Reducing DAC volume doesn't necessarily decrease bit-depth of audio data.

[Deleted member 58865]

OK - seeing as you insist :

(Hint - you are thinking about it wrong. More bits doesn't give you more "resolution" in terms of accuracy of the signal - it only gets you a lower noise floor - more dynamic range)

I don't know the physically smallest volume steps above the noise floor. But, if the DAC digital volume steps manage to be smaller than that, it's good.

The 32-bit DAC simply provides mathematical wiggle rooms to exceed physical limitations.

I'm not talking about perceptual limitations which are far worse than physical limitations.

 

[antcollinet]

The 32-bit DAC simply provides mathematical wiggle rooms to exceed physical limitations.

It really doesn't. Once your number of bits exceeds the number of "bits" in your dynamic range equivalent (and I'm not aware of any dacs that can do better than around 22 bits), then having more bits in the DAC doesn't get you anything.

24Bit is already better than you can get for any current (even the excellent) DACs.

 

[Deleted member 58865]

https://en.wikipedia.org/wiki/Audio_bit_depth says

In digital audio using pulse-code modulation (PCM), bit depth is the number of bits of information in each sample, and it directly corresponds to the resolution of each sample.

It says "resolution" of each sample. At least, internal digital mathematical resolution manages to be above 16-bits. I don't really know what you are saying here.

32-bit is accurate enough to minimize internal rounding errors. What I mean is that the digital numbers manage to be above 16-bits.

I don't know the actual resolution of analog signal that comes out of DAC.

The noise floor may be -124dB. But, the actual resolution of analog signals could be better than 21 bits above -124dB if it's physically possible for a DAC to vary analog signals in small steps.

-124dB is simply the thermal noise. I don't think it dictates resolution of analog signals above -124dB. I haven't met a theory that calculates analog resolution from the noise floor.

If analog resolution is 24-bits, then even with the noise floor at -60dB, the analog resolution should be 24-bits above -60dB. The noise floor doesn't seem to dictate the smallest steps between analog signal levels.

 

[antcollinet]

https://en.wikipedia.org/wiki/Audio_bit_depth says

It says "resolution" of each sample. At least, internal digital mathematical resolution manages to be above 16-bits. I don't really know what you are saying here.

32-bit is accurate enough to minimize internal rounding errors. What I mean is that the digital numbers manage to be above 16-bits.

I don't know the actual resolution of analog signal that comes out of DAC.

The noise floor may be 21 bits. But, the actual resolution could be better than 21 bits above -124dB if that's physically possible.

If you watch the video, it explains.

The resolution is the resolution of each sample. The errors from samples falling in between two possible values are called quantisation errors. After all the processing (including dithering and reconstruction) all these errors do is cause noise (quantisation noise) they DONT otherwise change the accuracy of the signal.

So 8 bits will still give you a perfectly reconstructed sine wave (or any other waveform) - it will just have more noise on the signal. Again, watch the video.

The BEST dac here has a noise floor 130dB (21.7 bits) below full scale. Any processing in the DAC at significantly higher bit levels doen't get you anything. 24Bits is a higher resolution than the very best DAC measured here can take advantage of.

 

[Deleted member 58865]

I doubt that you will hear much at 2 bits or 1 bit of internal mathematical resolution. You will hear only garbage.

Does the noise floor determine the smallest step in analog signal? You haven't said it does.

I think even if the noise floor is -10dB, a DAC's analog resolution could be 16-bits or more above -10dB because I don't see anything that couples the noise floor with analog resolution.

I think you are getting it backward. Analog resolution isn't 21-bit. It can be 21-bit, less than 21-bit, or more than 21-bit. Since the thermal noise is -124dB, 21-bit of analog resolution is required to hit the thermal noise floor.

Analog resolution can very well be below 16-bits although the thermal noise is -124dB. I think analog resolution is decoupled from the thermal noise.

I think there is a separate physical law that dictates the highest analog resolution.

 

[Trell]

 

[antcollinet]

I doubt that you will hear much at 2 bits or 1 bit of internal mathematical resolution. You will hear only garbage.

Does the noise floor determine the smallest step in analog signal? You haven't said it does.

I think even if the noise floor is -10dB, a DAC's analog resolution could be 16-bits or more above -10dB because I don't see anything that couples the noise floor with analog resolution.

I think you are getting it backward. Analog resolution isn't 21-bit. It can be 21-bit, less than 21-bit, or more than 21-bit. Since the thermal noise is -124dB, 21-bit of analog resolution is required to hit the thermal noise floor.

