Digital bit depth and analogue SPL

[Anonymous]

Hi Guys,

After reading http://www.soundonsound.com/sos/feb08/a ... dio.htmand Digital Myths

I have a fair understanding of how an analogue signal is converted to a digital.

I'm slighty unclear on how Bits relate to amplitude.
For example, if I have a classical piece of music which has a dynamic range of, say 70dB, and is then converted digitally into a four bit converter (which only has a 24dB dynamic range). Does this mean that it will be "compressed" in some way?

I use to think that each 6dB per bit was calibrated to the levels of sound pressure, which is clearly wrong right!

I now know that interpolation "fills in the gaps" but I am slightly unsure on how varying analogue sound pressure levels are represented by different bit depths.

Thanks

[dmills]

What actually happens is that (providing everything is dithered correctly!) the classical music on playback sounds like it is mixed with noise at the -24dB level....

Actually that -24 is not quite right but it will do for now.

So the quiet bits of the music fade smoothly down into the constant background of dither noise (which may be noise shaped to give a perception that the noise level is lower then -24dB).

Nothing gets compressed and everything is linear (just with added hiss).

Regards, Dan.

[Hugh Robjohns]

I'm slighty unclear on how Bits relate to amplitude.

The bits count the available quantising levels, and louder signals cross more quantising levels.

...a four bit converter (which only has a 24dB dynamic range).

That's not quite right. A 4 bit converter would have a signal-noise ratio of about 24dB -- the noise floor will be roughly 24dB below the maximum amplitude. However, if it is correctly dithered, as Dan says, the signal will remain audible even though it may be significantly quieter than than the noise floor. And noise shaped dither will make the apparent dynamic range even larger.

Does this mean that it will be "compressed" in some way?

No. There is no compression. The quieter stuff will just have to fight to be audible through the system noise.

I use to think that each 6dB per bit was calibrated to the levels of sound pressure, which is clearly wrong right!

You could calibrate the system so that a given SPL captured by a microphone was reproduced by a speaker at the same SPL... but that's an entirely operational consideration rather than anything to do with digital quantisation and bits per se.

I now know that interpolation "fills in the gaps"

Only in the error concealment system of CD and CAT machines, and only then if the error correction system fails. There is no interpolation in the quantisation process.

I am slightly unsure on how varying analogue sound pressure levels are represented by different bit depths.

analogue pressure variations are converted into electrical voltage variations by a microphone. Those voltage variations are compared against a scale, the various quantising levels of which are represented by binary numbers through the quantising process.

On replay, the binary numbers are used to generate analogue voltage pulses which are then filtered to rebuild the original analogue voltage waveform which is passed to a loudspeaker to recreate a varying acoustic sound pressure.

hugh

[Vandemonian]

By the way, 4 Bit means the signal will be quantised by 2^4 (16) levels.
SNR and the signals resolution depends on bit depth which is why it is better to convert at 16 Bit, and even better at 24 bit, than at 4 bit. Especially for classical recordings which usually have very large dynamic ranges.

[dmills]

Bad word! BAAAD Word, Hugh, he said the R word!

A correctly dithered quantiser does not have a RESOLUTION, it is **LINEAR** all the way down. What it has is noise, which is injected before quantization and has the effect of linearising the quantiser provided the noise has the right statistical properties.

Quantised systems (if done properly) are not particularly intuitive in that they have statistical properties that mean that the output is indistinguishable from the input plus a defined level of noise (even for input signals below the LSB), weird but the math stacks up.

Simple minded stair step drawings and join the dots "waveform" (They are nothing of the sort!) displays in DAWs have a lot to answer for.

Regards, Dan.

[Guest]

Yes it's all getting clearer now.

I see the differences of "noise" now.
Quantisation noise is used to linearise, and is relative to the original signal where-as dither is the noise added to convert to different bit depths.

Quantising is related to the discrete level which is modulated with a PCM signal right? This helps the reconstruction filter when it converts the signal to analogue.

The clock connects the exact timing between quantising and the sampling rate. So there is a balance between sample rates and bit depths but as long as the Jitter is precise then and the significant bits are working then a home studio should be able to compete with the big boys now.

