The truth about bit depth in digital

[Jim Audiomisc]

I've read a few times that a higher noise floor may actually sound nice to some people (euphonic).

The high(ish) noise floor one finds in some digitalised classical music of vintage analogue recordings is a bit obvious and detracts from the realism somewhat in my experience, particularly when compared to a good modern digital recording.
I don't really know what woul be the best adjective to describe it, maybe 'hazy'?

The noise floor from an LP can in part stem from 'modulation noise' caused by the ye olde analogue tape. This tends to produce 'noise' as sidebands of the component of the input to the recorder. Mechanism is the non-linear domain nature of the recording medium. Noise can also arise from the way the vinyl was pressed, etc. There are some old AES papers on this. Recording companies were generally shy of reporting on it, but people did so occasionally.

 

[Jim Audiomisc]

I'm posting to check that I understand this stuff. Correct me if I'm wrong.

Bit depth is word length, right? So when people talk about 'quantisation error' they are talking about the last digit (or so) of a long string of ones and zeros. Digital is binary - so it has to decide whether that last digit (or so) is a 1 or a 0. It can't be 'mostly 1'. So some signal is lost as quantisation error, and this is loss is greater when the word length/bit rate is low. Fortunately, dither compensates for this loss by introducing noise to cover the quantisation error. In effect, you swap out the last ones and zeroes with random values, giving you noise instead of quantisation error. So with low bit rates, because the word-length is shorter, you get greater quantisation error and you need to dither to cover this with greater noise. Have I got this right?

I've also read that at 24-bit, the existing noise in electronic circuits (thermal roar, etc) is sufficient to do the same job as dither - the quantisation error is low enough that it is buried beneath the noise floor of the electronics. Therefore, whether you need to dither at 24-bit is a digital audio topic of debate.

Note that the error can be fed back and used to provide that information as a 'correction' to later samples. Its the method called Noise Shaping. Means you can preserve more detail, say, at LF by shoving more (output) noise up into the HF where it is less audible. Its also why DSD/SACD works with just one bit-or-so per sample, but at a high rate.

 

[Jim Audiomisc]

It’s like say you have a ruler divided up into 16 small divisions.
...

If anyone’s got a good explanation I’d like to be reminded of it. Thanks!

The key point to bring out is that if you generate 16bit samples from >16 input you can 'save the error and use it to guide how you measure the *next* sample. This lets you 'carry' some of the apparently-lost detail and get higher accuracy. i.e. lower distortion, and alter the noise spectrum so less is at LF. Thus the audible SNR is better and the distortion is lower.

This should all be on my website somewhere. Up to others to decide how clear my explanations are, though!

 

[Jim Audiomisc]

I suspect the ‘quality’ of noise you get in a digital system is different to that in an analogue system. And I suspect that the brain reacts to the ‘unnatural’ nature of digital noise, whereas it is more capable of ‘tuning out’ analogue noise from vinyl sources because it has its origins in physical processes which the brain encounters in nature.

I also think the Lavry piece, upthread, is interesting because I believe the sort of improvements I’m hearing in my system, due to supports and cabling, affect the noise floor. And there is musical information below the noise floor which it is possible to perceive, so lowering that floor is likely to bring it out better.

I also think that the biggest issue with noise is probably some form of intermodulation with the signal.

Given that reality is quantised I'm puzzled by the idea that digital 'noise' MUST be more audible than analogue. What really matters is the details of the 'noise' process. You can make either a digital or analogue process well, or badly.

 

[Jim Audiomisc]

There was a nice old demonstration up at my University in St Andrews physics department where you could turn a dial and change the number of bits. You could hear the noise and artifacts coming in- sounded much as you’d imagine ‘digital’ problems would sound. I’ve no idea how it worked, maybe by just truncating off the lower significant bits but it was a fun demonstration.

@Jim Audiomisc might remember it.

Afraid not. But it would be a simple process to encode in a computer program for people to try out! In effect a demo of the various ways digital recording/processing can do a good job... or a bad one. Has anyone already written this?

 

[Jim Audiomisc]

When the digital signal is read back the error on the amplitude equates to an error in the time domain, the quantisation noise, and this limits the bit depth in practice so that your 16 bits ain't worth the paper they're written on. That's not to say that you won't still have enough bit depth to capture the dynamics of the vast majority of recordings.

Could you explain your description another way? I'm not clear what you mean by your "equates".

 

[gavreid]

Could you explain your description another way? I'm not clear what you mean by your "equates".