Analog resolution can very well be below 16-bits although the thermal noise is -124dB. I think analog resolution is decoupled from the thermal noise.

I think there is a separate physical law that dictates the highest analog resolution.

There aren't steps. That is the whole point of the video (have you watched it?). See the crossed out stair step waveform on the video "icon". Steps don't exist in digital audio.

And two bits will sound like garbage. The noise signal will be half as big as a full scale sine wave.


If the noise floor is at -10dB (That is effectively less than 2 bits dynamic range) any signal smaller than -10dBFS will be below the level of the noise - or to put it another way, the noise will be as big as the signal.

In fact a -10dB noise floor is higher than the noise floor of a 2 bit resolution signal - all the additinoal accuracy is smaller than the noise so won't benefit you. No you can't have a 16 bit signal above a -10dB noise floor.

See this image:

I'm estimating the noise level ther to be about 1/8th the level of the signal - so, if the signal is a full scale sine wave about, it has about 18dBFS (3 bits) of dynamic range.

Any variations in that sine wave that could be shown with more than 3 bits of resolution will not be seen in the wave form, because it would be lost in the noise. For example, if you added a sine wave at 20x the frequency, but (say) 1/32nd (-30dbFS) the magnitude - you would not see it because the noise is bigger. It is lost in the noise floor.

 

[antcollinet]

I doubt that you will hear much at 2 bits or 1 bit of internal mathematical resolution. You will hear only garbage.

Does the noise floor determine the smallest step in analog signal? You haven't said it does.

I think even if the noise floor is -10dB, a DAC's analog resolution could be 16-bits or more above -10dB because I don't see anything that couples the noise floor with analog resolution.

I think you are getting it backward. Analog resolution isn't 21-bit. It can be 21-bit, less than 21-bit, or more than 21-bit. Since the thermal noise is -124dB, 21-bit of analog resolution is required to hit the thermal noise floor.

Analog resolution can very well be below 16-bits although the thermal noise is -124dB. I think analog resolution is decoupled from the thermal noise.

I think there is a separate physical law that dictates the highest analog resolution.

PS - the equivalent of resolution in the analogue domain is dynamic range - the difference between the largest system signal, and the the noise floor. Anything smaller than the noise floor cannot be differentiated from noise.

This is normally described in dB. Divide this figure by 6 and you have the digital resolution equivalent of the dynamic range.

Eg DR - 120dB = 120/6 = 20 bits of dynamic ragne.

 

[BDWoody]

Does the noise floor determine the smallest step in analog signal? You haven't said it does.

 

[antcollinet]

View attachment 276687

Did ma best

 

[Music1969]

A digitally controlled stepped attenuator at the output of DAC, but this could be expensive?

There are already chips that do this

Used in iFi Gryphon and Neo iDSD for example

 

[Deleted member 58865]

There are already chips that do this

Used in iFi Gryphon and Neo iDSD for example

Quite expensive. I prefer the digital volume knob on FiiO K5 Pro ESS.

 

[Deleted member 58865]

I just spent an hour with this beard model.

I am still confused, but I learned a lot.

 

[Deleted member 58865]

Any processing in the DAC at significantly higher bit levels doen't get you anything.

Okay, now I understand that in the analog domain, there are noises. Signal amplitudes are calculated from samples. The more bits available, the less noise there is.

But, having more bits in the digital domain than in the analog domain doesn't hurt. A 32-bit DAC doesn't hurt.

A passive stepped attenuator would be limited by the thermal noise(-124dB) which is lower than SINAD of Topping D10s(-112dB). If I use a stepped attenuator after the DAC, then the stepped attenuator attenuates the DAC noise. -12dB attenuation in a stepped attenuator instead of DAC volume adds 2 bits(12dB) of dynamic range. Am I right?

 

[Music1969]

Quite expensive. I prefer the digital volume knob on FiiO K5 Pro ESS.

I was talking about the chip itself - cheap.

And maybe you didn't know a chip could what you described (the part I quoted).

The product price something different.

 

[antcollinet]

Okay, now I understand that in the analog domain, there are noises. Signal amplitudes are calculated from samples. The more bits available, the less noise there is.

But, having more bits in the digital domain than in the analog domain doesn't hurt. A 32-bit DAC doesn't hurt.