Thanks

[narcoman]

next person that comes on here quoting "bits is resolution" gets sold into serfdom....

[Zukan]

next person that comes on here quoting "bits is resolution" gets sold into serfdom....

Don't knock it m8. At least bit rate wasn't mentioned......

[illegal colors]

Bad word! BAAAD Word, Hugh, he said the R word!

A correctly dithered quantiser does not have a RESOLUTION, it is **LINEAR** all the way down. What it has is noise, which is injected before quantization and has the effect of linearising the quantiser provided the noise has the right statistical properties.

Yes, sort of. Under certain circumstances you can say that and be right more or less.
For example if you are trying to popularize the practice of recording at lower levels and increased bit depth then the notion of resolution being a bad word can come handy.
In this particular instance however nickluckman mentioned 4 bit audio which made use of the word rather more appropriate.

Let me give you an example to make my point more obvious.
Imagine you and I and maybe Hugh Robjohns if he has no better things to do are watching a good movie like Pineapple Express on a Blu-ray disc played back on a Blu-ray player properly connected to a high quality 42' full HD LCD TV. Everything is set-up right, image quality is excellent and from about 2 or 3 meters we all can appreciate advantages of Blu-ray format over good old DVD. From about 5 meters however you won’t be able to tell the difference between Blu-ray and 400-line DivX re-encode of the same Blu-ray source if everything is done properly of course. Incidently, the best and most natural looking upscaling algorithms are little more than added noise. But if you press zoom button to get rid of black bars for example then difference between the sources will become obvious again because resolution is different although someone may want to argue that level of video noise is the only difference.

Resolution is the right word if you keep in mind that when it comes to sound we rarely can ‘get closer’ to the sound than equivalent of 5 meters for a 42' TV but with a printed still photographic image we can get as close as we want.

[dmills]

Err even in video, resolution and noise are separate concepts.

Resolution is more akin to frequency response while noise is just noise.

I think what you are trying to say is that a very low wordlength system will have a dither noise floor above the background in most listening environments, where a 16 or 24 bit wordlength will have a dither noise floor below the background? True, but uninteresting.

Regards, Dan.

[narcoman]

Let me give you an example to make my point more obvious.
Imagine you and I and maybe Hugh Robjohns if he has no better things to do are watching a good movie like Pineapple Express on a Blu-ray disc played back on a Blu-ray player properly connected to a high quality 42' full HD LCD TV. Everything is set-up right, image quality is excellent and from about 2 or 3 meters we all can appreciate advantages of Blu-ray format over good old DVD. From about 5 meters however you won’t be able to tell the difference between Blu-ray and 400-line DivX re-encode of the same Blu-ray source if everything is done properly of course. Incidently, the best and most natural looking upscaling algorithms are little more than added noise. But if you press zoom button to get rid of black bars for example then difference between the sources will become obvious again because resolution is different although someone may want to argue that level of video noise is the only difference.

There is no direct correlation between pixel sampling and sound sampling .... at all. This common comparison carries as much weight as the Stork SB taste test.

A sound sample is a "point on a curve". As any A-level mathematician can tell you - three points will fully describe any sinusoidal curve to the exclusion of all other curves. ALL sound is sine waves - all a set of samples do is describe complicate multilevel sine waves. End of.... a continuous phenomena described by discrete points with the unfortunate side effect of errors being set as noise. A 24bit describes and samples a sine wave EXACTLY as accurately as a 4 bit one - but the 4 bit one will have greater quantisation error.... there is only noise!

[Hugh Robjohns]

Bad word! BAAAD Word, Hugh, he said the R word!

Hugh

[Hugh Robjohns]

Quantisation noise is used to linearise

Not quite, but we risk getting lost in the meaning of terminology and semantics. Most people use the term quantisation noise to refer to the error inherent in a simple quantisation process. If there are a lot of quantisation levels (ie, large wordlength) and the signal is large, then the quantisation distortion will have noise-like properties. Hence the term 'quantisation noise' -- but as the signal level or wordlength falls, those distortion products become more and more strongly related to the signal itself, and thus more and more obvious and unacceptable.