Instead of the digitisation error being on the amplitude you could get just the same effect by sampling slightly earlier or later. You have no way to determine which was true at playback.

 

[Sue Pertwee-Tyr]

Given that reality is quantised I'm puzzled by the idea that digital 'noise' MUST be more audible than analogue. What really matters is the details of the 'noise' process. You can make either a digital or analogue process well, or badly.

I don’t think I said ‘must’, and I’m talking about ‘perceptible’ rather than consciously audible, but actually something you said a few posts back is probably closer to what I’m getting at. In analogue systems, noise is often related to the signal in some regard, and therefore less apt to confound the brain. Whereas digital noise bears a much less significant relationship to the signal.

 

[davidsrsb]

Given that reality is quantised I'm puzzled by the idea that digital 'noise' MUST be more audible than analogue. What really matters is the details of the 'noise' process. You can make either a digital or analogue process well, or badly.

Analogue noise can be more audible. Think about the obvious "pumping" artifacts on a Dolby cassette tape, but you also have a LP with a fingerprint on it that gets very obvious with repetition every rotation.
Something else to consider is that most components are not just thermal noise sources, but also have signal related shot noise.

 

[darrenyeats]

'Noise' is error that's not correlated to signal (often random but doesn't need to be e.g. mains hum is noise - as long as not correlated to signal: noise).

Any error correlated to signal is 'distortion'. This would even include, say, an otherwise seemingly random error whose level is modulated by signal. Some digital distortions can be quite anharmonic and disturbing, many analogue distortions are harmonic.

 

[John]

Probably explains why I‘m perfectly happy listening to Spotify.

 

[John Phillips]

I'm posting to check that I understand this stuff. Correct me if I'm wrong.

Bit depth is word length, right? So when people talk about 'quantisation error' they are talking about the last digit (or so) of a long string of ones and zeros. Digital is binary - so it has to decide whether that last digit (or so) is a 1 or a 0. It can't be 'mostly 1'. So some signal is lost as quantisation error, and this is loss is greater when the word length/bit rate is low. Fortunately, dither compensates for this loss by introducing noise to cover the quantisation error. In effect, you swap out the last ones and zeroes with random values, giving you noise instead of quantisation error. So with low bit rates, because the word-length is shorter, you get greater quantisation error and you need to dither to cover this with greater noise. Have I got this right? ...

Not quite, I think. On quantization error (AKA quantization noise) the broad headline is that in a well-engineered digital system it does not occur. It's not a case of dither noise covering it up, the dither noise stops it happening in the first place.

The reason for this is that at the point of quantization (or re-quantization) adding dither noise to the signal-correlated quantization error de-correlates the error from the signal and replaces it with random noise having a spectrum you can choose. If you use flat spectrum dither noise you get just the same as the Johnson noise you get in an analogue system - but you can do better with noise shaping.

And dither means you can encode in 16 bits an audio signal whose peak value would not toggle the 16th bit. I have generated test files and verified personally on my previous and current audio systems that with the volume set at maximum (and a lot of care) I can hear test signals - with noise, of course - whose peak amplitude is one third of the 16th bit.

IMHO, quantization noise is not a real difference with which to conjour when arguing about the differences between a good analogue system and a good digital system.

 

[tuga]

I suspect the ‘quality’ of noise you get in a digital system is different to that in an analogue system. And I suspect that the brain reacts to the ‘unnatural’ nature of digital noise, whereas it is more capable of ‘tuning out’ analogue noise from vinyl sources because it has its origins in physical processes which the brain encounters in nature.

I think that the problem is not the 'unnaturalness' of the noise but the frequency range and characteristics. If you listen to 'flat' TPDF or pink-noise it's not objectionable, but if you get raising noise levels above 10kHz then the sound becomes 'agressive'.

 

[Jim Audiomisc]

Instead of the digitisation error being on the amplitude you could get just the same effect by sampling slightly earlier or later. You have no way to determine which was true at playback.

I'm not sure that 'equates' is the correct term for it. The noise itself represents an uncertainty - i.e. an unknown that should be 'random' of it is due to noise.

What is true is that if the initial digital recording uses a bit-depth that *isn't* more than enough to reach the analog input's noise level then some errors in measurement arise at that point. However this is a loss from the orginal (analog input) information load leading to a 'distortion' (in the widest sense) in the original record.

