two FFTs may well look exactly the same but we can hear two very distinctly different sounds.
 
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Don Hills

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Perhaps I should have been more precise in my words.
Yes, I'm sure analogue playback is much more noticeable when single tones are being played yet when music of some complexity is being listened to, it's my experience that clarity & sound stage are improved with low close-in jitter clocks. Now perhaps this is also the effect that is noticeable with a more stable platter speed - I don't know, I'm not that familiar with TTs - perhaps some analogue guys can answer this?

All that really happens is that the complexity of the music masks the effects. Our auditory system isn't that good at detecting the anomalies in the presence of complex signals. And if the "clarity and soundstage" of good analogue is good enough for a significant part of the audiophile community, the orders of magnitude lower anomalies of good digital also qualifies. As for your experience, I await some objective results showing that you can indeed hear a difference.

I'm not following you exactly - the graph I posted was one that I copied over form another thread to show that analogue playback wander/drift (although it was annotated as random jitter & deterministic jitter which is damn confusing when talking about analogue playback)

The point was that the underlying mechanisms may be different, but the audible (and measurable) results are the same.

Is close-in phase noise not going to produce micro sample to sample differences? If it is then your claim that "Micro" sample-to-sample differences produce HF noise, not "close in" (LF) jitter." is wrong because the FFT plots don't show HF noise for oscillators with close-in phase.

The usual definition is that "close-in phase noise" means frequencies between 1 to 100 Hz or so. So the sample to sample variations must extend over a long enough time to generate such frequencies. In other words, the clock frequency must be varying slowly, equivalent to "wow" in analogue terms. The "micro sample-to-sample" variations you gave examples of equate to high frequencies.

I think this is where FFTs can lead us astray - just because two plots look the same in an FFT doesn't mean that the underlying dynamic signal is the same.

I've also used this analogy before - an FFT is like a long exposure photo - objects that don't move get enhanced in the pic; objects that do move are very dim by comparison, maybe even invisible depending on the speed of their movement & their brightness to start with.

An FFT doesn't tell us much about the underlying dynamics of a changing signal - it just emphasise the things that are not fluctuating much & raises their significance. Therefore we have to be careful about FFTs & the conclusions we can draw from them. As I said two FFTs may well look exactly the same but we can hear two very distinctly different sounds.

I agree. You can look at a signal in the time or frequency domain. They both show the same thing, but each has its strengths. For an example, look at the turntable speed stability tests performed by Michael Fremer and Archimago. They show the results in the time domain, and the graph you quoted shows the same effect in the frequency domain. So long as you understand what you're looking at, there's no confusion.
In the present case, even from the FFT it's quite clear that the "jitter" performance of the analogue source is orders of magnitude worse than that of any competent digital source. Given that people who claim to have exceptional auditory acuity struggle to hear the effects on "complex" analogue sources, it stretches credibility that the effects on the equivalent digital source should be audible at those vanishingly lower levels. Which is why I am waiting for the equivalent of "pictures, or it didn't happen."

There appears to be some belief that the effect of phase noise on a complex signal is different than the effect on a single sine wave. Assuming that the oscillator isn't itself affected by the signal, the effect will be the same. The output will still be the signal modulated by the phase noise. It's simple mathematics. It's just a lot harder to quantify it, which is why simpler signals are used for the purpose.
 

jkeny

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All that really happens is that the complexity of the music masks the effects. Our auditory system isn't that good at detecting the anomalies in the presence of complex signals.
Sure, when testing for the presence of a single tone in the presence of a masking tone or noise, our auditory perception is not sensitive. But generalising that simple scenario to the complex, dynamically changing signal stream of music seems like an oversimplification to me. I mentioned before about the perception of 'roughness' where low frequency fluctuations in a tone are perceived as 'roughness' of the sound. I've mentioned before & shown by my analysis, that spectral impurity can be the result of close-in phase noise and spectral resolution is a well known area of research in speech recognition. Spectral modulation thresholds or spectral ripple thresholds have been shown to be most sensitive at 2-5Hz modulation frequency. Both of these perceptual characteristics directly contradict your presumption that only masking can happen with complex music-like signals.
And if the "clarity and soundstage" of good analogue is good enough for a significant part of the audiophile community, the orders of magnitude lower anomalies of good digital also qualifies.
Empirical evidence shows that this statement is not true so therefore there is some different mechanism at operation in digital audio.
As for your experience, I await some objective results showing that you can indeed hear a difference.
Indeed

The point was that the underlying mechanisms may be different, but the audible (and measurable) results are the same.
Can I ask you that rather than making bald statements as if they are fact, can you show the derivation of your claim please? I don't accept claims without at least some demonstrable derivation backing them up, as I have done.

