Watts Up...?

[Crgreen]

Look forward to listening to those files. I understand the Bridgewater Hall, a wonderful acoustic, has very good recording facilities

 

[PANURUS]

Post deleted because I have found my information.
 
 

 

[Peter Hyatt]

The million dollar question in a headphone forum... What's Rob's favourite headphone?

Rob when you travel with Dave in hotel use, do you have a portable speaker you enjoy for non critical but casual listening. Thanks.

 

[Rob Watts]

Yes but it's nothing special, just active computer speakers. Actually, I am looking to buy some portable passive loudspeakers with Dave driving them directly. For serious listening I use the AQ Nighthawks....
 
Rob

 

[maxh22]

  Yes but it's nothing special, just active computer speakers. Actually, I am looking to buy some portable passive loudspeakers with Dave driving them directly. For serious listening I use the AQ Nighthawks....
 
Rob

Which active computer speakers do you use?

 

[JaZZ]

  ...But to answer your question why transient timing improves with tap length I can illustrate the two extremes; a tap length of 1 tap (a NOS filter followed by analogue filtering) and an infinite tap length filter. Here is a couple of slides from my Mojo presentation:
 


 
Now this is just a simple illustration and it shows the two extremes one tap filter giving worst case 100uS or so timing error; and an infinite tap length filter reconstructing the transient perfectly. Somewhere in-between we will get acceptable levels of timing errors - but the only way we can test for this is to build long tap length filters, and change the parameters - tap length, oversampling rate, and algorithm - then keep listening - and that's what I have been doing for the past 20 years.
 
But what is really cool is that with Davina we can actually know for certain what the subjective losses are with 1M tap length filters. Ideally, the most powerful listening test is one where you can hear no difference from say 768>decimate 48>interpolate 768, and Davina will tell me how much difference we get in absolute terms. I will be publishing files - the original, and the decimated/interpolated version. In case the bandwidth limiting changes the sound (it will probably make it sound better) then I actually have three files - original, bandwidth limited, bandwidth limited/decimated/interpolated.
 
Sampling theory has nothing to say about bandwidth limiting - only that at FS/2 and greater it must be 0 output. I have already designed 300 db bandwidth limiting filters, so it will be very curious to see how these actually sound.
 
In 2013 a paper was filed in a physics journal, and this talks about the Fourier uncertainty, and the importance of timing. On this website, they have some samples where the signal has identical frequency response, but timing information has been destroyed, so try playing some of these tracks:
 
http://phys.org/news/2013-02-human-fourier-uncertainty-principle.html
 
The original paper is very interesting to read, but is not easy to follow. Now Fourier uncertainty is the timing problem characterized mathematically. Now I have always felt that we needed to minimize Fourier uncertainty by making sure the windowing function was greater than 1 second (this requirement was from listening to other problems) - and guess what - we only get windowing functions of greater than 1s with 1M 16FS filters.
 
Rob

 
Hi Rob
 
Above illustration is a bit puzzling to me. The main reason being that a bandwidth-limited signal can't start and stop immediately – sharp transients need infinite bandwidth, since they rely on high frequencies –, so it doesn't look right, even with the 1 million taps. My idea of the million-taps benefit actually was that the transient-corrupting low-pass filter resonance is concentrated on the filter frequency for the most part, whereas frequencies below show almost no pre- and post-ringing. Or more accurately: the ringing – which is still there – contains no audible frequencies anymore. With an infinite number of taps, resulting in an infinite filter sharpness and steepness, the ringing would last infinitely. And that's what I miss in above graph, too. Or what else am I missing?

 

[ecwl]

Above illustration is a bit puzzling to me. The main reason being that a bandwidth-limited signal can't start and stop immediately – sharp transients need infinite bandwidth, since they rely on high frequencies –, so it doesn't look right, even with the 1 million taps. My idea of the million-taps benefit actually was that the transient-corrupting low-pass filter resonance is concentrated on the filter frequency for the most part, whereas frequencies below show almost no pre- and post-ringing. Or more accurately: the ringing – which is still there – contains no audible frequencies anymore. With an infinite number of taps, resulting in an infinite filter sharpness and steepness, the ringing would last infinitely. And that's what I miss in above graph, too. Or what else am I missing?

Ever since Rob Watts posted the diagram and comments, I've been thinking about it and realized how little I understood or maybe how much I misunderstood before. I used to think that sharp transient is close to an impulse response or step response. But I realized maybe I was wrong. When we here a sharp transient let's say it's a primary tone. Well, we are really hearing a sine wave at a certain frequency that starts off at a high amplitude and then decay in amplitude really quickly, say half a second. It is not an impulse response. That's why sharp transients don't need infinite bandwidth. And that's what I got from the graph. When does the note start? How high is the amplitude? And short tap lengths get the amplitude and start time wrong which leads to distortions that unfortunately we are getting more and more used to because all non-Chord DACs sound like that and most of us don't listen to unamplified non-digital music. Sure a real sound has multiple frequencies in the audible range but the principle is the same. But I'm glad JaZZ is asking the question as I'm sure Rob Watts can answer it with much more clarity as I think I understand maybe only 20% of what he is really trying to say I think.

