[cjl]

You haven't shown that they resolve anything more though (resolution has a specific meaning, and standard DACs can have very good resolution), and those are ultrasonic artifacts that are created due to the zero order hold, not aliases (aliases have a specific meaning, and they tend to come from improper bandlimiting prior to ADC, not improper bandlimiting in the DAC)

 

[22906]

Neither of your claims are true.

We already established that the PDM bitstream used in SD converters literally cannot support the same resolution that a PCM signal and R2R conversion can.

Zero order hold causes roll-off of frequencies near the cutoff; whether it adds additional ultrasonics compared to a Dirac impulse sequence, I'm not sure.

The signal is automatically bandlimited at the microphone; any further filtering can only be detrimental to the phase coherence.

I respect your profession and degree etc. I must admit I was never that good at math.

 

[cjl]

  Neither of your claims are true.

We already established that the PDM bitstream used in SD converters literally cannot support the same resolution that a PCM signal and R2R conversion can.
 

 
No. You claimed this, but it was never supported by evidence, and we did not establish it.
 
 
Quote:

Zero order hold causes roll-off of frequencies near the cutoff; whether it adds additional ultrasonics compared to a Dirac impulse sequence, I'm not sure.
 

Zero order hold adds lots of ultrasonics, due to the square waveforms.
 

The signal is automatically bandlimited at the microphone; any further filtering can only be detrimental to the phase coherence.
 

The signal is somewhat bandlimited at the microphone due to the microphone's inherent frequency response, but unless the microphone rolls off to -100dB at 22.05kHz, you'll want some additional filtering to prevent aliasing of higher frequencies back into the audible band (unless your sample rate is quite a bit higher). This filtering to prevent aliasing is strongly beneficial to the signal quality in the audio band.

 

[22906]

I think it is established; at any given sampling point, the PCM encoded sample can describe 2^N discrete amplitude levels (N being the number of bits of resolution). The discrete amplitudes encodable by the PDM signal is dependent on the frequency of pulse generation. To match the resolution of 16-bit PCM sample, the PDM decoder would have to generate pulses at 2^16 Hz for a 1-bit decoder. That is my reasoning. Maybe I don't have an accurate view of things; correct me if I'm wrong. For me to revise my views, I would need to see proof that SD converters can match the resolution of R2R, sample for sample.

 

[cjl]

Your reasoning is wrong, as was mentioned before. If you did not use noise shaping, you would need to oversample by a factor of 2^30 to get 16 bit resolution from 1 bit (since it scales as 2^2N). However, with noise shaping, you can do a lot better than that. Here's a fairly good paper on the topic: http://www.analog.com/static/imported-files/tutorials/MT-022.pdf. It talks more about ADCs than DACs, but the basic principle isn't terribly different.
 
 
For example, from the last figure in that paper, a 1 bit third order modulator can achieve about 100dB SNR (16 ENOB) at around a 50x oversampling, or around 1MHz. With a second order system, you'd need more like 250x, or around 5MHz. With a multi bit sigma delta setup (http://www.analog.com/static/imported-files/tutorials/MT-023.pdf), you could get away with even lower sample rates.

 

[22906]

As you can see in Figure 3 B, the error in the paper and the error in the hi-fi industry today, is that people are mistaking resolution on the time axis for resolution on the amplitude axis. I agree than sigma-delta has amazing frequency-domain characteristics. But it cannot add real amplitude resolution unless there are 2^N discrete voltage or current references. These references can come from resistors, or set frequencies that are then integrated; but the sum of number of representable discrete amplitudes, for SD is way lower than R2R.

 

[cjl]

No, that's not true. Amplitude error would still show up in the frequency response. Trust me, the resolution is in fact there, and the math all does work out, though it isn't all necessarily intuitive.

 

[22906]

Next

 

[castleofargh]

  I think it is established; at any given sampling point, the PCM encoded sample can describe 2^N discrete amplitude levels (N being the number of bits of resolution). The discrete amplitudes encodable by the PDM signal is dependent on the frequency of pulse generation. To match the resolution of 16-bit PCM sample, the PDM decoder would have to generate pulses at 2^16 Hz for a 1-bit decoder. That is my reasoning. Maybe I don't have an accurate view of things; correct me if I'm wrong. For me to revise my views, I would need to see proof that SD converters can match the resolution of R2R, sample for sample.

