Debate of DAC design regarding DSD vs PCM among 5 VIPs

[mmerrill99]

On 4/28/2017 at 10:03 AM, Miska said:

 

There is no "good jitter". But random (uncorrelated) jitter is usually less audible than non-random (correlated) jitter. I picked up some examples...

 

This could be considered to be less bad "good" jitter:

 

And this could be considered to be more bad "bad" jitter:

 

You can see the first one has widening base of the main lobe, while the second one has narrower main lobe, but strong distinct side lobes.

Something that I hope might be answerable here - how to interpret the top FFT plot. I know it represents close-in phase noise, in other words the 1KHz signal is not always reproduced accurately at 1KHz because of this fluctuation of the clock frequency - its phase noise.

 

Looking at that plot in full size, the skirt spans about 500Hz either side of the 11KHz test signal. What this means is that a small amount of the time the signal is wrong by +/- 500Hz & as we move closer to the 11KHz signal the skirt increases in amplitude i.e. the signal is wrong more often as we get closer to the test signal frequency. So if we read this FFT plot as showing amplitude of the error signal either side of the 11KHz would seem to be mistaken. Do people agree with this?

 

Let's say we zoomed into around this 11KHz signal to a much more resolved FFT plot which showed 1Hz divisions on  the x-axis - we would see that the skirt @1Hz either side of the 11KHz was close in amplitude to the test signal. Which I interpret as the signal is wrong by 1Hz quiet often.

 

The point is that the skirts should not be read as down in amplitude @ -160dB growing to -90dB (test signal amplitude, in this case) - the frequency errors are at -90dB but at varying times - it's a statistical plot of how often the errors occur. But the same would apply if the test signal was -3dB - errors in frequency would have an amplitude of -3dB, not -150dB or whatever

 

If this analysis is correct, it's perceptually far different to have an frequency error of the signal at the same amplitude  rather than a frequency error -150dB down in amplitude.

 

Again, if my analysis is correct, the top FFT plot would certainly not represent "good" jitter or even "less bad" jitter - it could be perceptually very significant, blurring sound somewhat I would guess.   

[mmerrill99]

24 minutes ago, jabbr said:

 

As you note, these are frequency rather than phase plots, and with linear, rather than log, scale along frequency(?). I'd say that phase error is better than outright distortion -- so clearly "less bad"  ...but ... hard to predict what the actual @1Hz offset error would be ... but let's say @10Hz is -60 db/Hz ... not the best achievable, so perhaps that's why this plot is selected, to demonstrate the error. As @Miska alludes to, the clock phase error is the best, but once it is distributed into the circuit itself, the numbers get worse. These numbers are never published and who knows how often they are actually measured.

 

The errors seen on the bottom plot might be due to more basic electronics issues such as crosstalk, setup timing errors, duty cycle asymmetries in computed clocks etc etc. You know a violin that is a bit blurred is better than a chainsaw  

But remember as regards to perception, we are hearing modulating phase shifts, not fixed phase shifts & also remember that non-linear systems (all our playback systems) will produce intermodulation distortions as a result of the phase differences & these will also be modulating.

 

I have perceived a more stable, solid soundstage as a result of using a lower jitter clock

[mmerrill99]

1 hour ago, jabbr said:

 

As you note, these are frequency rather than phase plots, and with linear, rather than log, scale along frequency(?). I'd say that phase error is better than outright distortion -- so clearly "less bad"  ...but ... hard to predict what the actual @1Hz offset error would be ... but let's say @10Hz is -60 db/Hz ... not the best achievable, so perhaps that's why this plot is selected, to demonstrate the error. As @Miska alludes to, the clock phase error is the best, but once it is distributed into the circuit itself, the numbers get worse. These numbers are never published and who knows how often they are actually measured.

 

The errors seen on the bottom plot might be due to more basic electronics issues such as crosstalk, setup timing errors, duty cycle asymmetries in computed clocks etc etc. You know a violin that is a bit blurred is better than a chainsaw  

What is meant by -60dB/Hz?

I'm suggesting that the amplitude of the error due to a clock drifting around it's fundamental frequency (phase noise) will be the same signal amplitude but reproduced at a frequency slightly different to the correct frequency.

 

So if the original signal is @-6dB then these errors in frequency will also be @-6dB. Why would they be reduced in amplitude? 

 

FFTs are not intuitive (i.e. misleading) when plotting at anything other than narrow band signals

 

Just another point - IMO, this is also correlated jitter as Jabbr has said - I believe it tracks the signal i.e only 'blurring' the frequencies in the signal, not producing noise which is unrelated to the signal! 