 

[Rob Watts]

 

  ...But to answer your question why transient timing improves with tap length I can illustrate the two extremes; a tap length of 1 tap (a NOS filter followed by analogue filtering) and an infinite tap length filter. Here is a couple of slides from my Mojo presentation:
 


 
Now this is just a simple illustration and it shows the two extremes one tap filter giving worst case 100uS or so timing error; and an infinite tap length filter reconstructing the transient perfectly. Somewhere in-between we will get acceptable levels of timing errors - but the only way we can test for this is to build long tap length filters, and change the parameters - tap length, oversampling rate, and algorithm - then keep listening - and that's what I have been doing for the past 20 years.
 
But what is really cool is that with Davina we can actually know for certain what the subjective losses are with 1M tap length filters. Ideally, the most powerful listening test is one where you can hear no difference from say 768>decimate 48>interpolate 768, and Davina will tell me how much difference we get in absolute terms. I will be publishing files - the original, and the decimated/interpolated version. In case the bandwidth limiting changes the sound (it will probably make it sound better) then I actually have three files - original, bandwidth limited, bandwidth limited/decimated/interpolated.
 
Sampling theory has nothing to say about bandwidth limiting - only that at FS/2 and greater it must be 0 output. I have already designed 300 db bandwidth limiting filters, so it will be very curious to see how these actually sound.
 
In 2013 a paper was filed in a physics journal, and this talks about the Fourier uncertainty, and the importance of timing. On this website, they have some samples where the signal has identical frequency response, but timing information has been destroyed, so try playing some of these tracks:
 
http://phys.org/news/2013-02-human-fourier-uncertainty-principle.html
 
The original paper is very interesting to read, but is not easy to follow. Now Fourier uncertainty is the timing problem characterized mathematically. Now I have always felt that we needed to minimize Fourier uncertainty by making sure the windowing function was greater than 1 second (this requirement was from listening to other problems) - and guess what - we only get windowing functions of greater than 1s with 1M 16FS filters.
 
Rob

 
Hi Rob
 
Above illustration is a bit puzzling to me. The main reason being that a bandwidth-limited signal can't start and stop immediately – sharp transients need infinite bandwidth, since they rely on high frequencies –, so it doesn't look right, even with the 1 million taps. My idea of the million-taps benefit actually was that the transient-corrupting low-pass filter resonance is concentrated on the filter frequency for the most part, whereas frequencies below show almost no pre- and post-ringing. Or more accurately: the ringing – which is still there – contains no audible frequencies anymore. With an infinite number of taps, resulting in an infinite filter sharpness and steepness, the ringing would last infinitely. And that's what I miss in above graph, too. Or what else am I missing?

You are exactly right - that's why I say that it is a simple illustration and it's used to get the idea across that interpolation done perfectly would have no timing errors, but imperfectly would. What it does not show is a tone burst that is bandwidth limited, and as you correctly state, the sharp discontinuity at the start of the transient would require an infinite bandwidth input, which of course is not legal. But then using impulse responses to comment on filter performance using pure impulses is also not legal either from sampling theory POV. If I had used a bandwidth limited signal then it would get confusing, as the tone burst would have smooth curves at the start, plus pre-ringing if a linear phase signal filter is employed. Then you would not get the idea across so well. If I had shown a little curve at the start to indicate bandwidth limiting then the NOS example would have a small starting signal on reproducing it. So I decided that using a infinite bandwidth signal was the best way of easily showing the timing errors.
 
I spent many hours worrying about this issue - I decided that using a non bandwidth limited signal was OK in order to get the idea across - I could have stated that the illustration is not bandwidth limited. But remember the target audience is a typical Mojo user, and they may not actually know what bandwidth limiting actually is; so I decided to simply state that this is a simple illustration and leave it at that. The basic problem I have is that when people talk about timing errors they think about linear things like ringing etc.; I am not interested in that, but about the non-linear timing uncertainty that the interpolation filter introduces - and this seemed to me to be the easiest way of getting that idea across. The illustration is just to show how timing uncertainty comes about. 
 
Getting back to your main question - if I had used a bandwidth limited signal, then an ideal infinite sinc function filter would reproduce that bandwidth limited signal perfectly - with no added ringing at all. The interesting aspect about the theory is that it states that you must use an ideal sinc function filter to perfectly reproduce the original; that means that if you as a designer want a transparent filter that neither adds not subtracts then you must make your interpolation filter get as close to the ideal as possible - and that is simply what I have been trying to do over the past 20 years; and I will continue to do this until I can hear no change in SQ with a doubling of tap length. Every time I double the tap length, the difference between actual and ideal halves.
 