Hence you do need to 'know more' at the source point if you want more out. If you 'know' the input was 'really a pure sinewave', say, you can use that for some corrections. But that means you bring in more 'information' that the recording itself lost.

So a matter of the details of the case in hand.

 

[Jim Audiomisc]

IIn analogue systems, noise is often related to the signal in some regard, and therefore less apt to confound the brain. Whereas digital noise bears a much less significant relationship to the signal.

Agree about the first point, but less sure about your following assumption.

 

[gavreid]

I'm not sure that 'equates' is the correct term for it. The noise itself represents an uncertainty - i.e. an unknown that should be 'random' of it is due to noise.

While I agree that it's random I still think that it would be the equivalent of jitter - I think it must be. A slowly varying part of the signal will appear as a substantial temporal uncertainty and vice versa.

 

[Jim Audiomisc]

If you listen to 'flat' TPDF or pink-noise it's not objectionable, but if you get raising noise levels above 10kHz then the sound becomes 'agressive'.

Depends on the noise level, etc. That said, a possible problem is that some kit later in the chain may react poorly to HF noise along with the audible patterns at lower frequencies. Thus leading to a further alteration that *is* audible because of a vulnerability of later kit. Hence material which - in itself has no noticable impact of HF noise - may cause audible problems with some replay kit.

 

[tuga]

Depends on the noise level, etc. That said, a possible problem is that some kit later in the chain may react poorly to HF noise along with the audible patterns at lower frequencies. Thus leading to a further alteration that *is* audible because of a vulnerability of later kit. Hence material which - in itself has no noticable impact of HF noise - may cause audible problems with some replay kit.

Here's an interesting topic about DAC ultrasonic/RF output:

https://tinyurl.com/mw5jmepy

 

[gez]

Instead of the digitisation error being on the amplitude you could get just the same effect by sampling slightly earlier or later. You have no way to determine which was true at playback.

This is just a theoretical mathematical situation. Not a reflection of reality. The reality is we do know exactly what the time is, it's determined by the sampling rate, so barring the potential error in the sampling rate clocking, quantisation error is purely an amplitude error.

A typical DAC master clock is good for better than 100ps jitter (note this is DAC sampling clocking jitter which is impossible for any reviewer to measure directly, as opposed to the jitter of the DAC at it's output terminal which is not the same thing), which even at 192khz sampling is only a 0.00192% error in the time domain. How much could a 20khz sine wave vary in amplitude with such a time variation? (that's a question for the hall, I don't know). Or more importantly is that variation enough to alter the quantisation value (i.e more than 1/2 a bit at 16bit resolution - or any resolution even).

 

[gez]

I'm posting to check that I understand this stuff. Correct me if I'm wrong.

Bit depth is word length, right? So when people talk about 'quantisation error' they are talking about the last digit (or so) of a long string of ones and zeros. Digital is binary - so it has to decide whether that last digit (or so) is a 1 or a 0. It can't be 'mostly 1'. So some signal is lost as quantisation error, and this is loss is greater when the word length/bit rate is low. Fortunately, dither compensates for this loss by introducing noise to cover the quantisation error. In effect, you swap out the last ones and zeroes with random values, giving you noise instead of quantisation error. So with low bit rates, because the word-length is shorter, you get greater quantisation error and you need to dither to cover this with greater noise. Have I got this right?

I've also read that at 24-bit, the existing noise in electronic circuits (thermal roar, etc) is sufficient to do the same job as dither - the quantisation error is low enough that it is buried beneath the noise floor of the electronics. Therefore, whether you need to dither at 24-bit is a digital audio topic of debate.

Yes that's correct. Quantisation error is by definition only ever the last bit error. i.e the real value of the signal falls somewhere between the last digit being a 0 or a 1. That's why quantisation distortion as a % increases with decreasing signal level, because the absolute value of that last digit becomes a larger and larger % of the total value with smaller absolute values of measured levels. This is intrinsic to linear quantisation digital.

NB: interestingly in the telecoms world, they mitigate this (as they only use 8 bit samples to start with) by not using a linear quantisation model. The quanta levels are smaller down at small signal levels than they are at higher signal levels (I don't know by exactly how much, not sure we were ever given that level of information).

Edited to add: would appear that the way telecommunications equipment achieves this non linear quantisation is to compress the signal before sampling it, so the low level quantisation error is reduced. The actual quantisation is linear, but as the output is then expanded again after being converted to analogue the effect is to produce the equivilent as if the original signal had been quantised using 13 bit quantisation.

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