please explain 192 khz and 24bit.

[MatLz]

WTF? A 16 bit system (which the Audio CD is) has a dynamic range of 20 * log(65536) = 96.329598612473982468396446311838 dB

There is no "but not always".
Yeah that was that.
For all calculations, the constant is log(2^20) which is approximately 6.0206.

Max dB == number of bits * log(2^20)

[diogen]

I've been suckered into this trolling for too long.Indeed.
But ain't it entertaining...:D

Diogen.

[Groucho2004]

I cannot help but post a figure which is not mine (I'm on my internet PC that has nothing else)
http://www.solidstatelogic.com/music/X-ISM/images/Inter-Sample_Peaks_large.jpg

Imagine the 4 samples are MAX and MIN. See how the curve goes up to 1.1 (110%)? How much goes the reconstrued curve up depends on the frequency, or how close those 2 MAX samples are each to the other....

Your formula computes the dynamic of MAX-MIN, instead of computing the dynamic of the reconstrued curve ...

The formula computes the theoretically maximum dynamic range for a given bit depth. The data on an Audio CD is stored with 16 bit, hence the dynamic range is ~96 dB.
You can "reconstrue" and interpolate as much as you want, it won't alter the dynamic range of the data stored on an Audio CD.

[IgorC]

WTF? A 16 bit system (which the Audio CD is) has a dynamic range of 20 * log(65536) = 96.329598612473982468396446311838 dB

There is no "but not always".
It's possible to obtain much better dynamic range for 16 bits (~110dB, if not more) with smart 24->16 conversion.

http://www.hydrogenaudio.org/forums/index.php?s=&showtopic=40134&view=findpost&p=379082

http://wiki.hydrogenaudio.org/index.php?title=Noise_shaping
http://wiki.hydrogenaudio.org/index.php?title=Dither

[Ghitulescu]

I can't believe people still talk about jitter with digital audio. In reality, analog has much worse jitter (but not called jitter), thousands of times or even hundreds of thousands of times more than these nano- or picoseconds everyone worries about. Jitter is not a concern. Modern day DACs reclock the signal to have zero jitter before it hits the actual DAC. This is purely what sets new DACs apart from what you found in the 80s and 90s, and why things like USB DACs with added circuitry to fake deal with jitter, and they cost hundreds and up into thousands, make me laugh when a good sound card is all you need.
The jitter issue lies not in the cables or in the transport. Of course, provided the jitter is still within the allowed deviation.

It's in the DAC clock. Reclocking an old DAC (from an old CD-player) does improve more the sound than black CDs, "noise-free" power cables, audio cable suspenders and other wonder tricks sold for their weight in gold to stupid people with money that never heard the concept of placebo.

However, cheap [designed ancillary circuits for] DACs synch themselves to the incoming signal instead of buffering it and replaying it at a stable pace. For these, jitter in transmission is a problem.

[pandy]

I can't believe people still talk about jitter with digital audio.

...

I still don't buy that 16/44.1 is enough. A signal of music does not apply to that silly nyquist bullshit. It's a theorem. Notice the word theory in that?

OK, first jitter can be measured, there is very strong math behind jitter and jitter can be heard - theory and practice ALWAYS work - there is no practice without theory and theory without practice - they are complementary each other.

16/44.1 is acceptable from 99% listeners point of view, especially in real, natural listening environment - 16/88.2-96 is enough from human hearing system point of view.
With correct postproccessing (however before CD recording) 16/44.1 can match almost perfectly human hearing system.

What does that have to do with the actual content of an Audio CD?

I feel like I'm in the twilight zone.

Once again - dynamic digital audio is a bit tricky thing - without additional conditions dynamic of the 16 bit system can be higher than pure calculation with provided equation - human hearing system is not voltage meter - this very complex system and there is no simple and linear equation that describe this complex system.
i've asked about 1 bit system due of fact that 99% audio DAC use 1 or at "worst" case maximum 6bit conversion - so how this is possible that 1 bit DAC is able to provide 16 bit dynamics - taking literally You this can't work but it works quite well.