Dither is a noise-like signal with specific statistical properties that allows a crude quantisation process to become perfectly linear and totally distortion-free.

...dither is the noise added to convert to different bit depths.

Yes, as part of the truncation process, dither re-linearises the whole thing.

Quantising is related to the discrete level which is modulated with a PCM signal right?

Quantisation is the process that converts analogue signal levels into discrete digital signal levels. The result is a PCM signal.

This helps the reconstruction filter when it converts the signal to analogue.

The reconstruction filter is part of the sampling system and is completely separate from the quantisation process.

Sampling creates 'sidebands' which are the mathmatical product and difference of the audio signal and the sample rate. The reconstruction filter removes those sidebands from the reconstructed signal. Nothing to do with quantisation.

The clock connects the exact timing between quantising and the sampling rate.

Again, quantising and sampling are entirely separate things. The clock defines the sample rate. It ensures that the analogue input signal is sampled at regular intervals, and it ensures that the output samples are reconstructed at regular intervals.

So there is a balance between sample rates and bit depths

Yes there is, using technologies like oversampling and delta-sigma conversion. These allow data which is coded with very high sample rates but at low wordlengths to be transcoded to data with lower sampling rates but much higher wordlengths -- and vice versa. But the actual information content in other form is the same.

a home studio should be able to compete with the big boys now.

The technology hasn't been a problem for a decade or more, and even budget home studio equipment is better now than the highest quality analogue pro-audio could achieve ten years ago, and little differnt to the best digial gear now.

The difference has always been -- and remains -- the quality of home studio acoustics and the talent and skillbase of the person using the equipment.

Hugh

[Hugh Robjohns]

In this particular instance however nickluckman mentioned 4 bit audio which made use of the word rather more appropriate.

With respect, no it doesn't -- although clearly some people associate different meanings to the term 'resolution'. As far as I am concerned, 'high resolution' means 'low distortion and wide bandwidth', and it is perfectly possible to achieve both of these with a low wordlength systems. Indeed, the much praised Super Audio CD uses a one-bit PCM system (called DSD) ... and is trumpted as a 'high resolution' system -- and rightly so.

I wrote an article a while back (digital myths) in which I provided an audio example of a three-bit recording of some classical solo piano. The files are still available on the SOS website. While the signal is buried in noise, it is very obviously undistorted and therefore captured with high resolution. The use of noise-shaped dither renders this point even more obvious.

Low wordlength systems inherently result in a higher system noise floor, but that is the only compromise. Audio resolution is unaffected.

Imagine ... watching a good movie ... [on a] high quality 42' full HD LCD TV.

Your analogy is fatally flawed. You are talking about the differences in 'circles of confusion' created by the density of a fixed array of discrete image pixels. There is no meaningful relationship between this and audio sampling/quantisation.

hugh

[dmills]

The difference has always been -- and remains -- the quality of home studio acoustics and the talent and skillbase of the person using the equipment.

Quoted for truth, but it is amazing how many people don't want to hear it.

[narcoman]

.... I still say it's like the Stork SB taste test....

[illegal colors]

Gentlemen,
for the benefit of this discussion I will try to be as succinct as I can manage.

Err even in video, resolution and noise are separate concepts.

Resolution is more akin to frequency response while noise is just noise.

Well, if noise is just noise, what do you think happens when digital video is upscaled and dithered?

There is no direct correlation between pixel sampling and sound sampling .... at all. This common comparison carries as much weight as the Stork SB taste test.

Maybe if you are sampling one pixel but I was talking about resolution of digital video and digital audio. You guys all seem to be confused by the fact that you actually can see pixels on your screens.

A sound sample is a "point on a curve". As any A-level mathematician can tell you - three points will fully describe any sinusoidal curve to the exclusion of all other curves. ALL sound is sine waves - all a set of ...

Then a luma sample is also a "point on a curve" and a chroma sample is a point on a curve if you will continue in this manner your video will lose resolution completely and become totally linear. How do you like that?