The usual definition is that "close-in phase noise" means frequencies between 1 to 100 Hz or so. So the sample to sample variations must extend over a long enough time to generate such frequencies. In other words, the clock frequency must be varying slowly, equivalent to "wow" in analogue terms. The "micro sample-to-sample" variations you gave examples of equate to high frequencies.
I'm not sure you understood what I meant by "micro" - I was drawing attention to the difference between how speed fluctuations in analogue are at the "macro" level (they are not happening down at samples - there's no such thing as 'sample' in analogue) in comparison to the speed fluctuations that are happening in digital audio at the "micro" sample-to-sample level. I believe this was your confusion, not helped by the graph of the Linn TT which came from ASR & was incorrectly annotated by Amir with Random & deterministic "jitter"


I agree. You can look at a signal in the time or frequency domain. They both show the same thing, but each has its strengths. For an example, look at the turntable speed stability tests performed by Michael Fremer and Archimago. They show the results in the time domain, and the graph you quoted shows the same effect in the frequency domain. So long as you understand what you're looking at, there's no confusion.
In the present case, even from the FFT it's quite clear that the "jitter" performance of the analogue source is orders of magnitude worse than that of any competent digital source.
As I said in my previous post, the mechanism by which analogue (TTs for instance) introduce wow & flutter (the "macro" that I mentioned) is not the same as the digital sample-to-sample timing differences ("micro" ) & that's why I pointed out that just because they look the same on an FFT doesn't mean that they are the same & that we perceive them in the same way. FFTs are not the signal - they are an analysis over time of a certain part of the signal & care is needed in interpretation of this analysis. Again going back to the long exposure photo - we would perceive a moving light as clearly & brightly as a stationery light but on the photo the stationery light would be very bright point source whereas the moving light would be very dim (if even visible) & spread across the pathway of its travel.
Given that people who claim to have exceptional auditory acuity struggle to hear the effects on "complex" analogue sources, it stretches credibility that the effects on the equivalent digital source should be audible at those vanishingly lower levels. Which is why I am waiting for the equivalent of "pictures, or it didn't happen."
I believe you are coming at it from the perspective of looking at a long term exposure photo & basing your logic on that - which isn't the reality, it's just a particular analysis

There appears to be some belief that the effect of phase noise on a complex signal is different than the effect on a single sine wave.
No, there's a perceptual difference which is what we are ultimately interested in.
Assuming that the oscillator isn't itself affected by the signal, the effect will be the same. The output will still be the signal modulated by the phase noise. It's simple mathematics. It's just a lot harder to quantify it, which is why simpler signals are used for the purpose.
As I said, it's how auditory perception is not just an extrapolation from simple tone analysis - again, I believe you are coming at it from the wrong perspective.
 

jkeny

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.....
The usual definition is that "close-in phase noise" means frequencies between 1 to 100 Hz or so. So the sample to sample variations must extend over a long enough time to generate such frequencies. In other words, the clock frequency must be varying slowly, equivalent to "wow" in analogue terms. The "micro sample-to-sample" variations you gave examples of equate to high frequencies.
Let me deal with this in more detail - I believe you have the wrong idea of what clock phase noise actually means & that might be why you don't seem to understand what I'm posting. It's why, in the other closed thread, I gave the more understandable way of looking at jitter - a TIE analysis or Time Interval Error.

Clock phase noise of 1Hz doesn't mean that "sample to sample variations must extend over a long enough time" (i.e one second) before a timing error will occur - this 1Hz is an offset from the carrier frequency - it means that clock slips by 1Hz away from it's 'correct frequency' (being the carrier frequency) & on a clock phase noise plot what you see is a representation of how often the clock ticks will be 1Hz away from their correct frequency - the Y-axis is the dB measure of this. This is timing errors being expressed in frequency terms.