[mmerrill99]

BTW, as regards audibility of phase - it seems to be related to cochlea non-linearities - if two frequencies are in different critical bands then intermodulation products will not occur, however if they are in the same critical bands the cochlea will generate intermodulation products.

 

Edit: The critical band is an old concept that defines the frequency bands that the cochlea auditory filter splits the incoming signal into. The more modern & slightly different frequency ranges is called the ERBs

[mmerrill99]

23 minutes ago, jabbr said:

 

Typically phase error plots do not show frequency per se, rather frequency offset from the signal, and might be log, so 10^-3,10^-2,10^-1,1,10,10^2 on x-axis plotted against dB on y-axis.

 

so -60dB @1Hz means that the phase error component 1 Hz to either side of the carrier is diminished by 60dB

Ok, let's take it from first principles. We have two clock ticks one is at the exact correct frequency, 12MHz say & the next one is at 1Hz over 12MHz. Let's say this is the audio clock driving a DAC & the DAC is reproducing a pure tone of 11KHz. For simplicity let's not get into the shape of the sine wave & what part of this sine wave is being reproduced but rather that both digital samples should have produced a 11KHz signal at -3dB. The first sample does but the next sample (which is using the clock tick which has slipped by 1Hz) is producing the same amplitude signal but at the wrong time i.e it has shifted the frequency by 1Hz

 

My question is why would the amplitude be diminished? The frequency is wrong but I can't see how the amplitude is affected?

 

I know this skips lots of details & keeps it simplistic, in order to state my issue - maybe the answer is in the details that I'm not seeing?

[mmerrill99]

29 minutes ago, jabbr said:

The "correlation" of a phase error that rises as it gets closer to the carrier is correlated to the carrier -- this describes "slope". An uncorrelated error is flat regardless of distance from carrier i.e. slope is 0.

But again, this is what I have a problem with - FFTs do not show the correct amplitude of broadband signals - there's a certain process gain needed to calculate the correct amplitude of the broadband signal as it ranges across that 1KHz frequency range that the skirt encompasses.

 

I look on that FFT plot as a statistical representation of how many erroneous samples fall into (how much power is analysed)  the bins 1Hz away from the main signal;, 1.1Hz away, 1,2Hz away, etc. The further away from the fundamental signal the erroneous samples, the fewer the samples. The amplitude of each sample is the same BUT the power found in each bin diminishes towards the noise floor the further away from  the fundamental is plotted.

 

Essentially FFTS are like long exposure photography - if an object stays still  during the exposure, it will be reproduced sharply & brightly with fine detail - if an object moves during exposure its brightness will be diminished & it will be a blurry image (the equivalent of jitter). BUT the image that is captured is not a true representation of the brightness of these objects - their apparent brightness (the equivalent of amplitude) is simply due to the sampling happening during exposure  

[mmerrill99]

13 minutes ago, jabbr said:

 

Perhaps this can be considered like "conservation of energy" such that the SPL or energy is preserved, i.e. area under curve, so that when a peak is widened it loses peak amplitude -- holding energy constant ... otherwise a change in energy would be measured i.e. very accurate clocks would draw less power ... don't think that's the case.

 

Does that help? Remember that the FFT usually only shows the "real" or amplitude component, and being laplacian, there is the imaginary component. That's why its vector math, not simple addition/subtraction.

Sorry but this doesn't make sense to me - you are talking about how an FFT represents narrow Vs broadband signals - I'm saying that the representation is misleading to an understanding of what is actually happening with close in phase noise of audio clocks & its affect on signals.

[mmerrill99]

31 minutes ago, jabbr said:

If we are discussing the effect of phase error in a clock (12 Mhz example) on the reproduction of an 11 kHz tone, consider that the DSD DAC is integrating the pulse widths to product an analog signal and the pulse width variation is integrated

I didn't want to get into complexity & different variations of PWM Vs PCM - just wanted to keep it simple

31 minutes ago, jabbr said:

a PCM DAC will similarly use a series of multibit values that will change with the clock. Using vector math, a change in the voltage representing a signal will have a component change to both the amplitude and phase of the underlying signal (at each frequency component).

Sorry but you are losing me - I can't see how this integration can explain a reduction in amplitude to the extent that we see in the FFT plot here - maybe I'm being stupid? 

[mmerrill99]

deleted

[mmerrill99]

12 minutes ago, Daudio said:

 

Could it be that that FFT is representing the density of phase errors ? Such that they are most dense close to the target frequency (smaller deviations). and less dense as the error increasingly deviates from the norm, but occurring less often, thus the shape of the envelope. All of this occurring outside of any consideration of the consistent amplitude of the signal that contains clock jitter.