So theory is very simple - we have one and only one way to get perfection and that is unusual in audio, as often I am faced with many alternative ways of converging upon perfection. What is curious is that sampling theory has no message about the first bandwidth limiting filter before the signal is sampled - the ADC filter. Will pre-ringing be important? Will limiting to 22.05 kHz be audible? What is the best way to be able to do this? These important questions I hope to answer with the Davina project.
 
Going back to your original question too about ringing. One problem I have is that modern ADC's are spectacularly poor in the decimation process, and use filters that are half band - that is only -6dB at 22.05 kHz (it should be close to infinite attenuation and not simply halved) - and these are not ideal by any stretch of the imagination. Now the WTA filter actually accommodates for this, as it has been optimised with real recordings that employ poor decimation filters. Fortunately, the optimisation I use (based on thousands of listening tests I guess) still means that as you increase the tap length it still converges onto ideal (an infinite tap length WTA would become an ideal sinc function). Davina will be the first ADC that actually properly decimates to meet the requirements of sampling theory. So Davina will answer some fundamental questions, and that is why the possibility of comparing 768 kHz files with files that have been through the full decimation and M scaler interpolation process really excites me - we will know for sure what the SQ losses are. 
 
Rob 

 

[analogmusic]

Hi Rob, as you said " Now the WTA filter actually accommodates for this, as it has been optimised with real recordings that employ poor decimation filters"
 
How will music sound with your existing WTA filter (say on Mojo/Hugo/Dave) , if the ADC will be a DAVINA?
 
Regards
Ali

 

[Rob Watts]

That's the 64 k $ question - with timing problems removed on the decimation and interpolation side, it should sound pretty special...

 

[Doody]

  That's the 64 k $ question - with timing problems removed on the decimation and interpolation side, it should sound pretty special...

Are you saying the Davina will have a $64,000 USD price tag?
 

 
Doody

 

[Arpiben]

  That's the 64 k $ question - with timing problems removed on the decimation and interpolation side, it should sound pretty special...

 
Many years passed since I last opened my Theory Of Signal's books.
But, if I still remember well, under the asumption of a perfectly reconstructed digital signal (Bandwidth limited as per Nyquist-Shannon + ideal sinc function interpolation), we should have:

1. time resolution equivalent to 1/(2pi * quantization levels * sample rate),
2. with 16bits 44.1kHz PCM (no dither) this leads to a theoretical value of 55ps (picoseconds).

 
In a perfect world I would expect the timing accuracy to get close to the timing resolution.
In audio world,despite being at least a bit conscious of quantization/phase/jitter/interpolation and mainly of ear limitations I have no clues about common timing accuracies values.
The 100us example you provided helped bringing a figure.
 
Regarding WTA's interpolation characteristics,I would have liked to have an idea of its timing accuracy but not sure it can be disclosed.
Please correct me if I am wrong, as far I have understood one of WTA's main filter specifity lies in transients ' detection?
Rgds.

 

[Rob Watts]

The basic problem is that the timing of interpolated transients depends upon the sampling timing; but with an ideal interpolation filter, the timing of transients becomes completely independent of the sampling. Its the dependence on sampling that creates the sound quality problems. I don't have any numbers to show the sampling timing error against tap length.
 
What I plan to do with Davina is to have ideal bandwidth limited white noise at 768 kHz; then delay the right channel by half a sampling period; decimate the delayed and not delayed signals; interpolate the output back up to 768 kHz; then delay the left hand side by half a sampling period; subtract the two signals. Now with an ideal decimation/interpolation system the null should be zero. We should then see an error that depends upon tap length and algorithm, and this error signal will tell me how significant what I can hear actually is. I suspect that we will be seeing very small numbers when going from half a million taps to a full M scaler for example; but with NOS one will see huge error signals, and significant errors for conventional interpolation filters.
 
Rob

 

[Crgreen]

This may be an impossible question to answer, but is it likely that tests with Davina will make a difference to any further development of the M Scaler? The reason I ask is obvious, and is another reason why it might not be possible to reply. I just get the feeling that the book has not been closed on development. Commercial implemnatation is another matter.

 

[Rob Watts]

I think the most likely lesson to be learned is to get an idea of how far away we are from perfect transparency with decimation and interpolation. It's possible that further work would lead to improvements in the WTA algorithm; but I can do that now with the available recordings. It's also possible that having completely aliasing free recordings with no timing errors, would make the WTA improvements more obvious; but I do not think it would actually change the WTA algorithm in using Davina sourced recordings against ordinary recordings - there is nothing to suggest that in theory or the practical optimization of the algorithm; but it's possible I am wrong about that. It's also certainly possible that knowledge gained with the project will enable better performance in the future - that's what makes my work interesting - there is always more to learn.