Looking at it directly in timing diagrams makes it far easier to understand it's a time error issue & not a frequency error (as you seem to imply)
This document might be useful
http://literature.cdn.keysight.com/litweb/pdf/5991-4000EN.pdf
 

Don Hills

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... Spectral modulation thresholds or spectral ripple thresholds have been shown to be most sensitive at 2-5Hz modulation frequency. Both of these perceptual characteristics directly contradict your presumption that only masking can happen with complex music-like signals. Empirical evidence shows that this statement is not true so therefore there is some different mechanism at operation in digital audio. ...

The inability to hear, in complex music, the effects that are so clear when listening to a steady signal are not only due to masking. If they were, they'd be masked by the signal itself. The reason for the inability should be clear if, as you said, you "apply psychoacoustics & understand auditory perception". The clue, for those who aren't experts in the field, lies in the observation that the longer you listen to the steady signal, the more variation you hear. Music, with its complex spectrum and transients, doesn't give your auditory system the time to make that analysis.

Can I ask you that rather than making bald statements as if they are fact, can you show the derivation of your claim please? I don't accept claims without at least some demonstrable derivation backing them up, as I have done.

After you, my dear Alphonse. You're the one making the extraordinary claims. Note also that I'm not aiming to convince you, but just point out the flaws in your arguments and let the audience decide.

I'm not sure you understood what I meant by "micro" - I was drawing attention to the difference between how speed fluctuations in analogue are at the "macro" level (they are not happening down at samples - there's no such thing as 'sample' in analogue) in comparison to the speed fluctuations that are happening in digital audio at the "micro" sample-to-sample level. ...

You say that there's something fundamentally different between jitter in analogue and jitter in "digital" audio. Granted, the physical causing mechanisms are different. But digital sample-to-sample timing variations (phase noise) result in the same sidebands in the audio as the moment-to-moment timing variations in the turntable system. The math is the same. Only the magnitude is different - in any competent DAC, the jitter-generated effects are some 100 dB lower than those from the turntable. Given that people struggle to hear the effects in music played on a good turntable, and even allowing for your assertion that the effect of "digital jitter" on music is different and somehow more audible than the effect of "analogue jitter", it strains credulity to believe that signals quieter than the sound of air molecules hitting the eardrum in an anechoic chamber can have an audible effect on the perceived audio at regular listening levels. It's an extraordinary claim, for which you need to provide extraordinary proof.
 

Don Hills

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... Clock phase noise of 1Hz doesn't mean that "sample to sample variations must extend over a long enough time" (i.e one second) before a timing error will occur - this 1Hz is an offset from the carrier frequency - it means that clock slips by 1Hz away from it's 'correct frequency' (being the carrier frequency) & on a clock phase noise plot what you see is a representation of how often the clock ticks will be 1Hz away from their correct frequency - the Y-axis is the dB measure of this. This is timing errors being expressed in frequency terms.

Looking at it directly in timing diagrams makes it far easier to understand it's a time error issue & not a frequency error (as you seem to imply) ...

You were doing so well, then you contradicted yourself in the last sentence. As you said in the first paragraph, the variation can be represented in either the time or frequency domain, whichever is more convenient for what you are trying to do. It's both a timing error and a frequency error.
 

jkeny

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The inability to hear, in complex music, the effects that are so clear when listening to a steady signal are not only due to masking. If they were, they'd be masked by the signal itself. The reason for the inability should be clear if, as you said, you "apply psychoacoustics & understand auditory perception". The clue, for those who aren't experts in the field, lies in the observation that the longer you listen to the steady signal, the more variation you hear. Music, with its complex spectrum and transients, doesn't give your auditory system the time to make that analysis.

After you, my dear Alphonse. You're the one making the extraordinary claims. Note also that I'm not aiming to convince you, but just point out the flaws in your arguments and let the audience decide.
Making a statement as if it is a fact is not pointing out flaws in my argument - you are not dealing with my reasoned argument at all, just simply saying, "no, it's not". If you want to "let the audience decide" then make some reasoned argument to your claim "The point was that the underlying mechanisms may be different, but the audible (and measurable) results are the same." The question I am asking (maybe the audience is too) is by what process/logic do you claim this?

