[RRod]

Real dynamic range of CD in terms of information rather than max SNR is 96dB. You can lower the noise floor but I don't think anyone thinks there's real information to be had below -96.

Incidentally, Dolby SR on a fast analogue tape could give you over 100dB based on SNR according to the Wikipedia article on audio dynamic range though 95dB would be a more common claim, and the information content would be real to well below the noise. And no brickwall is needed.

Again, it all depends on how the ear works. Not on high level THD IMO. We don't listen to sine waves.

So does DSD have only 1-bit informational content? And aren't those Dolby numbers dependent on frequency? Re sine waves: if you make a trigonometric reconstruction based on the DFT, you will get something that sounds a gosh-awful like the music you are reconstructing...

 

[SimonPac]

No, obviously not. DSD uses delta sigma so 1-bit modulation and decimation. Totally different process. The Lavry paper talks about ADC resolution/sample rate limitations but seems to be assuming a delta sigma DAC running at a certain clock rate. PCM can achieve better resolution by oversampling but only if it's done at the ADC as actual extra samples. We are talking 44.1-16 not over-sampled at 88, 176 or whatever to give better amplitude resolution. Don't understand your last statement.

 

[RRod]

And tons of noise shaping, which is also possible in PCM. The point being that it seems perfectly possible to build an ADC that samples 44.1/16 but that can return partial information content for signals peaking under -96dBFS.

Re trig reconstruction: A signal that is bandlimited AND periodic can be perfectly reconstructed via its DFT. If you take a DFT of a track you like and make a cosine reconstruction based on the polar form, you will get essentially an infinitely repeating version of the track. Note that, of course, the number of cosine terms will be huge, but that just drives home the point that when we say "adding up sine waves", we don't mean a handful of them.

 

[71 dB]

And tons of noise shaping, which is also possible in PCM. The point being that it seems perfectly possible to build an ADC that samples 44.1/16 but that can return partial information content for signals peaking under -96dBFS.

Yes. This is easy to test: Create a -120 dBFS (amplitude = 0.000001) sine wave (for example 1000 Hz) at 32/44.1 floating point in Audacity. Then downmix it to 16 bit using shaped dither after which amplify the result by 50 dB * and listen to the sound loud. You should be able to hear very quiet 1000 Hz tone in the noise. The tone is not distorted! It is a distortion-free 1000 Hz sine wave summed with the dither noise. So, if you have a decaying piano sound, you can hear it decay down to about -120 dBFS (that is if you have volume turned so loud that the louder sounds on a CD cause pain to your ears) after which it becomes masked by the dither noise. The result sounds similar to analog media where sounds decay into the noise floor. So, the claim that digital audio doesn't allow sounds decay nicely into silence (noise floor) isn't true. Dither makes it possible. Dither is our friend.


* Or you can do elegant "bit scaling" in nyquist prompt giving the simple LISP commant

(mult s 1024)

which multiplies (scales) the signal by 1024 (amplifies ~60.2 dB) so that no additional noise is created.

 

[gregorio]

PCM can achieve better resolution by oversampling but only if it's done at the ADC as actual extra samples. We are talking 44.1-16 not over-sampled at 88, 176 or whatever to give better amplitude resolution.

Do you know of any commonly used pro-audio ADCs in the last 25 years or so which do not oversample into the mHz range?

G

 

[SimonPac]

Yes. This is easy to test: Create a -120 dBFS (amplitude = 0.000001) sine wave (for example 1000 Hz) at 32/44.1 floating point in Audacity. Then downmix it to 16 bit using shaped dither after which amplify the result by 50 dB * and listen to the sound loud. You should be able to hear very quiet 1000 Hz tone in the noise. The tone is not distorted! It is a distortion-free 1000 Hz sine wave summed with the dither noise.

With the right dither and an original quanitzation comfortably sufficient for -120dB, i.e 24-bit, yes for frequencies well below sample rate and particularly periodic signals. In the general case, no. You need the bit depth.

 

[SimonPac]

Re trig reconstruction: A signal that is bandlimited AND periodic can be perfectly reconstructed via its DFT. If you take a DFT of a track you like and make a cosine reconstruction based on the polar form, you will get essentially an infinitely repeating version of the track. Note that, of course, the number of cosine terms will be huge, but that just drives home the point that when we say "adding up sine waves", we don't mean a handful of them.

Yes you can FT reconstruct any periodic waveform perfectly including a repeating recording if you have an infinite resolution available in the complex frequency domain. The imaginary component provides the phase information. Band limiting curtails the maximum frequency you need. The length of the track curtails the minimum frequency you need to the reciprocal of the track length!

To do a DFT or FFT on a time interval sampled periodic signal, you just need frequency components spaced at the reciprocal of the sample time interval. The number of frequency components becomes finite if the signal is hard band limited.