 

Sorry to interrupt this interesting dialogue, but that just popped into my head as I was reading, so what the hell...

 

Yes, that's my thinking on it & what I'm trying to convey

As I said I look on that  FFT plot as a statistical representation of the phase errors - close in their occurrence is high, further out their occurrence is low

 

What I was trying to point up is what I often see as a misinterpretation of this type of plot, interpreting the low dB scale as representative of the actual amplitude of the error signals 

 

As I was saying - FFTs are like long exposure photographs - in this sort of photo a stationary car's headlights will be far brighter than a moving car's headlights - in real world they will both be equal brightness

[mmerrill99]

11 hours ago, jabbr said:

No, I'm not sure that the goal has been to represent amplitude per se. An FTT does have an amplitude component, but we have been focusing on phase. Assuming amplitude is constant with time, the idea of "bins" being filled is a way to look at it (hesitating only because I haven't entirely thought this through...)

 

What do you mean by "reduction in amplitude"? I very well might be assuming the wrong thing.

What I mean is that we look at a spike on an FFT  & read off the amplitude of that signal from the dBs on the Y-axis - so a signal is -3dB , -6dB, -90dB down from 0dB - this gives us the amplitude of the signal & would match an SPL reading taken in-room.

 

Other parts of an FFT, like the 'grass' at the bottom from which the spikes protrude, are often mistakenly read as the 'SPLlevel' of the "noise floor". As we know this is incorrect & to get the true noise floor level we need to calculate the process gain of the FFT & add this to the plotted level of the 'grass'

 

My point is that the skirt we see around the base of a signal spike, which in this case is dues to jitter from phase noise, is also not to be read directly off the FFT plot as-is but needs some different interpretation & I haven't seen anyone address this before to come up with the way to interpret signal skirts in an FFT.

 

I think the natural instinct is to view these skirts as down at -160dB -150dB, rising to meet the signal spike at  some dB level. What is the correct interpretation of this skirt? This isn't easy to discuss as most jitter FFTs use a x-axis HX scale which is too wide a range to see the detail of what's in close to the 11KHz jitter signal. The reason for this wide range is that they are examining the overlaid frequencies in the jitter test signal usually seen as spikes further away from the 11KHz main signal.

 

Here's something that illustrates - the first plot is two overlaid FFTs  (one black, one  red) of a jitter test signal - the black one is the result of using a clock with lower close-in phase compared to the red one. So looking at this plot, not much difference between them, right?

The x-axis in this case is the Hz offset from the signal spike.

 

So when the blue box is zoomed into, we see a difference which wasn't evident before

 

In this graph the x-axis is a much finer division - we are seeing 100Hz either side of the signal spike. From about 40Hz out we see the rise of the red skirt & it meets the signal spike up around -90dB (this is probably about 2Hz away from the signal?). Now if we zoomed in closer we could see the differences closer to the test signal - maybe in at 0.1Hz away from the spike - we would probably see it merging with the spike very much higher on the y-axis maybe higher than -20dB just based on eyeballing that slope.

 

That's one point about why Miska's FFT plot initially shown & annotated as "less bad 'good' jitter" may not be fully accurate.

 

My other point is that I find it less than intuitive trying to interpret what this skirt actually signifies. Looking at the zoomed in FFT plot above, to me, it doesn't signify that the error signal 20Hz away from the main signal is down @ -120dB & therefore of little concern to perception. This is my main focus - what is the perceptual effect of such error signals? Maybe I'm wrong in my thinking.

 

Allow me to talk through this & maybe at the end of this I'll have changed my thinking?

 

To my mind an FFT plots the energy in the bins into which the full signal is divided. So for a a narrow band signal which falls in few bins, the energy plotted is close to the actual SPL that would be measured on playback & therefore has perceptual significance. But for wideband signal such as noise, it's power does not fall into a small number of bins, it is spread across a wide number of bins. So, in this case, the FFT is showing the energy in each of the bins across the full frequency spectrum anlayzed. This will necessarily be plotted lower than the actual SPL which would be measured in room, on playback - so perceptually the effect will be greater than what is read as the dB level read directly from y-axis. We know how to compensate for this discrepancy - by calculating the FFT process gain & adding this to the y-axis level readout.

 

Now what way to treat FFT plots of signals which aren't narrow band & not full spectrum wide-band but wideish-band? How to translate from FFT dB level to actual dB level for these signals? In other words how can we correct it to better represent it's perceptual effect (just talking about amplitude here)

 

Let's not forget that FFTs are just a signal analysis which are at times useful to represent aspects of the signal but can also mislead & confuse in other areas aspects. They are NOT the signal itself & therefore we have to be careful of how to interpret the plots.