You say that there's something fundamentally different between jitter in analogue and jitter in "digital" audio.
Well first off there's no such thing as "jitter" in analogue - jitter has a particular definition which only applies to clocked, sampled systems. What I'm saying is that confusing wow & flutter in analogue with jitter in digital audio is a complete misunderstanding.
Granted, the physical causing mechanisms are different. But digital sample-to-sample timing variations (phase noise) result in the same sidebands in the audio as the moment-to-moment timing variations in the turntable system. The math is the same. Only the magnitude is different
You must not have understood what I posted before - speed variations in TT platters cause the full frequency spectrum to be shifted by the timing variation at a particular point in time. So let me ask you this does a sample timing error (caused by clock jitter) cause that only sample to be mistimed or the full frequency spectrum to be mistimed & shifted? See the difference?
in any competent DAC, the jitter-generated effects are some 100 dB lower than those from the turntable. Given that people struggle to hear the effects in music played on a good turntable, and even allowing for your assertion that the effect of "digital jitter" on music is different and somehow more audible than the effect of "analogue jitter", it strains credulity to believe that signals quieter than the sound of air molecules hitting the eardrum in an anechoic chamber can have an audible effect on the perceived audio at regular listening levels. It's an extraordinary claim, for which you need to provide extraordinary proof.
Ah, I see - you are attempting to "let the reader decide" by using such sciencey terms as "air molecules hitting the eardrums" "anechoic chamber". I believe the phrase you used "strains credulity" should actually read "strains MY credulity" - I'm would not be so sure that your credulity can be projected onto others.

So let me repeat again, if you want to engage in some analysis of my reasoned arguments then I'm interested. If instead you want to make statements as facts without any supporting logic or reasoning &/or if you just want to engage in a debating contest where all the subtle tricks of trying to sway an audience are used, then I'm not interested.

I'll leave something for you to explain to the audience: How the "micro" sample-to-sample variations of a clock at (for example) 96 KHz add up to generate jitter sidebands in the 2 to 5 Hz range you mentioned above.
First off, what has the clock frequency to do with this?
If there's a widened skirt around the base of a J-test FFT it signifies close-in phase noise, right?
The resolution of most such FFTs is not sufficiently fine enough to examine the timing errors that are 2-5Hz away from the correct clock frequency
Here's an FFT & the same FFT taken with much higher resolution




The second plot is still not really great for examining 2-5Hz away from the signal spike but let's look at 10Hz away & extrapolate
So what we see on this FFT is a particular tone being analysed. If it was reproduced as a pure tone correctly it would be seen as a thin line on the FFT at the frequency of the tone - there would be no widening of the line. This widening represents the fact that there are mistakes in the frequency reproduction of this tone. So this skirt is showing what the energy of the tone is at various frequency offsets away from the pure tone - the closer in to the correct frequency, the higher the energy. In other words if we look at the energy at 10Hz offset from the tone (& remember this is 10Hz above or below the correct frequency) by eyeballing it's about -100dB down but the slope of this skirt is rising logarithmically as we get closer to the correct frequency (every 3dB is a doubling in sound intensity). My contention is that the energy 2Hz away from the signal spike would be very much higher - I would hazard <-50dB down from the main signal energy. And what if we get even closer, say 1Hz away - even higher energy> so what does this mean? It means that we have a much higher number of times that the signal is being produced at 1Khz +/- 2Hz & as this offset moves closer to the pure tone frequency the number of occurrences of incorrect frequency tones is increased. So the tone is fluctuating - it's not a pure tone that is being reproduced/replayed

Now here's where care has to be taken in looking at FFTs - as I said before FFTS are not the signal we hear, they are an analysis that we have to be careful interpreting. When we see an FFT plot that shows at 10Hz offset from the signal that the 'energy' is down at -100dB does this mean that if we could isolate this particular waveform at 1010Hz it would be -100dB down form the signal waveform? No, it would not show that - it would show that it was at exactly the same amplitude as the main signal. If it wasn't the jitter would have to be changing the lower bits of the sample to reduce the volume. So we have a 1010Hz waveform being produced every so often instead of a 1000Hz waveform. How often this is occurring (the statistical average) is given by the FFT y-axis - which is in dBs. Does this mean that we can't have a number of waveforms in a row that are all at 1010Hz? No, there could be such a situation - FFT is showing an averaging analysis of occurrences

Do these dBs translate directly to what loudness level we perceive a signal to be? No! Our ears use different filter bands called critical bands or ERBs. For pure tones, the FFT dB readout is close enough but as we broaden a tone it may not be an accurate dB readout anymore. These cochlear filters do not map to the FFT filters & overlap, unlike the FFT filters (bins). So for instance, if the energy of a broadened signal (such as we have here) falls into one critical band, it will be sensed as a single tone with higher amplitude than if it fell between two critical filters.