Edit: To add, if the Nyquist-Shannon sampling theorem is wrong, then how did multiple people independently discover and prove it?

There is very big area when non Nyquist conversion is used - ie sub Nyquist sampling, IF sampling, equivalent time sampling, random - stochastic sampling.



Nyquist can NOT reproduce the EXACT shape of the original signal, it can only get close.

...

We also already KNOW that ultrasonic harmonics DO affect how we perceive audible sound, even all the way down to bass.

Please do not be confused - Nyquist is OK but in PERFECT system (such system do not exist thus we need oversample) - i don't know why You introduce ultrasound and trying to use sub Nyquist sampling?

I don't need to disprove it. Anyone with common sense (anyone who doesn't hold science and math as their religion) knows that theory is not fact. If it's so magical, it should have no problem proving itself and having its name changed to "information fact".

Please... don't be so confused and please read about work of this guy http://en.wikipedia.org/wiki/Tertullian
He write something like this "Et mortuus est Dei Filius, prorsus credibile est, quia ineptum est. Et sepultus resurrexit; certum est, quia impossibile est" - This is exactly what are You telling...

The formula computes the theoretically maximum dynamic range for a given bit depth. The data on an Audio CD is stored with 16 bit, hence the dynamic range is ~96 dB.
You can "reconstrue" and interpolate as much as you want, it won't alter the dynamic range of the data stored on an Audio CD.

nope, this is not true, check this http://www.ti.com/product/pcm1774 - is Texas Instruments lie us when they tell that 1 bit DAC is able to provide 93dB dynamics? Or perhaps SACD is one big fraud - http://en.wikipedia.org/wiki/Direct_Stream_Digital literally says:
"The signal is stored as [...] a sequence of single bit values..."
how this is possible that SACD with DSD provide on only 1 bit 120dB dynamics? So where is error? Perhaps equation is wrong?

[Groucho2004]

nope, this is not true, check this http://www.ti.com/product/pcm1774 - is Texas Instruments lie us when they tell that 1 bit DAC is able to provide 93dB dynamics? Or perhaps SACD is one big fraud - http://en.wikipedia.org/wiki/Direct_Stream_Digital literally says:
"The signal is stored as [...] a sequence of single bit values..."
how this is possible that SACD with DSD provide on only 1 bit 120dB dynamics? So where is error? Perhaps equation is wrong?

I recommend you do some research on digital signal processing.

I repeat - What various DAC technologies do with the data after it is read from the medium has nothing to do with the actual data on the disk.

When the data is digitized for Audio CD, the dynamic range is "cut" to 96 dB because quantization depth is 16 bit. All the information that was between these steps is lost forever. The same applies to the time domain - all information between the sample points (~23 us @ 44.1 KHz) is lost.

Methods like integration, upsampling, etc. will increase the SNR and dynamic range but the resulting signal is still an approximation.

DSD is a completely different technology, it works with noise shaping quantization (which is basically pulse width modulation). Obviously, the formula for calculating the dynamic range of PCM signals does not apply.

[pandy]

I recommend you do some research on digital signal processing.

Appreciate Your advise however i prefer to wait for You.


I repeat - What various DAC technologies do with the data after it is read from the medium has nothing to do with the actual data on the disk.


I repeat - using equation provided by You and based only on Your knowledge i must say that DSD (SACD) can't work.


When the data is digitized for Audio CD, the dynamic range is "cut" to 96 dB because quantization depth is 16 bit. All the information that was between these steps is lost forever.


No - You are completely wrong with this claim.


The same applies to the time domain - all information between the sample points (~23 us @ 44.1 KHz) is lost.


Yes, but we talking about bit depth and digital audio system dynamics.


Methods like integration, upsampling, etc. will increase the SNR and dynamic range but the resulting signal is still an approximation.


Not sure what are You trying to say - can You be more precise?


DSD is a completely different technology,


No, why completely different technology - bit is exactly same like in CD audio system and there is only one bit so DSD (SACD) accordingly to You offer something around 6.02dB dynamic.


it works with noise shaping quantization (which is basically pulse width modulation).


