Time resolution of Redbook (16/44) PCM

[j_j]

No, not quite. What’s the x-axis? Microseconds? I get that you can make the plots, but how to “choose” the bandwidth? You obviously cannot arbitrarily do that. For PCM there is a clear limit dictated by sample rate, for DSD, it’s not so clear, or is it?

Like it says "samples at 3072000 Hz". Seems pretty clear to me.

There is NO noise in those impulse responses, well, rather it's down 240dB, give or take. So that's as clean as it gets. Note that's abs(impulse response) so that I can plot it in a log domain.

 

[MusicNBeer]

This is a great thread. This rediculous argument against RBCD came up at Hoffman and annoyed be bigtime, but I was too lazy to waste time trying to debunk it. As I've learned, it wouldn't have mattered anyway.

Intuitively thinking about it, I don't know why there would be any mean timing error in a properly dithered digital signal. I understand instantaneous error/uncertainty due to quantization noise, but long term mean error should be perfect.

It's also good to think about the instantanteous timing error as nothing more than noise. The instantaneous timing error is a by-product of the quantization amplitude error. I know the concept has been shown via plots on earlier posts, so nothing new here....

 

[audio2design]

Who wants to do an experiment? Suppose we have two signals, both consisting of a 1 kHz sine wave, the only difference being that one is shifted in time. The difference between these signals will then also be a 1 kHz sine save with phase and magnitude dependent on the amount of time shift. With a time difference of 300 ps, the difference signal is a pure tone at about -114 dB:
View attachment 129290

If we round both signals to 16-bit precision (without dither) before calculating the difference, we get a very different result:
View attachment 129291

The difference is barely large enough to change the LSB of a few samples. The difference spectrum has components every 100 Hz, all around the same level. With this level of precision, all we can say is that something changed.

Adding TPDF dither before rounding to 16 bits gives a very different result:
View attachment 129293

Although, the waveform still bears little resemblance to a sine wave, the spectrum now shows a single spike of the correct frequency and amplitude. Compared to the reference, the only difference is the addition of uniform noise. It should be noted, however, that this spectrum was averaged over several seconds.

With a 10 kHz signal, keeping the 300 ps time shift, the difference is 10x larger in amplitude:
View attachment 129294

With rounding to 16 bits, the difference spectrum is still ugly, though now the 10 kHz component stands out from the rest at roughly the correct amplitude:
View attachment 129297

Once again, adding TPDF dither before rounding fixes things:
View attachment 129300

I'm not sure if this actually answers any of the questions posed above.

Looking back at this, I think the flaw in your logic (or more accurately you answered a different question) is that you did not use an equal number of waves for each frequency. Like any measurement system, sound, light, whatever, wavelength plays into the potential accuracy, however, the discussion was w.r.t. inherent timing resolution of Redbook, which is still a function of bandwidth and SNR or cross-channel SNR. To extract that highest resolution you would need to use the full bandwidth in the excitation signal. Let's call us both right with you more right ... The noise shaping gives you better timing resolution due to improved SNR at low frequencies at the loss of SNR at high frequencies.

Overall, though, it is a silly thought exercise as the people who roll out this trollop hold up Vinyl (and R-R) as the Holy Grail. The wickely high IMD of vinyl and low SNR means the cross-channel timing accuracy is very poor.

 

[Stereo Skunk]

Anyone else here love DSD and want it desperately to be better than redbook, especially in the time domain?

I know I am!

(but I still love you redbook, even if DSD is better)

 

[voodooless]

No?

 

[Stereo Skunk]

Yes?

 

[Katji]

No, he said no.

 

[Stereo Skunk]

hmm thanks for the clarification.

for me, yes. anyone else?

 

[Katji]

Anyone else here love DSD and want it desperately to be better than redbook, especially in the time domain?

I've never seen one. All the music I listen to comes in WAV /flac or MP3.

[edit, for more clarity, perhaps:] I have no idea where people get them. Maybe remastered whatever music from long ago.

 

[voodooless]

be better than redbook, especially in the time domain?

You can find find out if it’s actually better using the formula in https://www.audiosciencereview.com/...lution-of-redbook-16-44-pcm.22102/post-775884

 

[dc655321]

hmm thanks for the clarification.

for me, yes. anyone else?

I'm morbidly curious: please define "better in the time domain" (than redbook cd).

 

[Katji]

"morbidly curious," that's a good way of putting it.

 

[Stereo Skunk]

tmin = 1/(π * fs * (2^b -1))
Where fs = sampling rate and b = no of bits

so for my beloved DSD256

DSD256 theoretical tmin = 1/(π * 11.2MHz* (2^1 -1))
=1/(π * 11.2MHz)
=28.4ns?

redbook theoretical tmin = 110ps

uh oh!!!

 

[Stereo Skunk]

I'm morbidly curious: please define "better in the time domain" (than redbook cd).

nah no thanks

btw i hate ur avatar. clockwork orange. creative.

 

[mansr]

You can find find out if it’s actually better using the formula in https://www.audiosciencereview.com/...lution-of-redbook-16-44-pcm.22102/post-775884

That formula doesn't apply (directly) when noise shaping is involved. You need to look at the signal to noise ratio in the frequency band of interest.

 

[voodooless]

That formula doesn't apply (directly) when noise shaping is involved. You need to look at the signal to noise ratio in the frequency band of interest.

Yes, I realized it as soon as I posted.. but how translate SNR to timing? For this you’d need the apparent resolution of the resulting signal, right?

Same goes for dithered PCM of course.

 

[Music1969]

tmin = 1/(π * fs * (2^b -1))
Where fs = sampling rate and b = no of bits

so for my beloved DSD256

DSD256 theoretical tmin = 1/(π * 11.2MHz* (2^1 -1))
=1/(π * 11.2MHz)
=28.4ns?

redbook theoretical tmin = 110ps

uh oh!!!

Most DSD available for purchase has been mixed in DXD, no?

 

[mansr]

Yes, I realized it as soon as I posted.. but how translate SNR to timing? For this you’d need the apparent resolution of the resulting signal, right?

Same goes for dithered PCM of course.

You could use the equivalent number of bits.

 

[voodooless]

You could use the equivalent number of bits.

yes, but how to determine this based on the snr number? Just divide by 6?

 

[Katji]

Most DSD available for purchase has been mixed in DXD, no?

Yes - so far I know, so many times I've heard that it so.
So I'm still morbidly curious just what music is available in the format. I suspect that it's only old Rock classics or Classical.