I thought the sample rate had to be increased by a factor of 4 to gain 1bit more of resolution. so from 1bit you would need 4^(16-1). but that's not the problem, as long as you don't account for noise shaping, filtering and everything used in a modern sigma delta chip, of course you're going to fall short in resolution. that's just removing a the wheels of a car and then prove that it can't go as fast as a horse.
 
you have rejected filtering when it's a condition for digital systems. you have rejected the idea that only 1 trajectory is the right answer between 2 samples when it's the very basis behind digital signals. you decide that sigma delta doesn't have the resolution it pretends to have, but as measurements prove otherwise, you end up rejecting the measurements too.
now you're up to saying that time resolution isn't reflecting voltage resolution when the audio signal is a sine wave...
 
your confidence is certainly impressive, but isn't there a moment when you tune it down a little and accept the possibility that you just had the wrong idea?

 

[22906]

Thank you for the kind words. I will be honest; for me, this is a exercise in logic and argumentation. I know I am right only because no one can conclusively prove me wrong. Would you go back on your word for any other reason? It is my belief that for a man to mean what he says, and say what he means, is one of the highest virtues, and I aspire to be a virtuous person. I wouldn't take a position as extreme as I have unless I had full confidence that it was defensible, but to someone who can display a higher level of argumentative skill, I will glady submit.

 

[cjl]

  Thank you for the kind words. I will be honest; for me, this is a exercise in logic and argumentation. I know I am right only because no one can conclusively prove me wrong.

You have been conclusively proven wrong. I have shown you a paper explaining sigma-delta DAC and ADC design that shows that not only are you far too optimistic about how to gain resolution without noise shaping (you need 2^2n upsampling, with n being the number of additional bits of resolution you want, while your logic led you to believe that it was 2^n), but you also don't understand how massive a benefit noise shaping is, and how with noise shaping and multibit sigma delta, you can achieve excellent resolution with a far, far lower sample rate than you think. You have been shown the math and the measurements (both by me and by others).
 
Just because you are plugging your ears and ignoring the proof that you are wrong does not mean that the proof does not exist. It isn't a matter of argumentative skill, it's a matter of fact.

 

[sonitus mirus]

  ...this is a exercise in logic and argumentation.

 
Next.

 

[22906]

So I should back down because some guy with a degree is emotional about a flawed paper? You want to run around with delta-sigma DACs claiming they have 32-bit time-domain resolution? Now I see that is why the DIY community exists; money blinds us to reality. Ponder my definition of resolution for a while; eventually you will understand.
 
I DARE you to post a resolution measurement comparing R2R and SD DACs.

 

[22906]

   
Next.

I bet that felt good.

 

[castleofargh]

  Thank you for the kind words. I will be honest; for me, this is a exercise in logic and argumentation. I know I am right only because no one can conclusively prove me wrong. Would you go back on your word for any other reason? It is my belief that for a man to mean what he says, and say what he means, is one of the highest virtues, and I aspire to be a virtuous person. I wouldn't take a position as extreme as I have unless I had full confidence that it was defensible, but to someone who can display a higher level of argumentative skill, I will glady submit.

but when did this become a contest of argumentative skill? it's about theory, application, and facts.
by filtering with a low pass filter we increase the fidelity of the signal compared to it's original analog counterpart. we get rid of some signals that shouldn't exist by cutting frequencies. keeping that signal would absolutely reduce the signal fidelity.
and if before that we oversampled or used any noise shaping trick to move some of the noise energy up in high frequencies, then when we cut the ultrasounds lose with the filter, we also get rid of that moved noise. that once again improve fidelity by lowering the noise inside the recorded range of frequencies.
they are tricks of sort, you may not like them, but their effectiveness is doubted only by you it seems. you're just being unreasonable here.