You are wrong, PWM is something else than noise shaping, DSD doesn't use PWM at all.


Obviously, the formula for calculating the dynamic range of PCM signals does not apply.

suddenly bits are different?

Once again - how You explain that system with less than 16 bits depth is able to provide dynamics higher than 96dB?

How You can describe situation when i can provide to You signal sample - 16 bit, 44100 samples per second, LPCM, where i can store signal with level -130dBFS ie i can prove that on 16 bits i can have signal with 22 bit resolution and -140dBFS noisefloor?

[Groucho2004]

How You can describe situation when i can provide to You signal sample - 16 bit, 44100 samples per second, LPCM, where i can store signal with level -130dBFS ie i can prove that on 16 bits i can have signal with 22 bit resolution and -140dBFS noisefloor?

I can only assume that on your planet the laws of physics are different.

[pandy]

I can only assume that on your planet the laws of physics are different.

Or perhaps I've already done "some research on digital signal processing" and You still wait to discover and explore this very interesting world when theory and practice meets and work perfectly together.

[amtm]

There is very big area when non Nyquist conversion is used - ie sub Nyquist sampling, IF sampling, equivalent time sampling, random - stochastic sampling.

I know I said I wasn't going to respond anymore but this will be my last. Of course there is. The point is that if the Nyquist-Shannon sampling theorem were as bunk as ramicio is trying to make it out to seem there wouldn't have been multiple people to have independently have derived and proved it. That seems to be very wildly coincidental for multiple people to have derived and proved the same wrong thing. I'm not saying it can't happen but it's not very realistic. Also, if it were so bunk since it's only a theorem no one would ever bother with it. The fact that it is still relevant despite it's shortcomings, and there a number of them in practical situations, disproves the notion that it is worthless.

It's like trying to claim that Newton's Laws of Gravity are completely wrong just because they happen to break down at the quantum level. Both have their limitations but they are both still practically useful even when taking their shortcomings into account.

[ramicio]

You can't prove that the earth isn't flat and that the entire universe isn't just accelerating upwards at 9.8 m/s². Reality is based on observation and our understanding of that. Not absolute truths.

[Ghitulescu]

The formula computes the theoretically maximum dynamic range for a given bit depth. The data on an Audio CD is stored with 16 bit, hence the dynamic range is ~96 dB.
You can "reconstrue" and interpolate as much as you want, it won't alter the dynamic range of the data stored on an Audio CD.

We are discussing three items here.

The first one, which you are right about, is the dynamic provided by the numbers of 16b.

The second one is where I am right - it concerns the reconstruction of the original analog signal. -> http://www.tcelectronic.com/media/level_paper_aes109.pdf see figure 2.

The third one is the mapping of 16b into the electrical signal. The lower limit is the electronic noise. So, the higher the peak level, the higher the dynamic. So mapping 16b into a 18kV signal (electric trains supply) one can reach even 245dB. Conversely, mapping 24b into the regular consumer voltage (500mV, or -10dB), reduce its dynamic of 144dB to something less than 100dB.
The nicest part of this story is that there is no established method of mapping digital into analog.

[IanB]

16bit Linear PCM has ~96db dynamic range. It is by the very definition of the way the format is implemented.

Sure you can express more than 96db of dynamic range in a 16bit of data format. For example both the A-law algorithm (http://en.wikipedia.org/wiki/A-law_algorithm) and the Mu-law algorithm (http://en.wikipedia.org/wiki/%CE%9C-law_algorithm) provide schemes for encoding ~72db and ~78db respectively into just 8 bits. But there are tradeoffs for such schemes that use non-linear quantisation.

[IgorC]

16bit Linear PCM has ~96db dynamic range.
Noise shaping moves a quantization error to inaudible/less audible range (>20 kHz) during 24-> 16 bits conversion.

It means two LPCM files can have 96 db of dynamic range but sound totally different. Mathematically noise shaped LPCM still will have the same dynamic range than not processed LPCM but the first one will have better audio quality (as it had a higher dynamic range).

[LoRd_MuldeR]

I think this thread has gone off-topic long ago. So we will stop at this point.