A passive stepped attenuator would be limited by the thermal noise(-124dB) which is lower than SINAD of Topping D10s(-112dB). If I use a stepped attenuator after the DAC, then the stepped attenuator attenuates the DAC noise. -12dB attenuation in a stepped attenuator instead of DAC volume adds 2 bits(12dB) of dynamic range. Am I right?

No, it doesn't hurt - and most DACs have 32 bit processing pipelines in any case. But once you have 24 bits, you no longer need to worry. More doesn't bring any improvement.

In your example of the D10S,

1 - The SINAD isn't all noise it may well be distortion limited with a much lower noise floor.
2 - Even if the noise floor were at -112dB you could still be listening at 120dB, your DAC noise floor would be at 8dB - still lost in the noise of a quiet room. You still can't hear it. Yes, with a passive attenuator the dac noise floor would be reduced.... to an even more inaudible level

By the way - your -124dB for noise of a passive stepped attenuator is not a fixed value. It depends very much on the design, - in particular the resistor values chosen. And passive attenutors may be much worse than active buffered attenutors (see this benchmark discussion)

Relay-Controlled Volume - The Ultimate Solution for Analog Audio

Benchmark has introduced the new HPA4 headphone/line amplifier with four 256-step relay-controlled attenuators and four 16-step relay-controlled boost amplifiers. Together these form two fully-independent, fully-balanced stereo volume controls. One volume control is dedicated to the line output...

benchmarkmedia.com

 

[solderdude]

Okay, now I understand that in the analog domain, there are noises. Signal amplitudes are calculated from samples. The more bits available, the less noise there is.

The more bits there are the less quantization noise is there.
It has nothing to do with the actual noise floor of the circuits used.

But, having more bits in the digital domain than in the analog domain doesn't hurt. A 32-bit DAC doesn't hurt.

No it doesn't. But 32 bit format is not the same as 32 bit resolution and given that it is DS the final resolution is not 32 bits at all. The 'noise' that is used (and thus averaged by LPF) is based on just a few bits (between 3 and 8 depending on the used chip)

A passive stepped attenuator would be limited by the thermal noise(-124dB) which is lower than SINAD of Topping D10s(-112dB).

SINAD is 2V (SE) 1kHz distortion + noise component and can not be compared with thermal noise number of an attenuator in a specific (worse) condition as that is also dependent on the components before and after it. I would even dare to say the thermal noise of the attenuator will be irrelevant compared to the other parts.

If I use a stepped attenuator after the DAC, then the stepped attenuator attenuates the DAC noise.

Yep, so does a potmeter. However, the signal amplitude becomes smaller yet the noise of the amp behind the volume control will remain the same.
When one wants to really gain S/N ratio you need to lower the gain (not as easy as one might think) or pad the output of the following amp.

-12dB attenuation in a stepped attenuator instead of DAC volume adds 2 bits(12dB) of dynamic range. Am I right?

No. You continue to believe that quantization noise is key in your thesis. It isn't. Noise floor, gain, sensitivity of transducers and hearing limits are the restrictions.
Accepting 32 bit formats or 24 bit formats and filtering internally with 32 bit accuracy does not mean the quantization noise is 32 bit and not completely drowned by actual noise and distortion products in reality.

Quantization noise does not determine the noise floor. Components do (active + passive)

 

[antcollinet]

Personlly I manage the gain staging - either useing an amps volume control, or attenuator pads if needed - so that the volume with DAC at 0dBFS is the loudest I'm ever going to want (but still not loud enough to cause damage) and then use the DAC to turn it down from there.

This minimises the digtial attenuation needed while being fully protected from the DAC volume going unexpected to max.

 

[Deleted member 58865]

No. You continue to believe that quantization noise is key in your thesis. It isn't. Noise floor, gain, sensitivity of transducers and hearing limits are the restrictions.
Accepting 32 bit formats or 24 bit formats and filtering internally with 32 bit accuracy does not mean the quantization noise is 32 bit and not completely drowned by actual noise and distortion products in reality.

Quantization noise does not determine the noise floor. Components do (active + passive)

What I meant is that using a passive stepped attenuator gives me a bit less noise than reducing DAC volume because DAC's SINAD is higher than thermal noise.

 

[solderdude]

Less noise from the DAC. Not less noise from the amp which is the limiting factor here not thermal noise of a 2.5k resistor in worst case scenario (-6dB setting).
Reducing DAC volume (by say 3dB) is beneficial as it lowers distortion and allows for intersample overs.

So technically, -3dB digital + reducing gain of the following amp will give best results.
As the latter is not possible -3dB digital + passive attenuation will give you the most 'technical optimal' performance.