So the point is could we hear a tone (doesn't matter what frequency) fluctuating at 2Hz-5Hz fluctuations in the above scenario? I suggest my above analysis says it's possible.
 

jkeny

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You were doing so well, then you contradicted yourself in the last sentence. As you said in the first paragraph, the variation can be represented in either the time or frequency domain, whichever is more convenient for what you are trying to do. It's both a timing error and a frequency error.

If you read what I said carefully you would see that your correction is a strawman correction - it's just a tactic to deflection away from my pointing out your misunderstanding in the paragraph above it namely "equivalent to "wow" in analogue terms." & "The "micro sample-to-sample" variations you gave examples of equate to high frequencies." both of which show a distinct misunderstanding which you are deflecting from.
 

amirm

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Well first off there's no such thing as "jitter" in analogue - jitter has a particular definition which only applies to clocked, sampled systems.
There is such a concept in analog. We have a reference (stated speed) and variations from that are jitter just like variations from clock in digital systems. Here is a 1968 patent from RCA on a low-jitter drive for tape decks as an example: https://www.google.com/patents/US3387758

"When recording on tape and when playing back a recording, the recording tape should be driven at a constant speed past the recording and playback heads. Any variation in this speed is referred to as jitter. If recording tape is pulled or driven by a capstan that is in contact with the tape, as in conventional practice, the tape will stretch varying amounts and a proportional jitter will result in the tape. The jitter may not be enough to make it objectionable or even noticeable in some applications, but in other applications the jitter must be much less to be acceptable, as, for example, in the case of frequency spectrum analysis of signals."

It is just that in analog system the variation in speed is so large, and so audible that we describe them using their sounds: "Wow and Flutter." As Don has eloquently explained, the modulation effect is identical to digital systems. The moment you vary speed, you are FM modulating it and the math is the same and has no dependence on a system being digital in origin to matter. After all, the jitter itself is an analog concept, not digital!
 

Robh3606

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My contention is that the energy 2Hz away from the signal spike would be very much higher - I would hazard <-50dB down from the main signal energy. And what if we get even closer, say 1Hz away - even higher energy> so what does this mean? It means that we have a much higher number of times that the signal is being produced at 1Khz +/- 2Hz & as this offset moves closer to the pure tone frequency the number of occurrences of incorrect frequency tones is increased. So the tone is fluctuating - it's not a pure tone that is being reproduced/replayed

No that is not how it works with phase noise. You should not be using an FFT to look at this. You should be looking at this on a spectrum analyzer using a 1Hz bandwidth. This is an actual measurement using the correct equipment of an oscillators phase noise levels starting at 1hz away in 1 hz bandwidth. You do not have an ultra steep rise like you are predicting.

Rob:)
 

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jkeny

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There is such a concept in analog. We have a reference (stated speed) and variations from that are jitter just like variations from clock in digital systems. Here is a 1968 patent from RCA on a low-jitter drive for tape decks as an example: https://www.google.com/patents/US3387758

"When recording on tape and when playing back a recording, the recording tape should be driven at a constant speed past the recording and playback heads. Any variation in this speed is referred to as jitter. If recording tape is pulled or driven by a capstan that is in contact with the tape, as in conventional practice, the tape will stretch varying amounts and a proportional jitter will result in the tape. The jitter may not be enough to make it objectionable or even noticeable in some applications, but in other applications the jitter must be much less to be acceptable, as, for example, in the case of frequency spectrum analysis of signals."
Right, that's fair enough.

It is just that in analog system the variation in speed is so large, and so audible that we describe them using their sounds: "Wow and Flutter." As Don has eloquently explained, the modulation effect is identical to digital systems. The moment you vary speed, you are FM modulating it and the math is the same and has no dependence on a system being digital in origin to matter. After all, the jitter itself is an analog concept, not digital!

Sure it's FM modulation as I said before but I see & have spelled out what I see as a distinct difference between the speed variations in analogue that happen at a 'macro' level in that all frequencies are affected by a speed variation (all frequencies are modulated by the speed variation) & this rises slowly & falls back slowly (in comparison to the digital scenario) & the 'micro' level timing differences that happen in digital audio reproduction where a sample is affected by a clock timing error but the next sample's error can be any random timing - it is not part of a wave of speed fluctuation - the frequency modulation is not the same

So in these scenarios I see a fundamental difference to how the timing errors are expressed through the playback mechanism

I don't therefore agree that the modulation effect is identical - I have shown why it is both quantitatively & qualitatively different. I can't see anything which has addressed my analysis which contradicts this.
 