I believe I know how these ideas got into your heads. You are thinking about digital video as a pixel-for-pixel system throughout which is rarely the case. And as soon as you change resolution at least once your A-level mathematician goes out the window

With respect,

Also with respect,
if you apply the same logic of yours to real world digital video as opposed to ultra-simplified understanding the three of you seem to subscribe to then we also can't use the R word when talking about anything.

Cordially,
illegal colors

[Guest]

Semantics!

[narcoman]

I believe I know how these ideas got into your heads. You are thinking about digital video as a pixel-for-pixel system throughout which is rarely the case. And as soon as you change resolution at least once your A-level mathematician goes out the window

... they do teach this in A-level maths!! So how would you "change resolution" in audio? Since it's never "steps" then the idea has no meaning! The audio is not the discrete samples - these are descriptors of the curve from which they were taken.... not a value of the audio. When reconstructing audio from samples we don't join the samples up ...

A pictorial sample has no relation to an audio sample.... the only way it could is if your SINGLE pixel was changing value all the time according to sine waves - a video pixel sample bears some relation but does not necessarily follow the rule of all sound is sinewaves. ALL sound.

As for not knowing what we're talking about : Hugh's a recognised expert on this, I did a PhD in the field (published too: sampling satellite transmission signals... y'know? Published? Peer reviewed?... I thank you:)) and Mills is the chief onion collector... in other words... he KNOWS it!

What we're talking about is - bit depth is NOT resolution in audio. Not now, not in any shape or form. A sine wave is no more accurate sampled with 24 bits as it is with 4.... just the noise floor changes.

General shout out chaps - STOP APPLYING GRAPHICS ANALOGIES TO AUDIO. THEY MEAN NOTHING. You cannot apply video/pictorial graphic sampling semantics to audio - they are different things. We DO share areas in aliasing and filters - but not in the acquisition of time variant signals.

I quote Shannon:
If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart

Notice - hertz. A frequency based SI unit - wave functions are sinusoidal. You don't measure the sinusoidal aspect of light when sampling pictures (I would like to see the speed of THAT clock) nor could you as they are transverse electromagnetic waves.

A picture has resolution in pixels - there is no similar thing in audio, again : we don't reconstruct audio by joining samples up.

There is no resolution in audio - the samples are descriptors of curves. Errors reveal themselves as noise - not resolution. Or are you saying a 4 bit sample has lower resolution than a 24bit one?

[Richie Royale]

Yeh, but no, but yeh? Innit.

[dmills]

I don't do qualifications pissing contests, mostly because I tend to loose, but there are some scary misunderstandings about the nature of video betrayed so lets have a go at fixing those:

Ok, consider a digital photo (it has exactly the same issues as video in this context), you have a grid of pixels each quantised at some suitable wordlength.

Now that grid has a spatial sampling frequency (effectively) that can be measured in samples per cm at the sensor and this fact imposes a upper limit on the spatial frequency that can be captured by that sensor without aliasing (Consider what happens to a tweed jacket in front of a cheap SD video camera, that is aliasing). Better cameras have a spatial anti aliasing filter to remove the high spatial frequency components by in effect introducing a little blur.

Thus high resolution video is just another way of saying "high spatial sample rate", it says nothing about the number of quantization levels employed (Or the noise floor for analogue video, same thing).

I suspect that I could write a perfectly good (but slow) scaler using stock audio resampler codes and just applying them twice (once for X and again for Y scale), there are much faster ways, but I suspect I could use zita resampler or something to make a perfectly functional simple minded off line video scaler.

Each pixel is then quantised to a given number of bits and it is the dither associated with that (or possibly the sensor noise which I suspect makes the full wordlength rather academic in some cases) that sets the black noise level.

Thus re scaling is really a resampling operation and the usual methods apply, and word length reduction (say for printing) needs dither, no surprise there. Some image dither algorithms effectively combine the dither and a downsampling step, particularly when producing halftone output, but that is a detail.

Note that all the math needs to be done in a linear colour space at a suitable word length and the conversion from and to a non linear gamma may imply the application of dither.

One other issue with film and video is that due to its low frame rate, temporal subsampling can easily occur (hence wagon wheels spinning backwards), but that is a separate issue from the one of spatial sampling.