 

[bigshot]

the claim that digital audio doesn't allow sounds decay nicely into silence (noise floor) isn't true.

I hear a lot of funky fade outs, but they're because of engineers ham handedly getting to a point where they guess it's gotten quiet enough and just zipping to the finish line. That isn't the fault of the recording medium.

 

[71 dB]

With the right dither and an original quanitzation comfortably sufficient for -120dB, i.e 24-bit, yes for frequencies well below sample rate and particularly periodic signals. In the general case, no. You need the bit depth.

You can test yourself "general" cases, whatever those are. This works on signals typical in music. Even if it didn't, we are talking about sounds so quiet nobody is likely to hear them at reasonable listening levels. What's the point of imagining pathological signals which could theoretically cause problems? How well can we heard the pathological features of a pathological sound? After all, hearing is a bandlimiting system too which means any pathological signal is likely to lose it's pathological nature in our hearing anyway. How much are you likely to find these pathological signal on your CDs?The point is that with shaped dither CDs could have even 5-6 bits taken away and still have enough dynamic range. That means 24 bit audio has twice the number of bits that are really needed. This all goes for consumer audio. In production 24 bit or more is the way to go.

 

[71 dB]

I hear a lot of funky fade outs, but they're because of engineers ham handedly getting to a point where they guess it's gotten quiet enough and just zipping to the finish line. That isn't the fault of the recording medium.

Amateurish. It looks like silence on linear scale, but when you look at the waveform on dB-scale, you see when the silence really starts.

 

[SimonPac]

Dither is our friend.

Well I might not have any others if I keep obsessing about audio all day every day and arguing with people

Dither in PCM is primarily to reduce quantization noise or randomise non-linearity in the DAC. It can also push low level signals over the 1st bit threshold (if the DAC chip is good enough). However, it will do so only sporadically, though with a sine wave often enough for the ear or a spectrum analyser to get a spectral component. The ear is spectrally sensitive and if dither is chosen to move the quantization error to HF, then you'll hear something below the quantisation limit. The spectral component is low level but it still stands out from the wideband noise, especially at mid frequencies. At a given sample rate it is no way totally equivalent to extra bit depth. It's a far more complex function of the original signal that will come through. If it were equivalent, people would use it in that way rather than trying hard to get the DAC linear to low level. In the days of the PCM63, production intensive individual laser trimming of the ladder network was used; why bother if dither gave the same result? The data sheet for that device indeed shows a 1KHz sine wave resolved down to -104dB when used at 16-bit. Actually, the dither (unspecified in the data sheet) pushes the level of it up above linear; it's not reproduced in a linear way, see page 4:

http://pdf.datasheetcatalog.com/datasheets/270/37438_DS.pdf

This is probably because the quantization noise has a spectral component after dithering.

It is a distortion-free 1000 Hz sine wave summed with the dither noise.

At the input, yes. After the lower bit depth DAC, no. It depends whether the dither pushed you over the 1st-bit threshold.

Here is a paper discussing linearity errors at low level albeit in a fast 11-bit DAC.
http://www.ti.com/lit/an/sboa133/sboa133.pdf

The below noise/dither signal is handled in a non-linear way due to quantization error becoming correlated. How all this works out is rather complex; you'll get something through under the quantization threshold of the raw DAC but its relationship with the input signal is not a simple linear function.

 

[bigshot]

In one of of the AES seminars in my sig file, Ethan Winer presents a track with and without dithering. I can't hear any difference on my home stereo equipment. Dither is already gilding the lilly a bit. No need to worry about it. It's only a problem if it's done wrong.

SimonPac, what music are you listening to and thinking about today?

 

[SimonPac]

I listened to the Clapton thing again! I think about a lot of things unrelated to audio and this forum!

 

[71 dB]

Well I might not have any others if I keep obsessing about audio all day every day and arguing with people

Frankly I am getting tired of doing this. 16/44.1 audio works perfectly for me. If it doesn't do that to you, then it seems you need something like 128 bit/900 GHz audio, which will come available around the year 3000, when record labels want to sell the Pink Floyd albums again… …maybe the dirac impulses on the albums will FINALLY sound right after 1000 years of waiting!!

 

[gregorio]

Dither in PCM is primarily to reduce quantization noise or randomise non-linearity in the DAC. It can also push low level signals over the 1st bit threshold (if the DAC chip is good enough).

What low level signals? The only low level signals in commercial music releases are noise, the dynamic range virtually never exceeds 60dB, which is 10 bits or so, distributed in a 16bit container! You continue to post on what appears to be a purely mathematical/engineering level, without any regard to the practicalities of what that math/engineering is going to reconstruct. You then post inapplicable examples of 20+ year old 20bit DAC chips and an 11 bit converter, to demonstrate points/weaknesses which are anyway irrelevant to what is being reproduced and what is audible?

G