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jkeny

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No that is not how it works with phase noise. You should not be using an FFT to look at this. You should be looking at this on a spectrum analyzer using a 1Hz bandwidth. This is an actual measurement using the correct equipment of an oscillators phase noise levels starting at 1hz away in 1 hz bandwidth. You do not have an ultra steep rise like you are predicting.

Rob:)

Can you give some more detail of what & how this was measured - it's not easy to judge what's being shown?

When we look at an J-test FFT we see a skirt at the bottom of the signal spike - this is what I was referring to in the your quote of me so I'm not sure why or what you are saying "this is not how it works with phase noise"?
 

amirm

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Sure it's FM modulation as I said before but I see & have spelled out what I see as a distinct difference between the speed variations in analogue that happen at a 'macro' level in that all frequencies are affected by a speed variation & this rises slowly & falls back slowly (in comparison to the digital scenario) - a wave of speed variation & the 'micro' level timing differences that happen in digital audio reproduction where a sample is affected by a clock timing error but the next sample's error can be any random timing - it is not part of a wave of speed fluctuation.

So in these scenarios I see a fundamental difference to how the timing errors are expressed through the playback mechanism

I don't therefore agree that the modulation effect is identical - I have shown why it is both quantitatively & qualitatively different. I can't see anything which has addressed my analysis which contradicts this.
Due to Central Limit Theorem, the pdf for both will approximate a gaussian/poisson curve since the underlying mechanism below them are random (putting aside the deterministic ones). So we know at statistic level what the distribution is.

What is different is that the levels of jitter are so low in digital that the bessel coefficients beyond the first pair are essentially zero. For this reason it degenerates into AM modulation. In analog the levels are too high to ignore the other coefficients and you have to follow the full FM modulation.

Furthermore, due to the much higher level and fluctuations within, temporal masking comes into play in analog that doesn't apply in digital. This is where the 4Hz peak sensitivity comes from.
 

jkeny

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Due to Central Limit Theorem, the pdf for both will approximate a gaussian/poisson curve since the underlying mechanism below them are random (putting aside the deterministic ones). So we know at statistic level what the distribution is.
Yes, I already said that the statistical distribution seen in an FFT can be the same but the underlying mechanisms different - this is the problem with relying on FFT analysis - it doesn't adequately represent how we perceive a dynamically changing signal such as music

What is different is that the levels of jitter are so low in digital that the bessel coefficients beyond the first pair are essentially zero. For this reason it degenerates into AM modulation. In analog the levels are too high to ignore the other coefficients and you have to follow the full FM modulation.

Furthermore, due to the much higher level and fluctuations within, temporal masking comes into play in analog that doesn't apply in digital. This is where the 4Hz peak sensitivity comes from.
As I said dealing with statistical averaging of a signal doesn't tell us much about our perception of that signal.
What I would be more interested in would be any objections with the two scenarios I posted re analogue wow & flutter Vs digital jitter.
 

Robh3606

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Hello Jkeny

So this skirt is showing what the energy of the tone is at various frequency offsets away from the pure tone - the closer in to the correct frequency, the higher the energy. In other words if we look at the energy at 10Hz offset from the tone (& remember this is 10Hz above or below the correct frequency) by eyeballing it's about -100dB down but the slope of this skirt is rising logarithmically as we get closer to the correct frequency (every 3dB is a doubling in sound intensity). My contention is that the energy 2Hz away from the signal spike would be very much higher - I would hazard <-50dB down from the main signal energy.

What is plotted is phase noise of an oscillator using a spectrum analyzer. Unless I am misunderstanding you, the skirt you are talking about on the FFT Plot, you are attributing the noise as a direct result of the phase noise of the clock oscillator. What I have posted is a phase noise plot of a low noise oscillator. Even if you look at an oscillator with a higher noise floor the curve is the same. So close in you do see a rise in spectral power density but not anyway near as much as you were saying with your 50db Vs. 100db statement above. You don’t get a super steep increase from 10-1Hz It increases for sure but at a lower rate about 9db per octave.