Regards, Dan.

[Hugh Robjohns]

what do you think happens when digital video is upscaled and dithered?

Again, your analogies don't hold the water you think they do. Fundamentally, the fixed display pixelation of video and the process of up- (or down-) scaling can not be related (in the way you are trying) with audio sampling. These are entirely different concepts.

I was talking about resolution of digital video and digital audio. You guys all seem to be confused by the fact that you actually can see pixels on your screens.

These fixed capture and display pixels inherently provide an absolute visual resolution -- returning to the topic of 'circles of confusion' that you were alluding to earlier. Fewer pixels results in a blockier, distorted picture of low resolution. The approximately equivalents in correctly sampled audio is gross distortion and a limited audio bandwidth... but those are unrelated to wordlength which is the core of what was being discussed.

Correctly dithered low wordlength quantisation does not distort the audio signal in any way. The resolution is not altered. The only affect is that the noise floor is proportional to the wordlength.

if you apply the same logic of yours to real world digital video as opposed to ultra-simplified understanding the three of you seem to subscribe to then we also can't use the R word when talking about anything.

There is an appropriate appliction of the term 'resolution' when discussing digital video display devices. And while I recognise that there are many people far more clever than me, whose understanding of digital video goes to much greater depths than my own, I am confident that my understanding is a tad beyond 'ultra-simple'. It appears that I'm not alone in questioning your analogies.

Regardless, we're talking about digital audio here. Digital video is a whole different kettle of fish, few aspects of which can be directly compared with digital audio as the techniques and technologies are aimed at dealing with entirely different issues...

Returning to my previous definition of 'high resolution' as meaning 'low distortion and wide bandwidth' -- which is the interpreation most people appear to associate with it -- then I reitterate the point that 'audio resolution' is completely unaffected by the wordlength. Only the level of the noise floor is dependent on wordlength.

hugh

[Vandemonian]

So you're saying a 24 bit signal without dither isn't necessarily of higher resolution (ie an exacter representation of the original signal, which is what most people mean when talking about resolution) than a 4 bit signal smoothed over with a bit of dither?

I get your point but I meant resolution and I'll stick by it.

Who is to say dither-noise isn't distortion? If you're changing the waveform in adding dither, then it's distortion isn't it?

Open to criticism!!!

[dmills]

Nope, distortion is correlated with the signal, noise is uncorrelated (And this is not just semantics).

A 4 bit UNDITHERED quantiser has more distortion then the 24 bit one does of course as it is non linear and so generates all kinds IMD (plus the IMDs aliases of course), but add the dither and all of that goes away to be replaced my a constant noise floor.

In audio it makes sense to speak of a frequency (and sometimes a phase) response and a noise floor (possibly shaped), together with various measures of distortion and linearity but there is no reasonable way to define what is meant by resolution except by importing concepts from video or photography which really do not translate in a meaningful way.

A lot of this stuff is seriously non intuitive and it is usually very badly taught which does not help. Further many DAWs do a very bad job of representing waveforms when you zoom in which gives completely the wrong impression of how things actually work.

Work however, it does.

Regards, Dan.

[Hugh Robjohns]

So you're saying a 24 bit signal without dither...

You'll struggle to find one... but let's go with it...

...isn't necessarily of higher resolution (ie an exacter representation of the original signal, which is what most people mean when talking about resolution) than a 4 bit signal smoothed over with a bit of dither?

No. In fact a correctly dithered 4-bit signal will, technically, have lower distortion than a non-dithered 24 bit signal... if you could create one. In practice the analogue stage in the converter would dither the signal adequately anyway.

And dither doesn't 'smooth over' the quantising distortions -- it fundamentally linearises the quantising process.

Who is to say dither-noise isn't distortion?

Everyone -- because noise is random (ie, uncorrelated with the signal) whereas distortion is correlated. These are standard technical definitions of fundamentally different phenomena.

If you're changing the waveform in adding dither, then it's distortion isn't it?

No, it's noisy.

This highlights the importance of using accurate technical terms and meanings.

Hugh