Rob:)
 

jkeny

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Hello Jkeny



What is plotted is phase noise of an oscillator using a spectrum analyzer. Unless I am misunderstanding you, the skirt you are talking about on the FFT Plot, you are attributing the noise as a direct result of the phase noise of the clock oscillator. What I have posted is a phase noise plot of a low noise oscillator. Even if you look at an oscillator with a higher noise floor the curve is the same. So close in you do see a rise in spectral power density but not anyway near as much as you were saying with your 50db Vs. 100db statement above. You don’t get a super steep increase from 10-1Hz It increases for sure but at a lower rate about 9db per octave.

Rob:)

Would like to know what oscillator that is as it is exemplary for close in phase noise but I see PS anomalies at 6/120/180Hz & wonder how you can possibly produce such a plot with a PS intrusion such as this - something badly amiss with your plot - can you name the oscillator & do you have an Allan Variance plot for it?

Rob, it's not just me that attributes the skirt at the bottom of a J-test FFT signal spike to be the result of close-in phase noise - everyone recognises this as fact.
As i showed in that higher resolution FFT that skirt does rise very steeply as the plot approaches the signal spike
Don't know what more I can say about that as there are not many such high resolution FFTs
 
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amirm

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Even though there is substantial confusion shown in the above notations on the graph, I will not even deal with these but try to deal with the core of what's being stated
Here's one possible answer:

- wander & drift in analogue is fundamentally different to the same terms used when talking about jitter. In analogue wander/drift is the shifting of all frequencies by a set value caused by many things which effect the rotational speed of the platter, for instance. The important point about this type of drift/wander is that it affects the whole audio spectrum equally - all frequencies drift/wander in the same direction & by the same amount. It's a macro effect & at macro timings. Because this is a macro phenomena & not a sample by sample determination (it's analogue) this wander gradual, not instantaneous - it doesn't shift timing suddenly in one direction & stop suddenly or reverse direction suddenly - see jitter wander below. So a change in speed happens over an extended period of time

- wander & drift when talking about jitter is a completely different & more complex phenomena. A clock that wanders causes spectral impurity in the reproduced tones - in other words the frequencies fluctuate. But this fluctuation is caused by each sample being off by whatever the mistiming of the clock is when the sample is being converted to an analogue value. The next sample will have another random amount of mistiming in plus or minus direction so we end up with a series of samples all converted with mistimings which make up the waveform. The result is a slightly (hopefully) skewed waveform than what it should be. The point is that this clock mistiming is happening at the micro level of each sample conversion & it's a function of the mistiming of the clock at this conversion point. This mistiming is not a macro trend, as in the analogue playback where the whole waveform is shifted by the slowing down or speeding up of the platter from its ideal speed - this mistiming is a micro trend which can go plus for one sample & negative for the next sample. This is what's happening at the micro level. So when all the samples of a waveform have been converted to analogue with a clock which suffers wander/drift, we end up with a reconstructed waveform which is skewed in both amplitude & frequency (or phase). This skew in frequency is the spectral impurity that clock wander causes - it's nothing like the speed drift that analogue suffers from.

OK, I will briefly address this. You are painting an imaginary scenario with an arbitrary difference built into it. There is no justification for either one. The analog one for example could also have "sudden" jumps due to bearing of a platter. Or snaps of the rubber belt. The digital one also has slew limiting and won't all of a sudden jump from one value to another value that is too large. On and on.

But we don't care about any of this detail as we can measure the two systems and compare them. And such a measurement shows that both systems have random modulation of their speed in a similar manner at low frequencies. This is backed by my last post explaining that CLT will give us similar distribution when the contributions are many and random in nature.

The measurements show that the levels of the same distortion in analog is orders of magnitude higher than digital. There is nothing that makes that "more nice" than the same distortion type in digital. Here is another paired comparison using different instrumentation. First is a turntable measured by HiFi News:



And now one of the worst performing digital measurements I have:



We see similar widening of the main tone in both systems. The measurements are ultra sensitive showing lots of detail in the case of digital system. That aside, the digital system jitter is measured at 12,000 Hz versus 3.15 used for analog. Compensating for that, the skirts around the digital system would further collapse in level making it far, far, far cleaner than analog. To the extent there are no complains in that analog system (and psychoacoustics backs that), then there simply is no audible problem here.

If you want to counter any of this, you need to show measurements that capture those differences. What you describe would absolutely show up in objective measurements.
 

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